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Fluid Handling
Board of Studies
Prof. H. N. Verma Prof. M. K. GhadoliyaVice- Chancellor Director, Jaipur National University, Jaipur School of Distance Education and Learning Jaipur National University, JaipurDr. Rajendra Takale Prof. and Head AcademicsSBPIM, Pune
___________________________________________________________________________________________
Subject Expert Panel
Prof. Milind M. Kulkarni Ashwini PanditProfessor, Sinhgad College of Engineering Subject Matter ExpertPune
___________________________________________________________________________________________
Content Review Panel
Tejaswini MulaySubject Matter Expert
___________________________________________________________________________________________Copyright ©
This book contains the course content for Fluid Handling.
First Edition 2013
Printed byUniversal Training Solutions Private Limited
Address05th Floor, I-Space, Bavdhan, Pune 411021.
All rights reserved. This book or any portion thereof may not, in any form or by any means including electronic or mechanical or photocopying or recording, be reproduced or distributed or transmitted or stored in a retrieval system or be broadcasted or transmitted.
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I
Index
Content .................................................................................................................................................................. IIList of Figures ......................................................................................................................................................VIList of Tables ..................................................................................................................................................... VIIIAbbreviations .......................................................................................................................................................IXCase Study ......................................................................................................................................................... 134Bibliography ...................................................................................................................................................... 141Self Assessment Answers ................................................................................................................................... 142Book at a Glance
II
Contents
Chapter I ....................................................................................................................................................... 1Newtonian Fluid ........................................................................................................................................... 1Aim ................................................................................................................................................................ 1Objectives ...................................................................................................................................................... 1Learning outcome .......................................................................................................................................... 11.1 Introduction .............................................................................................................................................. 21.2 Newtonian ................................................................................................................................................ 21.3 Non-Newtonian (Time Independent) ....................................................................................................... 2 1.3.1 Shear Thinning ........................................................................................................................ 3 1.3.2 Shear Thickening .................................................................................................................... 31.4 Viscoplastic Fluids ................................................................................................................................... 31.5 Non-Newtonian (Time Dependent) ......................................................................................................... 3 1.5.1 Thixotropic .............................................................................................................................. 3 1.5.2 Rheopectic .............................................................................................................................. 3 1.5.3 Viscoelastic Fluids .................................................................................................................. 41.6 Flow of Fluids through Pipes ................................................................................................................... 41.7 Pressure Drop (Loss) ................................................................................................................................ 5 1.7.1 Calculation for Incompressible Fluids (Liquids) ..................................................................... 5 1.7.2 Compressible Fluid (Vapour, Gas) ........................................................................................... 6 1.7.3 Equivalent Length .................................................................................................................. 10 1.7.4 Determining Pipe Size for Specified Pressure Drop and Flow Rate ..................................... 151.8 Present Value of O & M Cost................................................................................................................. 161.9 Predicting Pressure Drop in Piping ........................................................................................................ 17Summary ..................................................................................................................................................... 19References ................................................................................................................................................... 19Recommended Reading ............................................................................................................................. 19Self Assessment ........................................................................................................................................... 20
Chapter II ................................................................................................................................................... 22Pipeline Sizing ............................................................................................................................................ 22Aim .............................................................................................................................................................. 22Objectives .................................................................................................................................................... 22Learning outcome ........................................................................................................................................ 222.1 Introduction ............................................................................................................................................ 232.2 Classification of Pipelines ...................................................................................................................... 23 2.2.1 Pipeline Sizing ....................................................................................................................... 23 2.2.2 Liquids ................................................................................................................................... 242.3 Economic Velocity for Different Piping Systems .................................................................................. 31 2.3.1 Liquid F low under Gravity .................................................................................................... 31 2.3.2 Hot Liquid Flow ..................................................................................................................... 32 2.3.3 Bypass Line for Equipment/Instrument ................................................................................. 33 2.3.4 Sample Line ........................................................................................................................... 33 2.3.5 Cooling Water Circulation ..................................................................................................... 34 2.3.6 Tank Overflow ....................................................................................................................... 34 2.3.7 Slurry Flow ............................................................................................................................ 342.4 Numerical for Line Size ......................................................................................................................... 352.5 Pipeline Sizing Criteria ......................................................................................................................... 37 2.5.1 Fluid Flow .............................................................................................................................. 372.6 Pipeline Sizing on Steam Velocity ......................................................................................................... 382.7 Pipeline Sizing on Pressure Drop .......................................................................................................... 40Summary ..................................................................................................................................................... 41References ................................................................................................................................................... 41Recommended Reading ............................................................................................................................. 41Self Assessment ........................................................................................................................................... 42
III
Chapter III .................................................................................................................................................. 44Non-Newtonian Fluids ............................................................................................................................... 44Aim .............................................................................................................................................................. 44Objectives .................................................................................................................................................... 44Learning outcome ........................................................................................................................................ 443.1 Introduction ............................................................................................................................................ 453.2 Classification of Non-Newtonian Fluids ............................................................................................... 45 3.2.1 Time Independent Fluids ....................................................................................................... 46 3.2.2 Time Dependent Fluids .......................................................................................................... 47 3.2.3 Elastico Viscous Fluid ............................................................................................................ 483.3 Mathematical Model to Express Non-Newtonian Behaviour ................................................................ 493.4 Laminar Flow ......................................................................................................................................... 513.5 Stress and Strain ..................................................................................................................................... 523.6 Viscosity Chart ....................................................................................................................................... 533.7 Numerical Example ............................................................................................................................... 54Summary ..................................................................................................................................................... 56References ................................................................................................................................................... 56Recommended Reading ............................................................................................................................. 56Self Assessment ........................................................................................................................................... 57
Chapter IV .................................................................................................................................................. 59Two Phase Flows and Practice .................................................................................................................. 59Aim .............................................................................................................................................................. 59Objectives .................................................................................................................................................... 59Learning outcome ........................................................................................................................................ 594.1 Introduction ............................................................................................................................................ 604.2 Two-Phase Flow .................................................................................................................................... 60 4.2.1 Capabilities of Two-Phase Flow ............................................................................................ 62 4.2.2 Different Types of Flow ......................................................................................................... 624.3 Two Phase Mixture ............................................................................................................................... 63 4.3.1 Capabilities of Two-phase Mixture ........................................................................................ 634.4 Types of Two Phase Flow ...................................................................................................................... 64 4.4.1 Focus ...................................................................................................................................... 654.5 Two-Phase Flow Regimes and Characteristic Linear Velocity .............................................................. 66 4.5.1 Dispersed Flow ...................................................................................................................... 66 4.5.2 Annular Flow ......................................................................................................................... 67 4.5.3 Stratified Flow ....................................................................................................................... 67 4.5.4 Slug Flow ............................................................................................................................... 67 4.5.5 Plug Flow ............................................................................................................................... 67 4.5.6 Bubble or Froth Flow ............................................................................................................. 674.6 Two-Phase Flow Regimes Type ............................................................................................................. 674.7 Baker Plot for a Two-Phase Flow Regime Correlation .......................................................................... 684.8 Pressure Drop Calculation for Gas-Liquid Systems .............................................................................. 694.9 Mitigating Erosion ................................................................................................................................. 70Summary ..................................................................................................................................................... 72References ................................................................................................................................................... 72Recommended Reading ............................................................................................................................. 72Self Assessment ........................................................................................................................................... 73
Chapter V .................................................................................................................................................... 75Pipeline Networks ...................................................................................................................................... 75Aim .............................................................................................................................................................. 75Objectives .................................................................................................................................................... 75Learning outcome ........................................................................................................................................ 755.1 Introduction ........................................................................................................................................... 76
IV
5.2 Network Analysis .................................................................................................................................. 76 5.2.1 Principles of Network Analysis ............................................................................................ 77 5.2.2 Head Balancing ..................................................................................................................... 78 5.2.3 Quantity Balancing ............................................................................................................... 80 5.2.4 The Calculation Procedure Based on Equation (C) .............................................................. 825.3 Equivalent Length (Le) ......................................................................................................................... 825.4 Restriction Orifice ................................................................................................................................. 835.5 Colour Coding of Pipelines ................................................................................................................... 84 5.5.1 Colour Coding to Pipelines (Ground Colour and Colour Bands) ......................................... 84 5.5.2 Colour Bands ........................................................................................................................ 85 5.5.3 Typical Practices Followed for Provision of Ground Colour and Colour Bands on
the Pipe Lines ........................................................................................................................ 855.6 Restriction Orifice Sizing ..................................................................................................................... 87 5.6.1 How the Meters Work ........................................................................................................... 88 5.6.2 Orifice Choices ..................................................................................................................... 88 5.6.3 Concentric ............................................................................................................................. 90 5.6.4 Eccentric and Segmental ........................................................................................................ 90 5.6.5 Annular .................................................................................................................................. 90 5.6.6 Integral .................................................................................................................................. 905.7 Types of Pressure Taps .......................................................................................................................... 90 5.7.1 Corner Taps ........................................................................................................................... 91 5.7.2 Radius Taps ........................................................................................................................... 91 5.7.3 Pipe Taps ............................................................................................................................... 91 5.7.4 Flange Taps ........................................................................................................................... 91 5.7.5 Vena Contracta Taps .............................................................................................................. 915.8 Orifice Selection Guidelines ................................................................................................................. 925.9 Figuring Flow Rate ............................................................................................................................... 935.10 Critical Flow ....................................................................................................................................... 94 5.10.1 Computer Program ............................................................................................................... 955.11 Restriction Orifices to Maintain Required Flow Rates ....................................................................... 96 5.11.1 Maintaining Minimum Flow in Pumps ............................................................................... 96 5.11.2 Safely Operating Critical Processes .................................................................................... 96 5.11.3 Maintaining Pump Flow for Multiple Applications ............................................................ 97 5.11.4 Providing Adequate Agitation Air Distribution in Tanks .................................................... 99Summary ................................................................................................................................................... 100References ................................................................................................................................................. 100Recommended Reading ........................................................................................................................... 100Self Assessment ......................................................................................................................................... 101
Chapter VI ................................................................................................................................................ 103Fluid Flow Theory and Practices ........................................................................................................... 103Aim ............................................................................................................................................................ 103Objectives .................................................................................................................................................. 103Learning outcome ...................................................................................................................................... 1036.1 Introduction .......................................................................................................................................... 1046.2 Schedule Number ................................................................................................................................ 1046.3 Tubing and Other Flow Conduits ........................................................................................................ 1046.4 Velocity Constraints ............................................................................................................................ 1056.5 Gravity Flow ........................................................................................................................................ 1056.6 Viscosity ............................................................................................................................................... 1056.7 Viscosity Classification ........................................................................................................................ 1066.8 Types of Fluids ..................................................................................................................................... 106 6.8.1 Newtonian Fluids ................................................................................................................. 106 6.8.2 Bingham Plastic Fluids ........................................................................................................ 107 6.8.3 Dilatants Fluids .................................................................................................................... 107
V
6.8.4 Pseudoplastic Fluids ............................................................................................................ 107 6.8.5 Thixotropic Fluids ................................................................................................................ 108 6.8.6 Rheopectic Fluids ............................................................................................................... 1086.9 Reynolds Number ................................................................................................................................ 1086.10 Velocity Head ..................................................................................................................................... 1096.11 Friction Factors .................................................................................................................................. 1096.12 Roughness (ϵ) .................................................................................................................................... 1096.13 Laminar Flow Friction ....................................................................................................................... 1096.14 Steps in Line Sizing ............................................................................................................................1106.15 Newtonian and Non-Newtonian Fluids DP (CGS System) ................................................................110Summary ....................................................................................................................................................111References ..................................................................................................................................................111Recommended Reading ............................................................................................................................111Self Assessment ..........................................................................................................................................112
Chapter VII ...............................................................................................................................................114Fluid Piping Systems.................................................................................................................................114Aim .............................................................................................................................................................114Objectives ...................................................................................................................................................114Learning outcome .......................................................................................................................................1147.1 Introduction ...........................................................................................................................................1157.2 Pressure Drop in Components in Pipe Systems ....................................................................................1157.3 Valves ....................................................................................................................................................116 7.3.1 Gate Valves ..........................................................................................................................116 7.3.2 Globe Valves .........................................................................................................................118 7.3.3 Ball Valves ............................................................................................................................119 7.3.4 Butterfly Valve ..................................................................................................................... 1217.4 Piping System Design .......................................................................................................................... 1227.5 Steam Distribution ............................................................................................................................... 1227.6 Energy Considerations ......................................................................................................................... 1237.7 Thermal Insulation ............................................................................................................................... 1237.8 Heat Losses from Pipe Surfaces .......................................................................................................... 1247.9 Calculation of Insulation Thickness ..................................................................................................... 1257.10 Insulation Material ............................................................................................................................. 1267.11 Economic Thickness of Insulation ..................................................................................................... 128 7.11.1 Calculations ........................................................................................................................ 129 7.11.2 Economics .......................................................................................................................... 130Summary ................................................................................................................................................... 131References ................................................................................................................................................. 131Recommended Reading ........................................................................................................................... 131Self Assessment ......................................................................................................................................... 132
VI
List of Figures
Fig. 1.1 Rheological behaviour of various types of non-Newtonian fluids ................................................... 4Fig. 1.2 Friction chart .................................................................................................................................... 7Fig. 1.3 Resistance in pipe fittings (using ‘K’ factor) .................................................................................. 13Fig. 1.4 Resistance coefficient of pipe fittings............................................................................................. 14Fig. 1.5 Resistance of valves and fittings to flow of fluids .......................................................................... 15Fig. 1.6 The equivalent length adjustment ................................................................................................... 18Fig. 2.1 Friction in pipes .............................................................................................................................. 24Fig. 2.2 ‘SI based’ Moody chart ................................................................................................................... 27Fig. 2.3 ‘Imperial based’ Moody chart (abridged) ....................................................................................... 28Fig. 2.4 Pipeline sizing chart ........................................................................................................................ 30Fig. 2.5 Liquid flow under gravity ............................................................................................................... 31Fig. 2.6 Hot liquid flow................................................................................................................................ 32Fig. 2.7 Bypass line for equipment/instrument ............................................................................................ 33Fig. 2.8 Slurry flow chart evaluation ........................................................................................................... 35Fig. 2.9 Moody friction-factor chart ............................................................................................................ 36Fig. 2.10 Concentric and eccentric reducers ................................................................................................ 37Fig. 2.11 Superheated and saturated steam pipeline sizing chart (velocity method) ................................... 39Fig. 2.12 Steam pipeline sizing chart (pressure drop method) .................................................................... 40Fig. 3.1 Newtonian fluids ............................................................................................................................. 45Fig. 3.2 Non-Newtonian fluids .................................................................................................................... 45Fig. 3.3 Pseudoplastic fluids ........................................................................................................................ 46Fig. 3.4 Dilatants fluids ................................................................................................................................ 46Fig. 3.5 Bingham plastic fluids (Newtonian Bingham plastic) .................................................................... 47Fig. 3.6 Time dependent fluid ...................................................................................................................... 47Fig. 3.7 Elastico vicious fluids ..................................................................................................................... 48Fig. 3.8 Non-Newtonian fluids .................................................................................................................... 49Fig. 3.9 Velocity profile for flow through pipe ............................................................................................ 50Fig. 3.10 Velocity profile for drag flow ....................................................................................................... 51Fig. 3.11 Thixotropic and rheopectic ........................................................................................................... 53Fig. 4.1 Pipeline flow pattern map for two phase flow ................................................................................ 61Fig. 4.2 Different types of flow.................................................................................................................... 62Fig. 4.3 Two fluids mixed on a flow sheet ................................................................................................... 63Fig. 4.4 Condensing in the presence of non-condensable gases .................................................................. 64Fig. 4.5 Two-phase flow .............................................................................................................................. 64Fig. 4.6 Two phase flow map ....................................................................................................................... 65Fig. 4.7 Gas-liquid system for two phase fluid flow .................................................................................... 66Fig. 4.8 Baker plot ....................................................................................................................................... 69Fig. 5.1 Typical network for cooling water distribution .............................................................................. 76Fig. 5.2 Typical network .............................................................................................................................. 78Fig. 5.3 Typical network .............................................................................................................................. 79Fig. 5.4 Typical colour band ........................................................................................................................ 85Fig. 5.5 Lettering size .................................................................................................................................. 86Fig. 5.6 Visibility of marking ....................................................................................................................... 87Fig. 5.7 The orifice meter measures pressure e.g., at point a and b determines the flow rate ..................... 87Fig. 5.8 Orifice shapes ................................................................................................................................. 88Fig. 5.9 Orifice meter with corner ............................................................................................................... 91Fig. 5.10 Orifice meter with corner taps ...................................................................................................... 92Fig. 5.11 An RO protects a centrifugal pump from cavitations ................................................................... 96Fig. 5.12 An RO sets minimum flow for safe operation of critical processes ............................................. 97Fig. 5.13 RO arrangement for multiple flows .............................................................................................. 97Fig. 5.14 Aero-filter ..................................................................................................................................... 99Fig. 6.1 Viscosity ....................................................................................................................................... 105Fig. 6.2 Newtonian fluids (a) ..................................................................................................................... 106
VII
Fig. 6.3 Bingham plastic fluids (b) ............................................................................................................ 107Fig. 6.4 Dilatants fluids (c) ........................................................................................................................ 107Fig. 6.5 Pseudoplastic fluids (d) ................................................................................................................ 107Fig. 6.6 Thixotropic fluids (e) .................................................................................................................... 108Fig. 6.7 Rheopectic fluids .......................................................................................................................... 108Fig. 7.1 Gate valve ......................................................................................................................................117Fig. 7.2 Globe valve ....................................................................................................................................118Fig. 7.3 Ball valve ...................................................................................................................................... 120Fig. 7.4 Butterfly valve .............................................................................................................................. 121Fig. 7.5 Types of piping layout .................................................................................................................. 122Fig. 7.6 Economic insulation thickness ..................................................................................................... 124Fig. 7.7 Insulated pipe section ................................................................................................................... 125
VIII
List of Tables
Table 1.1 Friction loss for water (M / 100 M) in smooth and new uncoated steel pipes (Hazen Williams Formula, C=140) ................................................................................................ 8
Table 1.2 Quantities passed by pipes at different velocities .......................................................................... 9Table 1.3 The life cycle cost of piping ......................................................................................................... 17Table 1.4 Approximate economic velocities estimated using the above concept ........................................ 17Table 3.1 Types of non-Newtonia fluids ...................................................................................................... 48Table 3.2 Laminar flow of fluids ................................................................................................................. 52Table 3.3 Viscosity chart .............................................................................................................................. 54Table 4.1 Flow regimes ................................................................................................................................ 68Table 5.1 (a) Quantity balancing .................................................................................................................. 80Table 5.1 (b) Quantity balancing ................................................................................................................. 80Table 5.2 Comparison between head and quantity balancing ...................................................................... 81Table 5.3 Some typical K value for friction head loss through fitting ......................................................... 83Table 5.4 Some typical equivalent length (Le) for fittings .......................................................................... 83Table 5.5 Colour coding to pipelines ........................................................................................................... 85Table 5.6 Orifice coefficient for different types of pressure taps ................................................................ 93Table 5.7 Expansion factors for different tap positions ............................................................................... 93Table 5.8 (a) Flow rate of compressible fluids under normal flow conditions ............................................ 95Table 5.8 (b) Output data ............................................................................................................................. 95Table 5.9 (a) RO calculation ........................................................................................................................ 98Table 5.9 (b) An RO in the line to Process B meets pressure requirements ................................................ 98Table 7.1 Minor loss coefficients ................................................................................................................116Table 7.2 Heat loss from Fluid inside Pipe (W/m) .................................................................................... 124Table 7.3 Correction factor ........................................................................................................................ 125Table 7.4 Coefficients A, B for estimating ‘h’ (in W/m2-K) ...................................................................... 126Table 7.5 Thermal conductivity of hot insulation ...................................................................................... 127Table 7.6 Specific thermal conductivity of materials for cold insulation .................................................. 128Table 7.7 Economic insulation thickness calculations ............................................................................... 129
IX
Abbreviations
CGS - Centimetre Gram Secondcp - CentipoisesCPI - Chemical Process Industriescst - Centistokesff - Friction Factormlc - Metres of Liquid ColumnNPSH - Net Positive Suction HeadPVC - Poly vinyl chlorideRe - Reynolds NumberRO - RestrictionOrificeRPM - Revolution Per MinuteSI - International System of Units
1
Chapter I
Newtonian Fluid
Aim
The aim of this chapter is to:
explainfluidbehaviour•
studyNewtonianandnon-Newtonianfluid•
discuss pressure drop loss•
Objectives
The objectives of this chapter are to:
explaincalculationofincompressiblefluids•
illustrate piping codes•
enlistthetypesoffluids•
Learning outcome
At the end of this chapter, you will be able to:
recognisecompressiblefluids•
identify pressure drop•
classifypipesizeforspecifiedpressuredropandflowrate•
understand pressure drop in pining•
Fluid Handling
2
1.1 IntroductionThebasicaimfordesigninganypipingsystemistohandleafluidorfluids.Afluidmaybeliquid,gaseousorsolidor a mixture of the two. Most low molecular weight substances such as organic and inorganic liquids, solutions of lowmolecularweightinorganicsalts,moltenmetalsandsalts,andgasesexhibitNewtonianflowcharacteristics,i.e., at constant temperature and pressure, in simple shear, the shear stress(s ) is proportional to the rate of shear (g˙)andtheconstantofproportionalityisthefamiliardynamicviscosity(h).SuchfluidsareclassicallyknownastheNewtonianfluids.
1.2 NewtonianAfluidinwhichthecomponentsofthestresstensorarelinearfunctionsofthefirstspatialderivativesofthevelocitycomponents.Thesefunctionsinvolvetwomaterialparameters(takenasconstantsthroughoutthefluid,althoughdepending on ambient temperature and pressure).
The shear stress ( ) is proportional to the shear rate.
(Velocity gradient, ).Theconstantofproportionalityisviscosity(μ).
𝑻
Units of viscosity - CGS system – poise (gm/cm-sec) Centipoises (Cp) = Poise/100
1 N-S/ = 10 poise
Kinematic Viscosity =
CGS system 1 stoke =
Centistoke (cst) = Stoke/100
SI Units m/
1m/ =10000 stoke.
1.3 Non-Newtonian (Time Independent)Non-NewtonianfluidsareonlytypeoffluidwhichdoesnotobeyNewton’slawofviscosity.Theshearstressisanon-linearfunctionoftheshearrate.Fig.1.2showstherheologicalbehaviourofseveraltypesoffluids.Theviscosityofatimeindependentnon-Newtonianfluidisdependentontheshearrate.Dependingonhowtheapparentviscositychangeswithshearrate,theflowbehaviourischaracterisedasfollows:
3
1.3.1 Shear Thinning
Theapparentviscosityofthefluiddecreaseswithincreasingshearrate.Thistypeofbehaviourisalsoreferred•to as ‘pseudoplastic’ and no initial stress (yield stress) is required to initiate shearing. A number of non-Newtonian materials are in this category, including grease, molasses, paint, starch and many •dilute polymer solutions. E.g. polymer melt, pulp suspension.•
1.3.2 Shear Thickening
Theapparentviscosityofthisfluidincreaseswithincreasingshearrateandnoinitialstressisrequiredtoinitiate•shearing. This type of behaviour is also referred to as ‘dilatants’.” Beach sand mixed with water and peanut butter are •examples of dilatants liquids. Dilatants liquids are not as common as pseudoplastic liquids. Dilatantsrheologicalbehaviourisalsoshowninfig.1.1.Forexample:quicksand,starchsuspensioninwater.•The shear rate • is dependent on shear stress.
1.4 Viscoplastic FluidsViscoplasticmaterialsarefluidsthatexhibitayieldstress.Belowacertaincriticalshearstressthereisnopermanentdeformationofthefluidanditbehaveslikearigidsolid.Whenthatshearstressvalueisexceeded,thematerialflowslikeafluid.Binghamplasticsareaspecialclassofviscoplasticfluidsthatexhibitalinearbehaviourofshearstressversusshearrateoncethefluidbeginstoflow.Anexampleofaplasticfluidistoothpaste,whichwillnotflowoutofthetubeuntilafinitestressisappliedbysqueezing.
1.5 Non-Newtonian (Time Dependent)Forthesekindsoffluids,theirpresentbehaviourisinfluencedbywhathappenedtothemintherecentpast.Thesefluidsseemtoexhibita‘memory’whichfadeswithtime.
The shear rate ( ) is dependent on shear stress.
Theapparentviscosityofthefluiddependsonanumberofpropertiesincludingshearrateandthehistoryoftheshearingprocess.Dependingonhowtheapparentviscositychangeswithtime,theflowbehaviourischaracterisedas below:
1.5.1 Thixotropic
A thixotropic liquid will exhibit a decrease in apparent viscosity over time at a constant shear rate. Once the •shear stress is removed, the apparent viscosity gradually increases and returns to its original value. Whensubjectedtovaryingratesofshear,athixotropicfluidwilldemonstratea‘hysteresisloop’.Drillingmud•and cement slurries are among the many materials which can exhibit thixotropic behaviour.
1.5.2 Rheopectic
Rheopectic liquid exhibits a behaviour opposite to that of a thixotropic liquid, i.e., the apparent viscosity of the •liquid will increase over time at a constant shear rate. Once the shear stress is removed, the apparent viscosity gradually decreases and returns to its original value.•Rheopecticfluidsarerare.Examplesincludespecificgypsumpastesandprinter’sinks.•
Fluid Handling
4
Fig. 1.1 Rheological behaviour of various types of non-Newtonian fluids(Source: http://t0.gstatic.com/images?q=tbn:ANd9GcQQTFnOQTys5HWZTudq-4EcqQ8L_4hu7H-
w00bNi6pFyGQ16sF0)
1.5.3 Viscoelastic Fluids
These materials exhibit both viscous and elastic properties. The rheological properties of such a substance at •any instant of time will be a function of the recent history of the material and cannot be described by simple relationships between shear stress and shear rate alone, but will also depend on the time derivatives of both of these quantities.Typical examples of viscoelastic material are bread dough, polymer melts and egg white.•
1.6 Flow of Fluids through PipesFluidflowinginpipeshastwoprimaryflowpatterns.Itcaneitherbelaminarwhenallofthefluidparticlesflow•inparallellinesatevenvelocitiesoritcanbeturbulentwhenthefluidparticleshavearandommotioninterposedonanaverageflowinthegeneraldirectionofflow.Thereisalsoacriticalzonewhentheflowcanbeeitherlaminarorturbulentoramixture.Ithasbeenproved•experimentallybyOsborneReynoldsthatthenatureofflowdependsonthemeanflowvelocity(v),thepipediameter(D),thedensity(ρ)andthefluidviscosity(μ).AdimensionlessvariableforthecalledReynoldsnumberwhichissimplyaratiooffluiddynamicforcesandthe•fluidviscousforces,isusedtodeterminewhatflowpatternwilloccur.TheequationfortheReynoldNumberis
Fornormalengineeringcalculations,theflowinpipesisconsideredlaminariftherelevantReynoldsnumber•is less than 2000, and it is turbulent if the Reynolds number is greater than 4000. Between these two values thereisthecriticalzoneinwhichtheflowcanbeeitherlaminarorturbulentortheflowcanchangebetweenthe patterns.Itisimportanttoknowthetypeofflowinthepipewhenassessingfrictionlosseswhiledeterminingtherelevant•friction factors.
Shea
r stre
ss
Dilatant-shear thickening
Newtonian
Pseudoplastic-shear thinningBingham plastic
Shear rate
5
Flow Regimes are categorised as follows •Laminar �Turbulent �Transitional �
Reynoldsnumber(Re)-TheflowregimedependsontheReynoldsnumber
up to 2000 - Laminar
10,000 & more - Turbulent
between 2000 to 10,000 - Transitional
d - pipe inside dia.in m. u - fluidvelocityinm/s. ρ - fluiddensityinkg/ µ - fluidviscosityin For conduits other than pipes (circular cross section)
d = 4 x
1.7 Pressure Drop (Loss)Duringtheflow,thefluidhastoovercomefrictionalresistancefromtheconduitwall(skinfriction)dependinguponthefrictionalresistance,thepressureoffluidreduces(pressureloss)inthedirectionofflow(upstreamsideto down stream side).
1.7.1 Calculation for Incompressible Fluids (Liquids)Forincompressiblefluids(liquids),thepressuredropiscalculatedusingtheDarcy/Fanningequation:
DP = 4ff x ……………….. (1)
DP = fm x ……………….. (2)
DP - Pressure drop (Loss) in mlc (meters of liquid column)
u - Fluid velocity in m/s.
L - Length of pipe in m (Or equivalent length of pipe-discussed later).
d - Inside dia. of pipe in m.g - Acceleration constant (9.81 m/s2)
Fluid Handling
6
Friction factor (ff or fm dimensionless)
ff - Fanning friction factor (equation 1)
fm - Moody friction factor (equation 2)
fm = 4x ff
upto = 2000
ff = (0.025-0.008)
Or
fm = (0.100-0.032)
For greater than 2000 ff or fm, vary with and Pipe roughness. (Refer Fig. 1.1 friction chart for f Vs )
Approximate equation
Ff = (k&n -- constants)
Typically,k=0.04andn=0.20whenliquidflowismeasuredas-
………………………... (3)
Forlaminarflow(fm) =
………………………… (4)
(Equation 3 and 4 are for pipes of circular cross section)
1.7.2 Compressible Fluid (Vapour, Gas)The Darcy/Fanning equation cannot be used directly as even under isothermal conditions as pressure decreases (due to pressure drop), the density decreases and velocity increases. In such cases the pressure drop can be calculated by considering segments of pipeline.
7
Reynolds number Re
2 3
4 5 6 8 010
2 3
4 5 6 8 2
3 4 5 6
8 107
106
105
104
103
1 3 4 6 8 10 20 30
00 005
40
0 0 01
00020004
0008 001 004002
006 008 015
01 0302 04 05
Pipe diameter d inches
011
012013014015016
018
020
022
024026028030 04 06 1009080705
10
21
Relative roughness E/D
Fig. 1.2 Friction chart (Source: http://t1.gstatic.com/images?q=tbn:ANd9GcQCAMi7VSkz2UljccTZNnan-O_B_
NswNn3kKNg7__8oSD2IcHQ7Hw)
Fluid Handling
8
Q1/s
Pipe diameter in mm (inch)
20 (3/4) 25 (1) 32(11/4)
40(11/2) 50 (2)
0.1 0.83 0.28 - - -0.2 3.0 1.0 - - -0.5 16.4 5.5 1.66 0.56 -1 65 (21/2) 20.0 6.0 2.0 0.68
1.5 0.4 80(3) 12.7 4.3 1.452 0.68 0.25 21.6 7.3 2.53 1.45 0.53 100 (4) 15.5 5.24 2.5 0.90 0.30 26.4 8.95 3.8 1.36 0.46 125 (5) 13.46 5.2 1.9 0.64 0.22 18.87 6.9 2.5 0.84 0.29 150(6)8 8.9 3.2 1.10 0.37 0.159 11.1 4.0 1.36 0.46 0.1910 13.4 4.9 1.66 0.55 0.2312 175 (7) 6.9 2.3 0.78 0.3214 0.20 9.1 3.1 1.04 0.4316 0.26 11.7 4.0 1.33 0.5518 0.32 200 (8) 4.9 1.65 0.6820 0.39 0.20 6.0 2.0 0.8325 0.59 0.31 9.0 3.0 1.2530 0.83 0.43 225 (9) 4.3 1.7635 1.10 0.58 0.32 5.7 2.340 1.41 0.74 0.42 7.3 3.045 1.76 0.92 0.52 250 (10) 3.750 2.1 1.11 0.3 0.38 4.560 3.0 1.56 0.88 0.53 6.370 4.0 2.1 1.17 0.70 300 (12)80 5.1 2.7 1.50 0.90 0.3790 6.3 3.3 1.87 1.12 0.46100 4.0 2.3 1.36 0.56120 5.6 3.2 1.90 0.78140 7.5 4.2 2.5 1.04160 5.4 3.2 1.33180 6.7 4.0 1.65200 8.2 4.9 2.0
Table 1.1 Friction loss for water (M / 100 M) in smooth and new uncoated steel pipes (Hazen Williams Formula, C=140)
9
Velocity of flow
m/s
Actual bore of pipe mm
5 0 8 0 1 0 0 1 2 5 1 5 0 1 7 5 2 0 0 2 2 5 2 5 0 3 0 0
Discharge in litres per second (l/s)
11.52
2.53
3.545
1.962.953.934.915.896.877.859.82
5.037.5410.0512.5715.0817.5920.1125.13
7.8511.7815.7119.6423.5627.4931.4239.27
12.2718.4124.5430.6836.8242.9549.0961.36
17.6726.5135.3444.1853.0261.8570.6988.36
24.136.148.160.172.284.296.2120.3
31.447.162.878.594.3110.0125.7157.1
39.759.679.599.4119.3139.2159.0198.8
49.173.698.2122.7147.3171.8196.4245.4
70.7106.1141.4176.7212.1247.4282.8353.4
Table 1.2 Quantities passed by pipes at different velocities
Alternatively, the general isothermal equation can be considered as the basis, i.e.
) X
……… (5)
w = massflowrateinkg/sec.
For engineering calculations:
2 in ( ) is generally much less than
Since = Q x ρ
…….. (6)
Special forms of equation 6
Unwin formula for steam flow:
DP in psi/100ft =
W - steamflowinlb/min.V - special volume in cubic ft/lbd - pipe dia in inches
Weymouth equation for compressed air:
Fluid Handling
10
Q in /s S in lb/ cub ft
d in inches (at standard condition)
and in PSIA in ⁰R
L in ft Z compressibility factor
Various units of pressure measurement:
1 atm = 1.033 kg/ =1.013 bar =14.70 psi
or
1 bar =1.02 kg/ =14.51 psi
0.981 bar =1kg/ =14.23 psi
For liquids the DP is measured in mlc (meters of liquid column) (P=hg)
1bar = 10.20 mWC
1atm = 10.33 mWC(mWC -meters of Water column)
1.7.3 Equivalent LengthAnefficientandsimplewaytocalculatethepressurelossinapipingsystemisthe“EquivalentPipeLengthMethod”.Since friction losses distil down to units of feet or meters, conversions have been developed to describe minor losses simply as an equivalent length of straight pipe.The lengths for a given diameter are summed.
If tables exist for friction losses (as they do for water and air), the total equivalent length is multiplied by the •factor in the table to yield the friction loss for that particular diameter. The equivalent length is given by
L _ KD/f whereK-ResistanceCoefficientD - Inside pipe diameter [ft]f-Frictionfactorintheturbulentflowregion
Otherwise, the equivalent length is used in the Darcy-Weisbach Equation with the friction factor f taken from •the Moody Diagram.This is a very convenient method as it requires no extra step in the calculation. Data exists for many common •fittingsandvalves.
Pressure drop through pipe fitting (elbows, valves, etc) and due to sudden change in flow area (expansion,contraction)
11
Liquids
DP = (refer k value charts)
Or
DP = (refer Le charts) Le =
Le =Equivalentlengthoffitting,dependsonKvalueandfm.
Forthemostengineeringpracticesitcanbeassumedthatpressuredroporheadlossduetoflowoffluidsinturbulentrangethroughvalvesandfittingsisproportionaltosquareofvelocity.
Toavoidexpensivetestingofeveryvalveandeveryfittingthatareinstalledonpipeline,theexperimentaldataareused.ForthatpurposeresistancecoefficientK,equivalentlengthL/DandflowcoefficientCv,Kvareused.These values are available from different sources like tables and diagrams from different authors and from valves manufacturers as well.
Kinetic energy, which is represented as head due to velocity, is generated from static head and increase or decrease invelocitydirectlyisproportionalwithstaticheadlossorgain.“Velocityhead”is:
where is: hL - head loss v - velocity gn - acceleration of gravity
Thenumberofvelocityheadslostduetoresistanceofvalvesandfittingsis:
where is: hL - head loss K -resistancecoefficient v - velocity gn - acceleration of gravity
Theheadlossduetoresistanceinvalvesandfittingsarealwaysassociatedwiththediameteronwhichvelocityoccurs.TheresistancecoefficientKisconsideredtobeconstantforanydefinedvalvesorfittingsinallflowconditions,astheheadlossduetofrictionisminorcomparedtotheheadlossduetochangeindirectionofflow,obstructionsandsuddenorgradualchangesincrosssectionandshapeofflow.Head loss due to friction in straight pipe is expressed by the Darcy equation:
Fluid Handling
12
where is: hL- head loss f - friction factor L - length D - internal diameter v - velocity gn- acceleration of gravity
It follows that:
where is: K -resistancecoefficient f - friction factor L - length D - internal diameter
The ratio L/D is equivalent length in pipe diameters of straight pipe that will cause the same pressure drop or head lossasthevalvesorfittingsunderthesameflowconditions.AstheresistancecoefficientKisconstant,theequivalentlengthL/Dwillvaryinverselywiththechangeinfrictionfactorfordifferentflowconditions.
Forgeometricallysimilarvalvesandfittings,theresistancecoefficientwouldbeconstant.Actuallythereare•alwayssmallerorbiggergeometricaldissimilarityinvalvesandfittingsofdifferentnominalsize,sotheresistancecoefficientisnotconstant.TheresistancecoefficientKforagiventypeofvalvesorfittingstendstovarywithsizeasdoesfrictionfactorforstraightcleancommercialsteelpipeatthesameflowconditions.Some resistances in piping like sudden or gradual contractions and enlargements, as well as pipe entrances or •existsaregeometricallysimilar.ThereforetheresistancecoefficientorequivalentlengthL/Disfortheseitemsindependent of size. ThevaluesforresistancecoefficientorequivalentlengthL/Darealwaysassociatedwithinternalpipediameter•where the resistance is occurring. IftheresistancecoefficientorequivalentlengthL/Dshouldbeusedfordifferentinternalpipediameterthen•the diameter for the existing values can be found following this relationship:
where is:
K-resistancecoefficient D-internal diameter
Where,subscript“a”definesKanddwiththereferencetointernalpipediameterand•subscript“b”definesKanddwiththereferencetotheinternaldiameterforwhichvaluesofKcanbefoundin•tables or diagrams.
ThisequationcanalsobeusedifthepipingsystemhasmorethanonesizeofvalvesandfittingstoexpresstheresistancecoefficientorequivalentlengthL/Dintermsofonesize.ResistancecoefficientKcalculatorforvalvesandfittingscanbeused.
13
VELOCITY OF LIQUID IN m/s
HEAD LOSSES DUE TO FRICTION INFOOT VALVES
(VALID UP TO 300 mm DIA.)NOTE : LOWER CURVE GIVES
FRICTION LOSS OF ONLY STRAINER
NOTE ON 'K' FACTOR FOR VALVES
Design factors of valves change frommanufacturer tomanufacturer, thereforeare NOT universal. They are to be usedas aguidanceonly.
Suction
strainers
Strainers
withfoot valve
Fig. 1.3 Resistance in pipe fittings (using ‘K’ factor)
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14
Fig. 1.4 Resistance coefficient of pipe fittings
To convert tool in the equation for h.v2 would be measured in m/s and feel would be changed to metres. The following values would also be changed from inches to millimetres 0.3 to 7.6, 0.5 to 12.7, 1 to 25, 4.2 to 50.5, 4 to 101.6, 6 to 152.4, 10 to 254 and 20 to 508 (hydraulic institute).
15
LONG RADIUS90 BEND0LONG RADIUS90 BEND0
SHORT RADIUS90 BEND0
Fig. 1.5 Resistance of valves and fittings to flow of fluids(Source:http://t0.gstatic.com/images?q=tbn:ANd9GcTwBs8LizuolGIMzE-WjHs_Y1jgktogRfK-flggUWB-
BmZEHi0oxg)
1.7.4 Determining Pipe Size for Specified Pressure Drop and Flow RatePressuredropandflowratecalculatorcanbeusedforpressuredropandflowratecalculationforallNewtonianfluidswithconstantdensity.YoucancalculatepressuredroporflowratethroughapipeincludingfrictioncoefficientandlocalresistancecoefficientKforvalvesandfittingscalculation.
Themostfrequentlyusedcalculationinfluiddynamicsprobablyisthecalculationofpressuredropthrougha•pipeorachannel.Alsowhenthedifferenceinpressureisknownthesamecalculationisusedtocalculateflowrate through pipe.
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16
Pressure drop calculator for closed pipe is based on the Bernoulli equation for calculation of pressure difference •between two points of pipe, including pressure losses due to friction and local pressure losses in valves and fittings.Pressuredropcalculatorcanbeusedforbothlaminarandturbulentflowregime.Itcancalculatepressuredrop•orflowratethroughapipeincludingfrictionlossesandlocalpressurelossescalculation.Pressure drop calculation due to friction is using friction factor values and pressure drop due to local resistance is •usingresistancecoefficientKforvalvesandfittingsvalues.Flowmeanvelocitycalculationforknownflowrateandpipediameterisalsousedincalculator.ValuesofReynoldsnumberandflowregime-laminarorturbulentare presented. Pressure difference due to change of height is not included in this version of calculator.
Iterative Procedures:Assume pipe ID as‘d’•Ascertaindensityandviscosityaswellasnatureoffluid(Newtonian/Non-Newtonian)•Determine • From chart or equation determine fm (or ff)•Using the Darcy equation determine DP•IfDPcalculatedisnotwithin±5%ofthespecifiedDPassumenewpipeID.•Repeat the procedure till the required convergence is achieved.•When convergence is achieved, select a standard pipe with ID nearest to and higher than that of the calculated •pipe ID.
Alternatively,Use equation 3 with the assumed value of fm.•After value of d is obtained using equation 3, check for convergence of values of fm.•Repeat procedure till convergence is obtained.•
Ifflowislaminar(asinthecaseofviscousliquids)useequation4toobtainthevalueof‘d’.
Optimum pipe size or optimum pipe velocity:
Foragivenflowrate–
Higher pipe size - Lower velocity and hence lower DP Lower DP means lower energy cost. Higher initial (capital) cost.
Life cycle cost of piping - Capital cost + present value of O & M cost. (O & M Operation and maintenance)
1.8 Present Value of O & M CostValue of annuity/perpetuity i.e., sum of money that would have to be invested at present to provide for periodic payment for the given period of time in the future. An appropriate discount factor is to be used. Usually the discount factor is the cost of borrowing the capital.
17
Pipe IDmm Velocity m/s Capital
CostAnnual
O & M costLife cycleCost (*)
77.5 2.68 21803 2795 38964
101.6 1.56 26543 1205 33942
154.7 0.67 37774 690 42011
Table 1.3 The life cycle cost of piping
Thelifecyclecostofpipingwouldbeoptimumforaspecificpipesize.•E.g.-Life cycle cost calculated using 10 year life and 10 % p.a. interest rate. •These can serve as guidelines for deciding pipe size.•
Densitykg/m3 1600 800 160 16 1.6 0.16
EconomicVelocity(m/s)
1.5to
2.5
2.0to
3.0
3.0to
5.0
6.0to
10.0
12.0to
18.0
24.0to
36.0
Table 1.4 Approximate economic velocities estimated using the above concept
(Note:-Economic velocities indicated above are based on aforementioned article in Chem. Engg. June 95 as well as some text books published earlier.)
Forgravityflows,velocityoftheorderof0.3m/sisrecommended.•
1.9 Predicting Pressure Drop in PipingThumbruletobeusedinthepreliminaryphaseofplantdesignafterflowsheetandplotplanshouldbereadybeforedetailedpiping.Theobjectiveshouldbetoestimatethefittingsandvalvesinapipelinewhereasapproximatestraightlength is known.
= 1+ ( + 0.216)
Le - Total equivalent length
d - Pipe NB in inches
L - Distance between two end points
Fc - Complexity factor
Note: Use pipe NB in inches is dimensionless
Example: 110 /hr of water, 150 NB (6” NB) pipe, = 1, L= 90 m.
= 1+ (0.347 x + 0.2161) x 1 = 2.065
Le = 90 x 2.065= 186m
Fluid Handling
18
Tota
l equ
ival
ent l
engt
h pe
r uni
t len
gth
of st
raig
ht p
ipe
(Le/
L)
Nominal pipe diameter (D). in.
Complexity Factor (Fc) 4
2
1
½
¼
0.5 0.75 1 2 4 6 8 10 16 24 36
11
10
9
8
7
6
5
4
3
2
1
0
Fig. 1.6 The equivalent length adjustment
Complexity Factor (Fc)•
Piping Type FC
Very complex Manifold 4
Manifold 2
Normal Piping 1
Long, Reasonably straight piping 0.5
Utility, OSBL (Yard) 0.25
19
SummaryNewtonianFluids:Afluidinwhichthecomponentsofthestresstensorarelinearfunctionsofthefirstspatial•derivatives of the velocity components.Non-NewtonianfluidsareonlytypeoffluidwhichdoesnotobeyNewton’slawofviscosity.•Theapparentviscosityofthefluiddecreaseswithincreasingshearrate.Thistypeofbehaviourisalsoreferred•to as ’pseudoplastic’ and no initial stress (yield stress) is required to initiate shearing. Theapparentviscosityofthefluidincreaseswithincreasingshearrateandnoinitialstressisrequiredtoinitiate•shearing. Viscoplasticmaterialsarefluidsthatexhibitayieldstress.•Whenthatshearstressvalueisexceeded,thematerialflowslikeafluid.•Non-Newtonian• (TimeDependent)fluidsseemtoexhibita‘memory’,whichfadeswithtime.A thixotropic liquid will exhibit a decrease in apparent viscosity over time at a constant shear rate.•Rheopectic liquid exhibits a behaviour opposite to that of a thixotropic liquid, i.e., the apparent viscosity of the •liquid will increase over time at a constant shear rate. Viscoelasticfluidsexhibitbothviscousandelasticproperties.Therheologicalpropertiesofsuchasubstanceat•any instant of time will be a function of the recent history of the material.
ReferencesSubramanian, R.S., • Non-Newtonian Flows [Online] Available at: <http://web2.clarkson.edu/projects/subramanian/ch301/notes/nonnewtonian.pdf>. [Accessed 7 April 2011].Rashaida. A., • Flow of a non-Newtonian Bingham plastic fluid over a rotating disk [Online] Available at: <http://www.collectionscanada.gc.ca/obj/s4/f2/dsk3/SSU/TC-SSU-08172005120844.pdf>. [Accessed 7 April 2011].Chitika, 2000. • Velocity and pressure drop in pipes[Online]Availableat:<http://4wings.com/lib/files/velocity_and_pressure_drop_in_pipes.pdf>. [Accessed 7 April 2011].Puddyman, 2007.• Cornflour, Water and Speakers Non Newtonian Expt[Online] Available at: <http://www.youtube.com/watch?v=GU3fOeDctbY&feature=related> . [Accessed 8 June 2011].
Recommended ReadingSiginer, D. A., Daniel, D. K., Chhabra, R. P., 1999, • Advances in the Flow and Rheology of Non-Newtonian Fluids, Volume 1., Elsevier.Böhme, G., 1987, • Non-Newtonian fluid mechanics, North-Holland.Saad, M. A., 1993, • Compressible fluid flow, 2nd ed, Prentice Hall.
Fluid Handling
20
Self Assessment
Whatisthebasicaimforanypipingsystemtohandleafluidorfluids?1. designinga. planningb. executingc. closingd.
___________________fluidsareonlytypeoffluidwhichdoesnotobeyNewton’slawofviscosity.2. Newtoniana. Non-Newtonianb. Viscoplasticc. Viscoelasticd.
Which liquid will exhibit a decrease in apparent viscosity over time at a constant shear rate? 3. newtoniana. thixotropicb. viscoplasticc. viscoelasticd.
Theviscosityofatimeindependentnon-Newtonianfluidisdependentonthe________________.4. viscoplasticfluida. thixotropicfluidb. rheopecticfluidc. shear rated.
Afluidinwhichthecomponentsofthestresstensorarelinearfunctionsofthefirstspatialderivativesofthe5. _______________.
compressiblefluidsa. pressure dropb. shear ratec. velocityd.
Which of the following is true?6. Afluidmaybeliquidorgaseous.a. Afluidmaybeliquidorsolidoramixtureofthetwo.b. Afluidmaybeliquid,gaseousorsolidoramixtureofthetwo.c. Afluidmaybesolid.d.
Which of the following is true?7. Dependingonhowtheapparentvelocitychangeswithshearratetheflowbehaviourischaracterised.a. Dependingonhowtheapparentviscoplasticchangeswithshearratetheflowbehaviourischaracterised.b. Dependingonhowtheapparentviscositychangeswithshearratetheflowbehaviourischaracterised.c. Dependingonhowtheapparentviscositychangeswithvelocityratetheflowbehaviourischaracterised.d.
21
Which of the following is false?8. Non-NewtonianfluidsareonlytypeoffluidwhichdoesnotobeyNewton’slawofviscosity.a. Afluidinwhichthecomponentsofthestresstensorarelinearfunctionsofthesecondspatialderivativesb. of the velocity components.A number of non-Newtonian materials are in this category, including grease, molasses, paint, starch and c. many dilute polymer solutions. Theapparentviscosityofthisfluidincreaseswithincreasingshearrateandnoinitialstressisrequiredtod. initiate shearing.
Which of the following is false?9. Whensubjectedtovaryingratesofshear,athixotropicfluidwilldemonstratea“hysteresisloop”a. Rheopectic liquid exhibits a behaviour opposite to that of a thixotropic liquidb. Anexampleofaplasticfluidisoil.c. An example of viscoelastic material is bread dough.d.
Which of the following is true?10. The Darcy/Fanning equation cannot be used directly as even under isothermal conditions as pressure increases a. the density decreases and velocity decreases.The Darcy/Fanning equation cannot be used directly as even under isothermal conditions as pressure decreases b. the density increases and velocity increases.The Darcy/Fanning equation cannot be used directly as even under isothermal conditions as pressure decreases c. the density decreases and velocity increases.The Darcy/Fanning equation cannot be used directly as even under isothermal conditions as pressure increases d. the density increases and velocity decreases.
Fluid Handling
22
Chapter II
Pipeline Sizing
Aim
The aim of this chapter is to:
understandclassificationofpipeline•
study economic velocity for different piping system•
learn numerical for line size•
Objectives
The objectives of this chapter are to:
explain pipeline sizing•
defineliquidflowundergravity•
enlist economic velocity for different piping system•
Learning outcome
At the end of this chapter, you will be able to:
recognise pipeline sizing•
identifyhotliquidflow•
classify sample line•
describe numerical for line size•
23
2.1 IntroductionThechemicalprocessindustryisinvolvedinmanyoperations,fordifferenttypesoffluids,withdifferentapplications.Though in principle, various guidelines and formulae are available for pipeline sizing for different services. Hence, it becomes critical at times and makes conceptualization necessary before deciding design parameters.
Whenfluidsaretobecarriedfromoneplacetoanotherlikehouseholdpipingtoacrosscountrypipeline,piping•andfittingconstitutesahighcost.The size of piping plays an important role in the pumping cost. Hence, the selection of the line size becomes •important. Though in principle, various formulae are available for sizing for different services, conceptualization is necessary before deciding parameters.
2.2 Classification of PipelinesGivenbelowisabriefclassificationofvarioustypesofpipelines.
2.2.1 Pipeline SizingInanychemicalprocessindustry,varioustypesoffluidsarebeingusedindifferentformslikeliquid,gaseous,slurry,etc.Rawmaterial,intermediateproductorfinishedproductproducedthroughvariousunitoperationsrequiresconnectivityofalltheunitswithpipelinesandfittingsduetothefollowingreasons:
Ease of operation �Safe handling of materials �Avoiding loss of material �Hygienic conditions of the plant �
For example, liquid feed is transported from its bulk storage area to day-storage using pump connecting bulk •storagetank,pumpanddaystoragetankwiththenecessarypipelines.Itisverydifficulttoimagineachemicalprocess industry complex without any pipeline work. Thedesignofanypipingnetworkinvolvesvariousactivitiesliketheselectionofpipingmaterial,specification•with respect to thickness, pipe size, its routing, etc.Though various formulae and thumb rules are available in literature and can be used directly for sizing of •pipelines,criticalitywithrespecttoexperienceinthefluidhandlingofrelatedchemicalprocessindustrycannotbe avoided. Over or under sizing of pipelines may even become a bottleneck for plant operations. For slurry applications, a larger size pipeline not only increases the plant cost but also creates operational •problems.Likewise,thesmallerpipesizemayconsumemoreenergyforfluidmovement.Oneshouldbearinmind that the larger pipeline size than necessary increases plant cost due to pipelines along with the connected valves,fittings,supportingstructures,etc.Many factors should be kept in mind before sizing any pipeline. The basic principle of pipeline size is based on •theavailablepressuredropbetweenitstwoends.Normallytomaintaincertainfluidvelocity(maybefromtheavailable thumb rules), e.g. considering 1.5 metre/second for clear water at pump discharge for the maximum possiblefluidflowratethroughthatpipeline,cross-sectionalarea(ordiameter)ofpipelineiscalculated.Basedon this, the nearest commercially available pipeline size (of inside diameter closely matching with the calculated value) is selected for application. With these preliminary calculations of pipeline sizing and pipe routing, pressure drop between start and end •point,incorporatingallfittings,iscalculated.Decisionoftheselectionofhigherorlowerpipelinesizeismadeaccording to the available pressure drop versus calculated pressure drop.Normally pipelines are sized after optimizing between the costs of material versus operating cost (incurred due •to line pressure drop). Higher the pipeline diameter (i.e., higher initial investment), lower will be the pressure drop (thus less operating cost) and vice versa.Velocitynormsarefixedfordifferentapplicationsbasedontheoptimumdesignconditions.Further,pipeline•sizes are calculated using these norms. In some typical applications discussed here, these guidelines are not valid and one needs to understand the typical application and size the pipelines accordingly.
Fluid Handling
24
The objective of the steam distribution system is to supply steam at the correct pressure to the point of use. •Hence, it follows that pressure drop through the distribution system is an important feature.
2.2.2 LiquidsBernoulli’sTheorem–Flowmetering:D’ArcyaddedthatforfluidflowtooccurtheremustbemoreenergyatPoint1 than Point 2 (see Figure 2.1). The difference in energy is used to overcome frictional resistance between the pipe andtheflowingfluid.
Pipe diameter {D}
Length (L)
Point 1
hf
h2
h1
Point 2
Flow velocity (u)
Fig. 2.1 Friction in pipes(Source: http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipes-and-pipe-
sizing.asp)
Bernoullirelateschangesinthetotalenergyofaflowingfluidtoenergylossexpressedeitherintermsofahead•losshf(m)orspecificenergylossghf(J/kg).This,initself,isnotveryusefulwithoutbeingabletopredictthepressure losses that will occur in particular circumstances.Here,oneofthemostimportantmechanismsofenergydissipationwithinaflowingfluidisintroduced,thatis,the•lossintotalmechanicalenergyduetofrictionatthewallofauniformpipecarryingasteadyflowoffluid.Thelossinthetotalenergyoffluidflowingthroughacircularpipemustdependon:•
L = The length of the pipe (m)
D = The pipe diameter (m)
u = Themeanvelocityofthefluidflow(m/s)
μ = Thedynamicviscosityofthefluid(kg/ms=Pas)
ρ = Thefluiddensity(kg/m)
ks = The roughness of the pipe wall* (m)
Since the energy dissipation is associated with shear stress at the pipe wall, the nature of the wall surface will •beinfluential,asasmoothsurfacewillinteractwiththefluidinadifferentwaythanaroughsurface.All these variables are brought together in the D’Arcy-Weisbach equation (often referred to as the D’Arcy •equation), and shown as Equation 1. This equation also introduces a dimensionless term referred to as the frictionfactor,whichrelatestheabsolutepiperoughnesstothedensity,velocityandviscosityofthefluidandthe pipe diameter.
25
The D’Arcy equation:
................(1)
Where for equation 1 using SI based units:
hf = Head loss to friction (m)
f = Friction factor (dimensionless)
L = Length (m)
u = Flow velocity (m/s)
g = Gravitational constant (9.81 m/s2)
D = Pipe diameter (m)
Where for equation 1 using Imperial based units:
hf = Head loss to friction (ft)
f = Friction factor (dimensionless)
L = Length (ft)
u = Flow velocity (ft/s)
g = Gravitational constant (32.17 ft/s2)
D = Pipe diameter (ft)
Interesting pointReaders in some parts of the world may recognise the D’Arcy equation in a slightly different form, as shown in Equation 2. Equation 2 is similar to Equation 1 but does not contain the constant 4.
................(2)
The reason for the difference is the type of friction factor used. It is essential that the right version of the D’Arcy equation be used with the selected friction factor. Matching the wrong equation to the wrong friction factor will result in a 400% error and it is therefore important that the correct combination of equation and friction factor is utilised. FrictionfactorscanbedeterminedeitherfromaMoodychartor,forturbulentflows,canbecalculatedfromEquation3, a development of the Colebrook-White formula.
................(3)
Where:
Fluid Handling
26
f = Friction factor (Relates to the SI Moody chart)
ks = Absolute pipe roughness (m)
D = Pipe bore (m)
Re = Reynolds number (dimensionless)
However, Equation 3 is difficult to use because the friction factor appears on both sides of the equation,and it is for this reason that manual calculations are likely to be carried out by using the Moody chart.
Example 1-Water pipeDetermine the velocity, friction factor and the difference in pressure between two points 1 km apart in a 150 mm constantborehorizontalpipeworksystemifthewaterflowrateis45m³/hat15°C.
Inessence,thefrictionfactordependsontheReynoldsNumber(Re)oftheflowingliquidandtherelativeroughness(ks/d) of the inside of the pipe; the former calculated from Equation 10.2.6, and the latter from Equation 10.2.7. Reynolds Number (Re)
................(4)
Where:
Re = Reynolds number
ρ = Density of water = 1000 kg/m
u = Velocity of water = 0.71 m/s
D = Pipe diameter = 0.15 m
μ = Dynamicviscosityofwater(at15°C) = 1.138 x 10-3 kg/m s (from steam tables)
From Equation 4:
The pipe roughness or ‘ks’ value (often quoted as ‘e’ in some texts) is taken from standard tables, and for ‘commercial steel pipe’ would generally be taken as 0.000045 meters.
From this the relative roughness is determined (as this is what the Moody chart requires).
27
................(5) From Equation 5:
The friction factor can now be determined from the Moody chart and the friction head loss calculated from the relevant D’Arcy Equation.
From the European Moody chart (Figure 2.2),
Where: ks/D = 0.0003 Re = 93585: Friction factor (f) = 0.005
Fig. 2.2 ‘SI based’ Moody chart(Source: http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipes-and-pipe-
sizing.asp)
0.013
0.012
0.011
0.010
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
Relative roughness
0.01
0.008
0.0060.0050.004
0.003
0.002
0.0010.00080.0006
0.00040.0003
0.0002
0.0001
0.000060.00004
0.000020.00001
Coe
ffici
ent o
f fri
ctio
n f
Reynolds number Re
103 2 3 4 5 104 2 3 4 5 105 2 3 4 5 106 2 3 4 5 107
kS
D
Fluid Handling
28
From the European D’Arcy equation (equation 2.2.1):
From the USA / AUS Moody chart (Figure 2.3): Where, ks/D = 0.0003 Re = 93 585 Friction factor (f) = 0.02
Fig. 2.3 ‘Imperial based’ Moody chart (abridged)(Source: http://www.spiraxsarco.com/resources/steam-engineering-tutorials/steam-distribution/pipes-and-pipe-
sizing.asp)
29
From the USA / AUS D’Arcy equation (equation 2):
The same friction head loss is obtained by using the different friction factors and relevant D’Arcy equations. In practice whether for water pipes or steam pipes, a balance is drawn between pipe size and pressure loss.
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30
Fig. 2.4 Pipeline sizing chart(Source:http://www.spiraxsarco.com/images/resources/steam-engineering-tutorials/14/3/fig_14_3_5.gif)
31
2.3 Economic Velocity for Different Piping SystemsHere typical applications are discussed for conceptualizing pipeline sizing.
2.3.1 Liquid F low under Gravity
Liquidflowsundergravityduetotheelevationdifferencebetweenthestartpoint(alwaysathigherelevation)•and the end point (at lower elevation), i.e., difference in potential energy. The elevation difference mainly governs the pipeline sizing. Additional effects of pressure conditions for start/•end point matter in pipeline sizing. If the available elevation difference is higher, a high liquid velocity (i.e. with high allowable pressure drop) can be considered for pipeline sizing. Thus, a lower pipeline size can be selected for such a condition.In case, the end point is connected to a pressurised system, e.g. distillation column, the equivalent pressure shall •be deducted from the available elevation difference and the effective available differential pressure is reduced. Thus, even with the higher available elevation difference, for the end point of the pipeline connected to the pressurised system, the pipeline size will be of a lower size. Similarly, if the start point of the pipeline is under vacuum, i.e., in barometric condensers, pipelines of high •diameters are selected to reduce pipeline friction losses. Thus, increasing the available differential pressure.
Previous strataImpervious strata
Artesian well
Saturation Level
Fig. 2.5 Liquid flow under gravity(Source: http://www.littledippers.com/geocaching/ArtesianWell.jpg)
Pascal’s law predicts the theoretical hydrostatic pressure P:
Where,p(rho)isthedensityofthefluidg is the acceleration due to gravityz is the elevationIn practical terms the pressure is expressed as meters water column (zr-zw).
Fluid Handling
32
2.3.2 Hot Liquid Flow
Various problems are commonly observed in the process plants handling hot boiling liquids. These are mainly due •tovaporisationofflowinghotliquid,i.e.,thephasechangeofliquidtovapour,insidethepipelineorequipment.Thisphenomenonisalsocalledtheflashingofliquid.Atypicalexampleiscentrifugalpumpcavitations,whichis due to low available Net Positive Suction Head (NPSH).The higher pipeline size is preferred to lower down pressure drop and thus, to achieve higher available NPSH •atpumpsuctionport.Similarlyinotherpipelines,thepressuredropduetosuddenchangeintheflowdirectionor the reduction of the line size, hot liquid vaporisation takes place which generates vapour bubbles inside thepipeline.Duetothismorespaceisoccupiedbythemixtureofgeneratedvapoursandflowingliquidandsubsequentlyfluidflowisobstructed.Similar type of phenomena is observed in case of liquids carrying dissolved gases, which expand at higher •temperatures. For these types of applications, normally higher pipeline sizes are recommended.
Fig. 2.6 Hot liquid flow(Source: http://2.bp.blogspot.com/-3WAVHmvZ2Rk/TavHaVNagiI/AAAAAAAAAPc/sxigxOyb_5M/s1600/diag
ram+of+flow+in+heat+exchanger.gif)
Hotfluid
Coldfluid
T
Hotfluid
Coldfluid
T
Hot in
Hot out
Cold in
(a)Parallelflow
Cold out
Hot in
Hot out
Cold out
(b)Counterflow
Cold in
Different flow regimes and associated temperature profiles in a double-pipe heat exchanger.
33
2.3.3 Bypass Line for Equipment/Instrument
Equipment/instruments especially which create a high-pressure drop and are provided with a bypass line (to •have the facility for maintaining process continuity even during maintenance work). i.e., plate heat exchangers, control valves, etc. are provided with a bypass arrangement, which normally has two isolation valves in line of theunitandaflowregulationvalveinparalleltothisunit.Innormaloperations,asfluidpassesthroughthemainunitseithertheplateheatexchangerorcontrolvalve,•itexertsanadditionalpressuredrop.Accordingly,thesupplypressureforthefluidstreamisestimated,whichthe connecting unit like the centrifugal pump creates. The centrifugal pump is selected based on this created pressure drop by the unit. During bypassing of the connected unit, this additional pressure is eliminated, while running pump discharges •thehighflowrateasperthetypicalpumpcharacteristics.Toavoidthissituation,itisalwaysrecommendedtouse a lower size bypass line with a regulation valve to create pressure equivalent to the main connecting unit.
Tc, i
Tc,o
Th,iTh,o
Teflonhead
Teflonhead
Cold water
Quartz crystal tube
Cold waterHot water
Copper tube
Fig. 2.7 Bypass line for equipment/instrument(Source: http://www.informaworld.com/ampp/image?path=/713770473/915051932/
ueht_a_410066_o_f0002g.png)
2.3.4 Sample LineNormally,asmallfluidquantityiscollectedforanalysistodetermineitscomposition.Itisapplicableforanystageofprocessinglikeforrawmaterial, intermediateproduct,finishedproductoritmaybeevenutilityoreffluent.Evenforsmallquantityofsamplecollection,linesizemainlydependsuponthetypeoffluidbeinghandledandthelocation of the sample point in the process.
Forexample, forgasesunderpressurizedconditions,small lineswithvalves (e.g.6mm)aresufficient for•withdrawingtherepresentativesamplequantity.Providingahighsamplelinesizewillnotonlybedifficulttocontrol but higher wastage of gases during sample collection cannot be avoided. On the other hand, small sample line will create trouble for slurries where solid particles may choke the sample •line quite frequently. Thus, irrespective of material losses and the cost of the pipeline and valve, the sample line size is dependent upon the solid particle size and the characteristics of the slurry. Similar are the experiences for viscous liquids.Even for clear liquids, the sample line size depends upon its location like at the atmospheric tank, pump suction/•ordischarge,etc.Thoughitisverydifficulttodefineproperguidelinesforsamplelinesizing,thefollowingpoints should be kept in mind while sizing:
Characteristicsofsamplefluid �Lessfluidlosses �Safety during sample withdrawal �Ease of operation �Location of sample point, etc. �
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34
2.3.5 Cooling Water CirculationHigher velocities are preferred for cooling water circulation pipelines. This is mainly due to the following two reasons:
Cooling water, in the cooling tower, is exposed to sunlight that helps in the development of algae formation. •This generated algae material goes to the circulating cooling water. At a lower liquid velocity in the pipelines, algae starts growing within the pipeline and after some time, they start blocking cooling water circulation or it passes to the connected heat exchanger unit. Thus, a higher liquid velocity (e.g. 1.8-2.5 metre/second) for circulation line is recommended to avoid algae development within the pipeline.Normallyhighercoolingwatercirculationflowratesareencounteredinthechemicalprocessindustriesthat•require large size pipelines with longer lengths to cover various heat exchanging units. Thus, to reduce the cost of pipe material even with high power consumption (due to increased pressure drop) will be an appropriate choice.
2.3.6 Tank OverflowOverflowlinesinthetanksareprovidedforthefollowingreasons:
Toavoidliquidlosses(overflowedliquidisrecoveredinanothertank) �To avoid unwanted spillage of liquid around plant building �To maintain liquid levels in the overhead tanks �
Inalltheabove-mentionedcases,overflowlineissizedforthemaximumpossibleinputliquidflowratetothe•tankirrespectiveoftheoutletliquidflowrate.Otherdesignguidelinesaresimilartothepipelinesizingforgravityliquidflow,i.e.,aspertheavailabilityofverticalavailableheightbetweenthehighestendpoints(whereitcomesincontactwiththeatmosphere)oftheoverflowpipeline.Herethehighestpointwhichisalsothestartpointoftheliquidflowlineislocatedalmostatthetopofthetank•(overflownozzleofthetank),whiletheendpointmaybesomewherenearthedraingutter(closetoground).Thismaynotalwaysbetrue,astheoverflowlinemayalsobeterminatedatthehigherelevationfloor.Inthat•casetheavailabledifferentialheadwillbelower.Henceasperthepipelinelocation,theoverflowlineshallbesized,basedonthegravityflowprinciple.
2.3.7 Slurry FlowSlurries, a mixture of suspended solids in liquids, are kept in agitated conditions to maintain homogeneity, other wise, depending upon the solid’s characteristics, lighter or heavier than liquid; particles float or settle downrespectively.
Agitated conditions are maintained in equipment, like tanks by the use of agitators or gases sparing. While in •thepipelines,itisachievedbymaintainingturbulentfluidflowconditions.Atalowerfluidvelocityinthepipeline,solidshaveatendencytoseparateoutfromtheliquidphase.Thus•sufficientlyhighfluidvelocityshallbemaintainedinthepipelines,irrespectiveofencounteringahigh-pressuredrop in the pipelines for slurries (beyond the guidelines for optimum pipeline sizing for clear liquids).On the other hand, when very small pipeline size is used for slurries, choking is quite frequently observed in •plants. Thus, a small pipeline size is also not recommended for these applications. Apart from this, some slurry containingabrasivesolidparticlesmaycausepipelineerosionatveryhighfluidvelocities.Hence,highfluidvelocitiesarenotrecommended.Variousslurriesbehaveindifferentfashionsatdifferent•fluidvelocities;hencepipelinesizeismorecritical.Alongwiththebasicdesignguidelines,pastexperiencetounderstand slurry behaviour shall also be used during pipeline sizing.Apart from above discussion, many other applications can be seen in any chemical process industry. i.e., very •lowfluidvelocitiesareconsideredfordesigningpipelinescarryinghighlyviscousliquids,storagetankventlines (depending upon the tank design pressure), tank drain lines (related with the vent line size as well as the time required for the draining out tank), etc.
35
Fig. 2.8 Slurry flow chart evaluation(Source: http://www.micromagazine.com/archive/01/07/ultrapure2.gif)
2.4 Numerical for Line SizeExample 1Select pipe size for the following design parameters:Liquidflowrate,Q = 300 /hrLiquid density, ρ = 1000 kg/Liquid viscosity, µ = 1.0 CP or 0.001kg/m-secPipe roughness, ∈ = 0.4 mmPipe schedule = 40Pipe straight length = 100m
SolutionLet liquid velocity = 2.5 m/sec
= 206.01mm
Selected Pipe Internal Diameter, = 202.7mm
Internal pipe cross section area = 0.032269
Liquid velocity in selection pipe, = 300/ (0.032269 x 3600) = 2.582 m/sec
=
FLO
W R
ATE
(ml/m
in)
PRES
SUR
E (p
sD)
SLURRY FLOW
DAYS
FILTER DELTA PRESSURE
120
100
80
60
40
20
0
25
20
15
10
5
0
0 2 4 6
Fluid Handling
36
= 523371.4
∈/ = 0.4/202.7 = 0.00197From Moody Friction Factor Chart, for NRe and ∈/
Friction factor, f = 0.024
= 0.4027 kg/
Thus for the selected pipeline, 200 NB schedule 40 of 100 metres pipe length pressure drop is 0.4027 kg/ . If the available pressure drop is more than 0.4027 kg/ ,liquidflowispossible.
Fig. 2.9 Moody friction-factor chart
37
2.5 Pipeline Sizing Criteria A natural tendency exists, when choosing pipe sizes, to be guided by the size of connections on equipment to which theywillbeconnected.Ifthepipeworkissizedinthisway,thenthedesiredvolumetricflowratemaynotbeachieved.The use of concentric and eccentric reducers can be used to correct this, enabling pipework to be properly sized.
Pipe sizes may be chosen on the basis of either:•Fluid velocity �Pressure drop �
Steam
Concentric Eccentric
Steam
Fig. 2.10 Concentric and eccentric reducers
The optimum pipe size should be based on minimizing the sum of energy cost and piping cost. However, velocity •limitations causing erosion or aggravating corrosion must be taken into consideration. Sometimes, the line size must satisfy process requirements such as pump suction line. Although pipe sizing is •mainly concerned with pressure drop, sometimes for preliminary design purposes when pressure loss is not a concern, process piping is sized on the basis of allowable velocity. Whenthereisanabruptchangeinthedirectionofflow(asinelbowortees),thelocalpressureonthesurface•perpendiculartothedirectionofflowincreasesdramatically.Thisincreaseisafunctionoffluidvelocity,densityandinitialpressure.Sincevelocityisinverselyproportionaltothesquareofdiameter,highvelocityfluidsrequirespecial attention with respect to the size selection.
2.5.1 Fluid FlowFluidflowinginpipeshastwoprimaryflowpatterns.
Itcanbeeitherlaminarwhenallofthefluidparticlesflowinparallellinesatevenvelocitiesanditcanbeturbulent•whenthefluidparticleshavearandommotioninterposedonanaverageflowinthegeneraldirectionofflow.Thereisalsoacriticalzonewhentheflowcanbeeitherlaminarorturbulentoramixture.Ithasbeenproved•experimentallybyOsborneReynoldsthatthenatureofflowdependsonthemeanflowvelocity(v),thepipediameter(D),thedensity(ρ)andthefluidviscosity(μ).AdimensionlessvariableforthecalledReynoldsnumber,whichissimplyaratioofthefluiddynamicforces•andthefluidviscousforces,isusedtodeterminewhatflowpatternwilloccur.TheequationfortheReynoldsNumber is
Fornormalengineeringcalculations,theflowinpipesisconsideredlaminariftherelevantReynoldsnumberisless than 2000, and it is turbulent if the Reynolds number is greater than 4000. Between these two values there is thecriticalzoneinwhichtheflowcanbeeitherlaminarorturbulentortheflowcanchangebetweenthepatterns. Itisimportanttoknowthetypeofflowinthepipewhenassessingfrictionlosseswhendeterminingtherelevantfriction factors.
Fluid Handling
38
2.6 Pipeline Sizing on Steam VelocityIf pipe work is sized on the basis of velocity, then calculations are based on the volume of steam being carried •in relation to the cross sectional area of the pipe. For dry saturated steam mains, practical experience shows that reasonable velocities are 25-40 m/s, but these •should be regarded as the maxima above where noise and erosion will take place, particularly if the steam is wet. Even these velocities can be high in terms of their effect on pressure drop. In longer supply lines, it is often •necessary to restrict velocities to 15 m/s if high pressure drops are to be avoided. Itispossibletoselectpipesizesfromthesteampressure,velocityandflowrate.•Alternatively, the pipe size can be calculated by following the mathematical procedure as outlined below. In •ordertodothis,weneedtodefinethefollowinginformation:
Flow velocity (m/s) C
Specificvolume(m3/kg) v
Massflowrate(kg/s)
Volumetricflowrate(m³/s) = (kg/s) x v(m3/kg)
From this information, the cross sectional area (A) of the pipe can be calculated:
Cross sectional area (A) =
i.e. = 4 C
This formula can be rearranged to give the diameter of the pipe:
This will produce the diameter of the pipe in metres. It can easily be converted into millimetres by multiplying by 1000.
Example 2 - It is required to size a pipeline to handle 5000 kg/h of dry saturated steam a 7 bar g, and 25 m/s required flowvelocity.
Flow velocity (C) = 25 m/s
Specificvolume(v) =0.24m³/kg(fromsteamtables)
Massflowrate( ) = = 1.389 kg/s
39
Volumetricflowrate( ) = = 1.389 kg/s x 0.24 m3/s = 0.333 m3/s
Therefore using,Cross sectional area (A) =
D = 0.130 m or 130 mm
Fig. 2.11 Superheated and saturated steam pipeline sizing chart (velocity method)
Fluid Handling
40
2.7 Pipeline Sizing on Pressure DropSometimesitisessentialthatthesteampressureisnotallowedtofallbelowaspecifiedminimum,inorderto•maintain temperature.Here, it is appropriate to size the pipe on the ‘pressure drop’ method, by using the known pressure at the supply •end of the pipe and the required pressure at the point of use.An alternative and quicker method to sizing pipelines on the basis of pressure drop is to use • Figure 2.13 if the following variables are known:
steam temperature �pressure �flowrate �pressure drop requirements �
Fig. 2.12 Steam pipeline sizing chart (pressure drop method)
41
SummaryVarious guidelines and formulae are available for pipeline sizing for different services.•Whenfluidsaretobecarriedfromoneplacetoanotherlikeinhouseholdpipingtocrosscountrypipeline,piping•andfittingconstitutesahighcost.Inanychemicalprocessindustry,varioustypesoffluidsarebeingusedindifferentformslikeliquid,gaseous,•slurry, etc.Thedesignofanypipingnetworkinvolvesvariousactivitiesliketheselectionofpipingmaterial,specification•with respect to thickness, pipe size, its routing, etcFor slurry applications, a larger size pipeline not only increases the plant cost but also creates operational •problems.Many factors should be kept in mind before sizing any pipeline. The basic principle of pipeline size is based •on the available pressure drop between its two ends.Normally pipelines are sized after optimizing between the costs of material versus operating cost.•Various problems are commonly observed in the process plants handling hot boiling liquids. These are mainly •duetovaporisationofflowinghotliquid.Asmallfluidquantityiscollectedforanalysistodetermineitscomposition.Itisapplicableforanystageof•processinglikeforrawmaterial,intermediateproduct,finishedproductoritmaybeevenutilityoreffluent.Slurries, mixtures of suspended solids in liquids, are kept in agitated conditions to maintain homogeneity, other •wise,dependinguponthesolid’scharacteristics,lighterorheavierthanliquid;particlesfloatorsettledownrespectively.
ReferencesFluid piping systems & insulation• [Online] Available at: <http://www.energymanagertraining.com/bee_draft_codes/best_practices_manual-PIPING.pdf>. [Accessed 12 April 2011].Mohitpour, H.G., Matthew, A, M., 2007, • Pipeline design & construction: a practical approach, 3rd ed., ASME Press.George, A., 2003, • Piping and pipeline engineering: design, construction, maintenance, integrity, and repair, Marcel Dekker.
Recommended ReadingEvett, J., 1989, • 2500 Solved Problems In Fluid Mechanics and Hydraulics, 1st ed., McGraw-Hill.McAllister, E.W., 2009, • Pipeline Rules of Thumb Handbook: A Manual of Quick, Accurate Solutions to Everyday Pipeline Engineering Problems, 7th ed., Gulf Professional Publishing.Murray, A,. 2007, • Pipeline Sizing Construction: A Practical Approach, (Pipelines and Pressure Vessels), 4th ed., ASME Press.
Fluid Handling
42
Self Assessment
Whenfluidsaretobecarriedfromoneplacetoanotherlikeinhouseholdpipingtocrosscountrypipeline, 1. pipingandfittingconstitutesa__________________.
high costa. low costb. high qualityc. inferior qualityd.
For ______________ applications, a larger size pipeline not only increases the plant cost but also creates 2. operational problems.
slurrya. pipelineb. liquidc. gaseousd.
The elevation difference mainly governs the pipeline _______________.3. qualitya. sizingb. shapesc. installationd.
If the start point of the pipeline is under vacuum, i.e., in barometric condensers, pipelines of high diameters are 4. selected to __________ pipeline friction losses and thus increase the available differential pressure.
reducea. increaseb. stopc. eliminated.
Small sample line will create trouble for _____________ where solid particles may choke the sample line quite 5. frequently.
slurriesa. gasesb. liquidsc. solidsd.
Which of the following is true?6. Lower velocities are preferred for cooling water circulation pipelines.a. Higher viscosities are preferred for cooling water circulation pipelines.b. Higher velocities are preferred for cooling water circulation pipelines.c. Lower viscosities are preferred for cooling water circulation pipelines.d.
Which of the following is true?7. Theslurryflowisselectedbasedonthecreatedpressuredropbytheunit.a. The centrifugal pump is selected based on the created pressure drop by the unit.b. The small line is selected based on the created pressure drop by the unit.c. Theliquidflowisselectedbasedonthecreatedpressuredropbytheunit.d.
43
Which of the following is false?8. Liquidflowsundergravityduetotheelevationdifferencebetweenthestartpointandtheendpoint.a. Liquidflowsundergravityduetotheelevationdifferencebetweenthestartpointandthemedianpoint.b. With the higher available elevation difference, for the end point of the pipeline connected to the pressurized c. system, the pipeline size will be of a lower size. Various problems are commonly observed in the process plants handling hot boiling liquids.d.
Which of the following is false?9. The higher pipeline size is preferred to lower down pressure drop and thus to achieve higher available NPSH a. at pump suction port.The lower pipeline size is preferred to higher down pressure drop and thus to achieve higher available NPSH b. at pump suction port.Equipment/instruments especially which create a high-pressure drop and are provided with a bypass line.c. Small sample line will create trouble for slurries where solid particles may choke the sample line quite d. frequently
Which of the following is false?10. Cooling water, in the cooling tower, is exposed to air that helps in the development of algae formation.a. Cooling water, in the cooling tower, is exposed to sunlight that helps in the development of algae b. formation.Highestpoint,whichisalsothestartpointoftheliquidflowline,islocatedalmostatthetopofthetank.c. Agitated conditions are maintained in equipment like tanks by the use of agitators or gases sparing.d.
Fluid Handling
44
Chapter III
Non-Newtonian Fluids
Aim
The aim of this chapter is to:
explainnon-Newtonianfluids•
studyclassificationofnon-Newtonianfluids•
discusslaminarflow•
Objectives
The objectives of this chapter are to:
explain mathematical model to express non-Newtonian behaviour•
illustratenon-Newtonianfluids•
elucidate numerical examples•
Learning outcome
At the end of this chapter, you will be able to:
recognizenon-Newtonianfluids•
identifylaminarflow•
classify mathematical model to express non-Newtonian behaviour•
understandelasticoviciousfluid•
45
3.1 IntroductionTheelastico-viscousfluidsexhibitbyandlargePseudoplasticbehaviourwhentheyflowthroughaclosedchannellike a pipe.
ThegraphforshearstresswithshearrateforNewtonianfluids,asindicatedinFig3.1islinear.•Fire hydrant systems should be designed in rings so as to receive water at a place via two routes. In case where •the number of hydrant posts in the system is less than 100, the system may be designed in a single ring with pipe sizes as per the table a simple and pre-engineered design.
Shear Rate (r)
SLOPE=μ
Shearstress(τ)
Fig. 3.1 Newtonian fluids
Thefluidsforwhich,atconstanttemperatureandpressure,theviscosityvaluesarenotconstantareknownas•Non-Newtonianfluids.
Rat
e of
shea
r, du dy
Shearstress,τ
Fig. 3.2 Non-Newtonian fluids
3.2 Classification of Non-Newtonian FluidsNot all non-Newtonian Fluids behave in the same way when stress is applied – some become more solid, others morefluid.Somenon-Newtonianfluidsreactasaresultoftheamountofstressapplied,whileothersreactasaresultof the length of time that stress is applied.
Fluid Handling
46
3.2.1 Time Independent FluidsAtconstanttemperatureandpressure,thecoefficientofshearviscosityofthefluidsisafunctionoftheshearrate.
Forsomefluids,theviscositydecreaseswithanincreaseinshearratei.e.,flowrateandthefluidsareknown•asshearthinningfluidsorpseudoplasticfluids.Forthesefluids,atlowshearrates,theviscosityisconstant,termed as zero shear viscosity. The viscosity reduces as the shear rate increases over a certain range of shear, and at very high shear rates, the •viscosityisconstantandistermedasinfinitiveshearviscosity.Thevariationofshearstressandviscositywithshearratesforapseudoplasticfluidisindicatedinfig3.2
τ
r r
μ
μ0 μ∞
Fig. 3.3 Pseudoplastic fluids
Polymer melts, polymer solutions, dispersion of compressible solids in water (paper pulp), oil-water emulsions •areexamplesofpseudoplasticfluids.Forsomefluids,theviscosityoffluidsincreaseswithincreaseinshearrateatconstanttemperatureandpressure•and this effect takes place over a certain range of shear rates. At low as well as very high shear rates, the viscosity is constant. The variation of viscosity and shear stress with shear rates is shown in Fig. 3.3.
τ
r r
μ
μ0 μ∞(a) (b)
Fig. 3.4 Dilatants fluids
47
Thesetypesoffluidsareknownasshearthickeningfluidsordilatantsfluids.Dispersionsofnon-compressible•solids in liquids exhibit this type of behaviour. Hence PVC plastisols, petroleum mud are examples of these typesoffluids.ThegraphicalvariationofviscosityandshearstresswithshearrateforthistypeoffluidsisindicatedinFig3.4.•Toothpaste,creamsanddough’sareexamplesofthefluids.Sometypeoffluidsexhibitayieldstressi.e.,belowacertainvalueofshearstressthereisnoflowornoshearing•takingplace.Oncetheyieldstressiscrossed,thefluidsmaybehaveasNewtonianorpseudoplasticordilatantsfluids.ThesefluidsareknownasBinghgamPlasticFluids.AsshowninFig.3.5
τ
y
r
μ
μ0 μ∞(a) (b)
Fig. 3.5 Bingham plastic fluids (Newtonian Bingham plastic)
3.2.2 Time Dependent FluidsAtconstanttemperatureandpressuretheviscosityofthesefluidschangeswithtimeforacertainrangeoftimeofflow.
IfafluidisagitatedinacontainerwiththehelpofanagitatorandifprovisionsforfixingtheR.P.M.ofrotation•and measurement of torque required for the rotation are made, one can measure the torque required for the agitator to rotate at different speeds. ForNewtonianfluidsifthespeedofrotationisgraduallyincreasedfirsttoacertainvalueandthengradually•decreased to zero and the torque required to rotate is plotted with RPM, the graph will not exhibit any hysteric effect and will be as shown in Fig 3.6
TOR
QU
E (T
) LOWt.HIGHt.
(a)Newtonianfluid (b)Thixotropicfluids (c)Rheopecticfluids
t = Time t = TimeT T
R.P.M R.P.M R.P.M
LOWt.HIGHt.
Fig. 3.6 Time dependent fluid
Fluid Handling
48
Forcertainfluidsthetorque,RPMcurveswillbeasshowninFig3.6-(b).Itindicatesthatasthetimeofflow•increasesthetorquerequiredtoaffectthesameRPMreducesi.e.,theviscosityreduceswiththetimeofflow.Thesekindsoffluidsareknownasthixotropicfluids.Forthesefluids,thereexistsaninternalstructuredueto•secondaryvalenceforcesorotherphysicaleffectsandhenceatrest,theirviscosityishigh.Onagitationorflow,theinternalstructurecollapsesandtheliquidscanflowmoreeasilyexhibitingareductioninviscosity.Lumpfreetomatoketchup,printinginks,somepharmaceuticalsyrups,liquidresins,containingfillersandoil•paints exhibit thyrotrophic behaviour by adding thyrotrophic agents.Forsomefluids,thetorque:RPMcurveisasshowninFig3.6-(c),i.e.,forthesefluids,theviscosityincreases•withtheincreaseofthetimeofflow.Thesefluidsareknownasantithixotropicfluidsorrheopecticfluids.Someclay suspensions exhibit this type of behaviour.
3.2.3 Elastico Viscous FluidForsomefluidsthedeformationisnottotallyviscousbutpartofthestrainisrecoveredwhenthestressisnolongeractingonthefluid.Polymersmeltwhentheyleaveaclosedchannelofflowlikecapillary;aswellingofthemeltisobserved at the exit of the channel. This swell is due to elastic recovery.
Forthesefluidstwoimportantmanifestationsofelasticeffectsareobserved:The recovery at the exit •Thedevelopmentofnormalforcesperpendiculartothedirectionofflowwhenthefluidisshearedinaclosed•geometry
Polymer melts and solutions exhibit elastic viscous behaviour.
Stress(τ)
Stra
in (r
)
Rec
over
y
Time Time
(a) (b)
Fig. 3.7 Elastico vicious fluids
Thetablebelowsummarisesfourtypesofnon-Newtonianfluids.
Type of behaviour Description Example
Thixotropic Viscosity decreases with stress overtime
Honey – keep stirring, and solid honey becomes liquid.
Rheopectic Viscosity increases with stress overtime
Cream – the longer you whip it the thicker it gets.
Shear thinning Viscosity decreases with increased stress Tomato sauce
Dilatants of Shear thickening Viscosity increase with shear stress Oobleck
Table 3.1 Types of non-Newtonia fluids
49
3.3 Mathematical Model to Express Non-Newtonian BehaviourForcalculationofpressuredropforflowoffluidsthroughachannelatadesiredflowrate,therelationshipbetweenshearstressandshearrateshouldbeknown.Forapseudoplasticanddilatantsfluidtheviscosityisafunctionofshear rate.
ForBinghamplasticsthefluidsmayexhibitpseudoplasticordilatantsorNewtonianbehaviouroncetheyield•stressiscrossed.Forthyrotrophicandrheopecticfluids,thechangesinviscositytakeplaceforacertaintimeandwhenflowtimeexceedsthattimevalue,thebehaviourcanbedescribedasNewtonianorpseudoplasticordilatants.The elastic viscousfluids exhibit, by and large, pseudoplastic behaviourwhen theyflow through a closed•channel like a pipe.
Fig. 3.8 Non-Newtonian fluids(Source: http://t0.gstatic.com/images?q=tbn:ANd9GcQQTFnOQTys5HWZTudq-4EcqQ8L_4hu7H-
w00bNi6pFyGQ16sF0)
Foralltypesoffluids,asimplemathematicalmodelrepresentingtherelationshipbetweenshearstressratesisknownas the power law model and is represented as:
τ = K(
Where,τ = shearstress
= shear rate
K = consistency indexN = flowbehaviourindexFor Newtonian Fluids K = Viscosity and n = 1For Pseudoplastic Fluids, n<1For Dilatants Fluids, n>1ForBinghamPlastics(τ- ) = K (
Shea
r stre
ss
Shear Rate, k
Newtonianfluid
Bingham plastic
Pseudoplasticfluid
Dilatantfluid
Fluid Handling
50
Where, = Yield stress
ThusK,theconsistencyIndexcanbedefinedasthestressrequiredtogenerateshearratesof1 , or the viscosity ofthefluidwhenthefluidisshearedatarateof11/sec.
If is the zero shear viscosity,
µ= ( is another form of the power law.
The followingare two important formulae for theflowofNewtonianandNon-Newtonian (PowerLaw)fluidsthroughapipe:VelocityprofileforflowthroughpipeandVelocityprofilefordragflow
Velocity profile for flow through pipe
Fig. 3.9 Velocity profile for flow through pipe
Theproblemofdeterminingfluidvelocityprofileshasgenerateda largenumberofdifferent experimental•procedures. Methodsusedtomeasuretheflowpropertiescanbecharacterisedasinvasiveornon-invasive,dependingon•whethertheflowpropertiesaredisturbedbythemeasurementprocess.The techniques employed utilize the electrical, optical, chemical, thermal and kinetic properties of the •medium. Making the use of the shear dispersive properties of the concentration of a material tracer down a pipe to deduce •theunderlyingvelocityprofileofthemedium.Thefollowingtheoremfollowstoprovetheinverseproblemofdeterminingthedecreasingvelocityprofile:•
Theorem1:Theinverseproblemofdeterminationofthestrictlydecreasingvelocityprofilehasawell-posedsolutionprovided that c0 (0) 0 and 0, Q C [0, ].
Thus for example if c0 (t) = c02 is constant,
……….. (1)
Another useful special case is when the upstream input concentration isthe pulse function, c0 (t) = c0 (H (t)-H (t-L)), L > 0.
………... (2)
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And velocity v can be determined from,
….……(3)
A related inverse problem is determining the functional relationship betweenthe rate of shear and the shear •stress.The determination of • f is an ill-posed problem.Theoperatormappingthemeasureddatatothevelocityprofileisnowassociatedwiththederivativeofboth•data inputs, and again is unbounded.Thedeterminationofthevelocityprofileassumesthat• v(r) is a strictly decreasing function. Asimilartheoryappliestoplasticmaterialswhichdisplayafiniteyieldstress.Howeverbecauseplasticmaterials•can be suitably approximated by pseudoplastic materials the theory offers little extra insight.
Velocity profile for drag flow
Fig. 3.10 Velocity profile for drag flow
The• meanvelocityprofileandfrictionfactorinturbulentflowswith polymer additives are investigated using Prandtl’s mixing-length theorem. This study• reveals that the mixing-length theorem is valid to express the drag-reducing phenomenon and that the presence of polymer additives increases the damping factor B in van Driest’s model; subsequently reducing the mixing-length, this interprets that the polymer hampers the transfer ofturbulentmomentumflux,thevelocityisincreased,andflow drag is reduced. This study also discusses the onset Reynolds• number for drag reduction to occur. The predicted velocity, friction
factor, and onset Reynolds number are in good agreement with the measured data in the literature.
3.4 Laminar FlowLaminarflow,sometimesknownasstreamlineflow,occurswhenafluidflowsinparallellayers,withnochangeoccurring between the layers.
Atlowvelocitiesthefluidtendstoflowwithoutlateralmixing,andadjacentlayersslidepastoneanotherlike•playing cards. Therearenocrosscurrentsperpendiculartothedirectionofflow,noreddiesorswirlsoffluids.•
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Inlaminarflowthemotionoftheparticlesoffluidisverysystematicwithallparticlesmovinginlineartothe•pipe walls. Influiddynamics,laminarflowisaflowregimecharacterizedbyhighmomentumdiffusionandlowmomentum•convection.Whenafluidisflowingthroughaclosedchannelsuchasapipeorbetweentwoflatplates,eithertwotypesof•flowmayoccurdependingonthevelocityofthefluid:
Laminarflow �Turbulentflow �
Laminarflowistheoppositeofturbulentflowwhichoccursathighervelocitieswhereeddiesorsmallpackets•offluidparticlesformleadingtolateralmixing.Innon-scientifictermslaminarflowis“smooth”,whileturbulentflowis“rough.”•ForlaminarflowoffluidsthroughapipeoflengthL,radiusR,pressuredropΔPwithflowrateQ,various•quantities derived is as follows:
Table 3.2 Laminar flow of fluids
3.5 Stress and StrainIn science, stress means that a force is applied to a body. The result of that stress is described as strain.
Imagine hitting a metal with a hammer. The force that is applied on the metal causes stress to that particular •area. The result of that stress is then described as strain – in this case, possibly a deformation of the metal. Newtonianfluidsdon’tresistmuchstressthatisappliedonthemlikesolidswoulddo,sotheydon’tshowthe•signs of strain. If you hit water with a hammer, the liquid will not resist much to the stress applied and will also not show signs of strain.
Quantity Newtonian Fluid Power- Law Fluid
Shear stress at walls
Shear rate at walls
Law Obeyed
Pressure Drop
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Fig. 3.11 Thixotropic and rheopectic(Source: http://www.sciencelearn.org.nz/Science-Stories/Strange-Liquids/Sci-Media/Images/Thixotropic-and-
rheopectic)
Non-Newtonianfluidschangetheirviscosityorflowbehaviourunderstress.•Ifyouapplyaforcetosuchfluids(sayyouhit,shakeorjumponthem),thesuddenapplicationofstresscan•cause them to get thicker and act like a solid, or in some cases it results in the opposite behaviour and they may get runnier than they were before.Remove the stress (let them sit still or only move them slowly) and they will return to their earlier state.•Let’s take an example, •
Say you want to get some tomato sauce out of the bottle. You know there is some in there, but when you turn the bottle upside down, nothing comes out. So what do you do? You shake or hit the bottle. This causes the tomato sauce to become more liquid and you can easily squirt some out. In this case, the sauce’s viscosity decreases and it gets runnier with applied stress.
3.6 Viscosity ChartOfallthecharacteristicsalubricantmaypossess,themostimportantisitsviscosity.Theviscosityofafluidandhowthatfluidreactstocertainvariableswilldeterminehowwellthefluidcanperformthebasicfunctionsofalubricant.Viscosity can be viewed in two different ways.
Thefirstisafluid’stendencytoflowasisvisuallyindicated.Onecanthinkofthisasthetimeittakestowatch•afluidpouroutofacontainer.Thetermusedtodescribethisis“KinematicViscosity”anditisexpressedinunitsindicatingflowvolumeoveraperiodoftime.ThemostcommonlyusedunitofKinematicViscosityisthe centistokes (cSt).Afluid’sviscositycanalsobeindicatedbymeasuredresistance.Ittakeslittleenergytostirwaterwithaspoon.•However,significantlymoreenergyisrequiredtostirhoneywiththatsamespoon.Thetermusedtodescribethisis“ApparentViscosity”anditisexpressedinunitsknowsascentipoises(cP).Viscosityisveryimportantbecauseitisdirectlyrelatedtoafluid’sload-carryingability.Thegreatafluid’s•viscosity,thegreatertheloadsthatitcanwithstand.Theviscosityofafluidmustbeadequatetoseparatemovingpartsattheoperatingtemperatureoftheequipment.Knowingthatafluid’sviscosityisdirectlyrelatedtoitsabilitytocarryaload,onewouldthinkthatthemoreviscousafluidis,thebetteritcanlubricateandprotect.Thefactis,theuseofhighviscosityfluidcanbejustasdetrimentalasusingtoolightanoil.Fluids thicken as their temperatures decrease and thins as their temperatures increase (like candle wax). To the •extent that they change is indicated by their viscosity index (VI). A viscosity index number indicates the degree ofchangeinviscosityofanoilwithinagiventemperaturerange,currently40-100°C.Oilwithahighviscosityindex, say 160, would look and behave similarly at these two temperatures. However, low viscosity index oil, say90,wouldbequitedifferent.Itwouldbecomeveryfluidandthinandpoureasilyathightemperatures.Honey will do the same if you heat it up on a stove.
Rheopectic
Thixotropic
Viscosity
Stress (application of force) over time
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Viscosity:Ameasureoftheresistanceofafluidtoflow. �Thixotropic:Describesmaterialsthataregel-likeatrestbutfluidwhenagitated. �Centipoises: Water is the standard at 1 cps. �
MATERIAL APPROXIMATE VISCOSITY (IN CENTIPOISE)
Water @ 70 F 1 to 5Blood or Kerosene 10Anti-Freeze of Ethylene Glycol 15Motor Oil SAE10 or Mazola Corn Oil 50 to 100Motor Oil SAE30 or Maple Syrup 150 to 200Motor Oil SAE40 or Castor Oil 250 to 500Motor Oil SAE50 or Glycerine 1,000 to 2,000Karo Corn Syrup or Honey 2,000 to 3,000Blackstrap Molasses 5,000 to 10,000Hershey Chocolate Syrup 10,000 to 25,000Heinz Ketchup or French’s Mustard 50,000 to 70,000Tomato Paste of Peanut Butter 150,000 to 250,000Crisco Shortening or Lard 1,000,000 to 2,000,000Caulking Compound 5,000,000 to 10,000,000Window Putty 1,000,000,000
Table 3.3 Viscosity chart
3.7 Numerical ExampleCalculatethepressuredropforfluidflowingthroughapipeofdiameter5cmandlength10metreswithaflowrate20 litres/sec.
For the following cases:Newtonianfluidwithviscosity10poise•
Q= 20 litres/sec. = 20,000 /secR= 2.5 cm, L= 10 metres = 1000 cm.
Fluidwithzeroshearviscosity10poiseandflowbehaviourindexn=0.9.•
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=8000 x1.0249656 x 777.87189= 6.37933 x /
Fluidwithzeroshearviscosity=10poiseandflowbehaviourindexn=1.1•
=800 x 0.9750 x 3414.5392
∆P=26.622405 x dynes/∆P Newtonian = 13.037973 x dynes/∆P Pseudo plastic = 6.37833 x dynes/∆P Dilatants = 26.633405 x dynes/
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SummaryWater, vegetable oils, and most of the low and moderate molecular weight organic liquids are Newtonian •fluids.Atconstanttemperatureandpressurethecoefficientofshearviscosityofthesefluidsisafunctionofshear•rate.Forsomefluids,theviscositydecreaseswithanincreaseinshearratei.e.,flowrateandthesefluidsareknown•asshearthinningfluidsorpseudoplasticfluids.The viscosity reduces as the shear rate increases over a certain range of shear, and at very high shear rates, the •viscosityisconstantandistermedasinfinitiveshearviscosity.Sometypeoffluidsexhibitayieldstressi.e.,belowacertainvalueofshearstressthereisnoflowornoshearing•takingplace.Oncetheyieldstressiscrossed,thefluidsmaybehaveasNewtonianorpseudoplasticordilatantsfluids.ThesefluidsareknownasBinghgamPlasticFluids.Atconstanttemperatureandpressure,theviscosityofthesefluidschangeswithtimeforacertainrangeoftime•offlow.ForBinghamplasticsthefluidsmayexhibitpseudoplasticordilatantsorNewtonianbehaviouroncetheyield•stress is crossed.
ReferencesChhabra R. P., & Richardson, J. F., 2008. • Non-Newtonian Flow and Applied Rheology: Engineering Applications, 2nd ed., Butterworth-Heinemann.Ferry J. D., 1980, • Viscoelastic properties of polymers, 3rd ed., John Wiley and Sons.Lagerstrom, P. A., 1996, • Laminar flow theory, Princeton University Press.Viscosity Chart,• [Online] Available at: <http://www.research-equipment.com/viscosity%20chart.html>. [Accessed 12 June 2011]. Fowler, M., 2006. • Calculating Viscous Flow: Velocity Profiles in Rivers and Pipes, [Online]. Available at: <http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/RiverViscosity.pdf>. [Accessed 12 June 2011].
Recommended ReadingBeaumont, J. P., 2008, • Runner and Gating Design Handbook: Tools for Successful Injection Molding, 2nd ed.Dafermos, C., Ericksen L., & Kinderlehrer, D., 1987, • Amorphous Polymers and Non-Newtonian Fluids, 1st ed., Springer.Schowalter, W.R., 1978, • Mechanics of Non-Newtonian Fluids, 1st ed., Pergamon Press.
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Self Assessment
Water, vegetable oils, and most of the low and moderate molecular weight organic liquids are 1. ____________.
Newtonianfluidsa. Non-Newtonianfluidsb. Dilatantsfluidc. Elasticoviciousfluidsd.
ForNewtonianfluid,K=____________________.2. consistency indexa. shear stressb. shear ratec. flowbehaviourindexd.
Printing ink is an example of time ___________________.3. Newtonianfluidsa. Non-Newtonianfluidsb. Dependentfluidc. Elasticoviciousfluidsd.
__________________isanexampleofdilatantsfluids.4. Petroleum muda. Paper pulpb. Oilc. Slurryd.
ForNewtonianfluidshearstressis_______.5. a. τb. Kc. Nd.
Which of the following is true?6. Atfluctuatingtemperatureandpressure,thecoefficientofshearviscosityofthesefluidsisafunctionofa. shear rate.Atconstant temperatureandpressure, thecoefficientofshear rateof thesefluids isa functionofshearb. viscosity.Atconstanttemperatureandpressure,thecoefficientofshearviscosityofthesefluidsisafunctionofshearc. rate.Atconstanttemperatureandflow,thecoefficientofshearviscosityofthesefluidsisafunctionofsheard. rate.
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Which of the following is true?7. Forsomefluids,thevelocitydecreaseswithanincreaseinshearrate.a. Forsomefluids,theviscositydecreaseswithanincreaseinshearrate.b. Forsomefluids,theviscosityincreaseswithanincreaseinshearrate.c. Forsomefluids,thevelocityincreaseswithanincreaseinshearrate.d.
Which of the following is false?8. Forsomefluids,thedeformationisnottotallyviscousbutpartofthestrainisrecoveredwhenthestressisa. actingonthefluid.Forcalculationofpressuredropforflowoffluidsthroughachannelatadesiredflowrate,therelationshipb. between shear stress and shear rate should be known.Theelastico-viscousfluidsexhibitbyandlargePseudoplasticbehaviourwhentheyflowthroughaclosedc. channel like a pipe.Thefluidsforwhich,atconstanttemperatureandpressure,theviscosityvaluesarenotconstantareknownd. asNon-Newtonianfluids.
Which of the following is false?9. Toothpaste,creamsanddough’sareexamplesofthedilatantsfluids.a. Onagitationorflow, the internal structure collapses and the liquids canflowmore easily exhibiting ab. reduction in viscosity.Lumpfreetomatoketchupisanexampleoftimedependentfluid.c. Polymersdissolvewhentheyleaveaclosedchannelofflowlikecapillary;aswellingofthemeltisobservedd. at the exit of the channel.
Match the following10.
MATERIAL APPROXIMATE VISCOSITY (IN CENTIPOISE)
Water @ 70 F1. 50,000 to 70,000A.
Blood or Kerosene2. 10,000 to 25,000B.
Hershey Chocolate Syrup3. 1 to 5C.
Heinz Ketchup or French’s Mustard4. 10D.
1-C, 2-D, 3-A, 4-Ba. 1-B, 2-A, 3-C, 4-Db. 1-C, 2-D, 3-B, 4-Ac. 1-D, 2-A, 3-B, 4-Cd.
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Chapter IV
Two Phase Flows and Practice
Aim
The aim of this chapter is to:
understandtwophaseflow•
study and calculate pressure drop•
learntwophaseflowcapabilities•
Objectives
The objectives of this chapter are to:
explain two phase mixture capabilities•
grasptwophaseflowregimesandcharacteristiclinearvelocity•
listdifferenttypesofflowregimes•
Learning outcome
At the end of this chapter, you will be able to:
recognisetwophaseflowtype•
identifyflowregimes•
classifybakerplotforatwo-phaseflowregimecorrelation•
understand mitigating erosion•
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4.1 IntroductionInfluidmechanics,two-phaseflowoccursinasystemcontaininggasandliquidwithameniscusseparatingthetwophases.Pipelinescarryingtwo-phasefluids(Liquidandgas)arecalledtwo-phaseflow.Theanalysisoftwo-phaseflowpipingismorecomplexandlessunderstoodthanthatofincompressibleorcompressiblefluidflow.Theterm‘two-phaseflow’isalsoappliedtomixturesofdifferentfluidshavingdifferentphases,suchasairandwater,or oil and natural gas.
4.2 Two-Phase Flow Thetwophaseflowmoduleallowstwophaseliquid-gascalculationstobeaccomplished.Twophaseflowoccurs•in many industrial processes. Examples are petroleum, chemical, nuclear, refrigeration, space, and geothermal industries.FluidFlowcananalysesystemswherethevapourqualitychangeswithpipepositionaswellastwophaseflow•wherethevapourqualityisfixed.FluidFlow uses a modelling approach for the pressure loss calculation, this is a hybrid between the rigorous •and empirical methodsThereareseveraltechniquesusedtopredicttheheadlossduetofluidfrictionfortwo-phaseflow.•Twophaseflowfrictionisgreaterthansinglephasefrictionforthesameconduitdimensionsandmass•flowrate.Thedifferenceappearstobeafunctionofthetypeofflowandresultsfromincreasedflowspeeds.• Two-phase friction losses are experimentally determined by measuring pressure drops across different piping •elements. The two-phase losses are generally related to single-phase losses through the same elements. •One accepted technique for determining the two-phase friction loss based on the single-phase loss involves the •two-phasefrictionmultiplier(R),whichisdefinedastheratioofthetwo-phaseheadlossdividedbytheheadloss evaluated using saturated liquid properties
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Fig. 4.1 Pipeline flow pattern map for two phase flow(Source:http://www.fluidflowinfo.com/images/FlowPatternMap.jpg)
ThehorizontalflowpatternmapfortheBeggsandBrillmethodisshownopposite.Thiscorrelationisapplicable•to the entire range of pipe inclination angles, although it usually underpredicts pressure loss for vertical upward flow.Inthisexamplethepredictedflowpatternisintheintermittentregion.•Usingamechanisticmodellingapproachamoreaccuratemodeloftheflowpatternmapcanbeachieved.•
Theavailablepressurelossrelationshipsthatcanbeusedintwo-phasefluidfloware:Friedel: This method is based on the paper published by Friedel and utilises a two phase multiplier to the liquid •pressure loss calculation.Chisholm: Proposed an extensive empirical method (1973), which also uses a two phase multiplier.•LockhartMartinelli:Proposedaseparatedflowmodel,butthisshouldonlybeappliedtohorizontalflow.•
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Comparison of the above 3 methods to a recent two phase database was made by Whalley who made the •following recommendations:(µL/µG)<1000andamassfluxof<2000kg/m2s use the Friedel method. (µL/µG)>1000andamassfluxof>100kg/m2s use the Chisholm method. (µL/µG)>1000andamassfluxof<100kg/m2s use the Lockhart Martinelli method.
4.2.1 Capabilities of Two-Phase FlowFollowingarethecapabilitiesoftwo-phaseflow:
Complete thermodynamics: phases appear and disappear as conditions warrant.•Two-phaseheattransfercorrelationsarebuilt-inoruser-defined.•Two-phasepressuredropcorrelationsarebuilt-inoruser-defined.•Automaticflowregimemapping•Fromquasi-steadyhomogeneousequilibriumtofullytransienttwo-fluidmodelling.•Optionalslipflowmodelling(separatephasic)•Optional, no equilibrium transients (separate phasic energy and mass equations)•Capillary modelling tools for static or vaporising wicks•Optional tracking of liquid/vapour interfaces•
4.2.2 Different Types of FlowThedifferenttypesofflowareasgivenbelow:
Fig. 4.2 Different types of flow
Bubbly• : The gas bubbles are dispersed in the liquid with the high concentration of the bubbles in the upper half of the tube due to their buoyancy. When shear forces are dominant, the bubbles tend to disperse uniformly in thetube.Inhorizontalflows,theregimetypicallyonlyoccursathighmassflowrates.Slug• : At higher gas velocities, the diameters of elongated bubbles become similar in size to the channel height. The liquid slugs separating such elongated bubbles can also be described as large amplitude waves.Annular• :Atevenlargerflowrates,theliquidformsacontinuousannularfilmaroundtheperimeterofthetube,similartothatinverticalflowbuttheliquidisthickeratbottomthanthetop.Theinterfacebetweentheliquidannulus and the vapour core is disturbed by small amplitude waves and droplets.
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Stratified• :Increasingthegasvelocityinastratifiedflow,wavesareformedontheinterfaceandtravelinthedirectionofflow.Thewavesclimbupthesidesofthetube,leavingthinfilmofliquidonthewallafterthepassage of the wave.
4.3 Two Phase Mixture
Fig. 4.3 Two fluids mixed on a flow sheet(Source:http://www.fluidflowinfo.com/images/BeggsBrillCalculation.jpg)
Theflowsheetshowstwoknownflows(onefluidair(2),onefluidwater(1))combiningandbeingheatedviaaplateexchanger,thenflowingtoaseparationvessel(5).ThereddotontheKnockoutPot(separator)representstheliquidoutletandtheyellowdotrepresentsthevapouroutlet.Thisisanexampleoftwophaseflowwithconstantquality.
This means that the vapour mass fraction is constant and there is no mass transfer between the phases. •It does not mean that the pressure loss per unit length is constant or that the velocity between the two phases •is constant. Inthefirstpipesectionaftermixing(pipe-6)youcanseethatthegassuperficialvelocityincreasesfromthe•start to the end of pipe -6. For 60m of pipe -6, the total pressure loss is 145997 Pa, but the friction loss is 144529 Pa. Since the pipe is horizontal the difference is the acceleration loss.
4.3.1 Capabilities of Two-phase MixtureFollowing are the capabilities of two phase mixture:
Mixtures of up to 26 liquids and/or gases.•Optional condensable /volatile component in mixture, including effects such as diffusion-limited •condensation.
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Optional dissolution of any number of gaseous solutes into any number of liquid solvents, including homogeneous •nucleation models.
Fig. 4.4 Condensing in the presence of non-condensable gases
4.4 Types of Two Phase FlowThe different types of two-phase flows are:
Gas-liquid•Gas-solid•Liquid-solid•
Biocatalist (microbes)
Gas
Liquid
Gas
Liquid Taylor bubble
Fig. 4.5 Two-phase flow(Source: http://www.isso.uh.edu/publications/A2002/images/balakotaiah1-f2.gif)
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Two-typesofflowpatternsmayoccurinthenitrifiertube.•Whenthegasflowrateishigh(orthetubelengthissmall),annularflowpatternisobtained.•Intheabovefigure,theliquidmovesasanannularfilmwhilethegasflowsinthecore.•Oxygenandnutrientsaretransferredfromtheairtotheflowingwaterfilmandthentothebiomassgrowingon•thewall.Thesecondtypeofflowpatternistheslugflow(alsocalledTaylorflow)inwhichtheairmovesaslong bubbles of diameter slightly less than that of the tube and the bubbles are separated by liquid slugs.Shearimposedbythetwo-phaseairandwaterflowmustbelargeenoughtokeepthemicrobelayerthin,yet•must be low enough such that the microbes are not removed from the wall. In addition, characteristics of the two-phaseflowmustbesuchthatoxygenandwastewaternutrientsareeffectivelydeliveredtothemicrobes.Theincidenceofdifferentflowpatternsdependsontherelativeflowratesofeachcomponent.Thecharacteristics•ofslugflowareintermittencyandgasentrainmentatthefrontofthepropagatingslug.
Liq
uid
flow
rat
e
Gas flow rate
Dispersedbubbleflow
AnnularflowStratifiedflow
Slugflow
Fig. 4.6 Two phase flow map(Source: http://www.smithinst.ac.uk/Projects/ESGI59/ESGI59-NorskHydro/Report/Images/Internal/FlowMap)
4.4.1 Focus
Gas liquid systems•Orientationofflow•Whetherhorizontalorverticalflow•
Gas Liquid SystemBoth gases and vapours correlate similarly in two-phase systems except for certain conditions of continuous •vapourcondensationorliquidflashingintheflowingsystem.
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Liquid outlet
Separator head (gas expansion chamber)
Gas outlet
Fluid joint
Pressure housing (external casing)
Helix joint (intermediate casing)
Gas Annulus
Liquid discount tubing (internal casing)
ESP (internal casing)
Separate gasSeparate liquidMultiphaseflow
Fig. 4.7 Gas-liquid system for two phase fluid flow(Source: http://images.pennwellnet.com/ogj/images/off2/1298usap2.gif)
Gas/liquid two-phase flow system is a complex, nonlinear and dynamic system, therefore is difficult to•measure.Basingontheapplicationofelectricalresistancetomography(ERT)ingas/liquidtwo-phaseflowofvertical•pipe, wavelets transform is used to analyse the measured data from ERT system.Furthermore, according to the multi-resolution analysis (MRA), the feature vector of multiple scales wavelet •energythatcanexpresstheessentialinformationofgas/liquidtwo-phaseflowisconstructed.At last, the support vector machine (SVM) method in statistics theories is adopted to validate the feasibility of •thefeatureextractionmethod,andthehigherrecognisingrateofflowregimeisobtained.
4.5 Two-Phase Flow Regimes and Characteristic Linear VelocityTwo-phaseflowexhibitvariousflow• regimes,orflowpatterns,dependingontherelativeconcentrationofthetwophasesandtheflowrate.Asimplebutgenerallyadequatesetofdescriptivephrasesformostoftheimportantliquid-vapourflowregimes•consistsofbubbleflow,slugflow,chumflow,annularflow, anddropletflow.
4.5.1 Dispersed FlowAlsoreferredtoassprayormistflow,dispersedflowoccursatveryhighgasvelocitieswiththeliquidphasedispersedasdropletsthroughoutthegasphase.Theliquiddropletvelocityapproachesthegasphasevelocityinthisflowregime because the droplet terminal velocity is negligible and the slip velocity approaches zero.
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4.5.2 Annular FlowAnnularflowoccursatrelativelylowergasvelocitiesthandispersedflow.Theliquidphaseformsanannulusaboutthecircumferenceofthepipewiththegasflowingthroughthecentralcore.Thereissignificantlymoreslipwithannularflowthanwithdispersedflow.
4.5.3 Stratified FlowStratifiedflowoccursonlyinhorizontalpipeswhenthegasphasevelocityisnotgreatenoughtomaintainanannulusofliquidaboutthecircumferenceonthepipe.Oneformofstratifiedflow,called“wavyflow”ischaracterisedbytheformationofwavesonthesurfacesoftheliquidphase.Wavyflowisformedclosetothetransitionpointwherestratifiedflowcanbetransformedintoslugflowwithafurtherincreaseingasvelocity.
4.5.4 Slug FlowSlugflowischaracterisedbyanintermittentpatternofalternatingliquidphasesandgasphasesalongthelengthof the line. The entire pipe cross-section area can be occupied by a slug of either liquid or gas at different points alongtheflowpath.
4.5.5 Plug FlowPlugflowoccurswhentheliquidphaseformsanearlycontinuousphasewithlargeelongatedbubbleplugsofgaslocated within the liquid phase.
4.5.6 Bubble or Froth FlowBubbleorfrothflowliketheplugflow,hasadominantliquidphase,buttheliquidphaseinbubbleflowisatahighervelocitythantheliquidphaseinplugflow.Thishighervelocitycausesthevapourphasetodisperseintomany smaller bubbles within the liquid phase.
4.6 Two-Phase Flow Regimes TypeEachflowregimebehavesdifferently.Eachflowregimehasitsownsetofempiricalcorrelationsforpredictingflowbehaviour.Themostoftenusedmethodtodeterminetheflowregimeisthebakerplot.
Baker plot horizontal axis: x = ( / ) λΨWhere,
=liquidmassflowrate,lb/h
=gasmassflowrate,lb/h
and
Where, µL = liquid viscosity, lb/ft-h ρg = gas density, lb/ft3Where, ρL = liquid density, lb/ft3 δ = surface tension, dyne/cm
Baker plot vertical axis y =
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68
Where,
= /A=superficialmassfluxofvapourphase,Ib/ft2-h
A = total internal cross sectional area of pipe (ft2)
Once the values of x and y have been calculated, their point of intersection on the Baker Plot determines the expected two-phaseflowregime.TheBakerplotcanbeusedforhorizontalflowandwithlimitedsuccessforverticalflowtoo.
Regime Liquid phase, ft/s Vapour phase, ft/s
Dispersed Close to vapour velocity >200
Annular <0.5 >20
Stratified <0.5 0.5 -1.0
Slug 15 (but less than 3-50
Plug vapour velocity) <4
Bubble 2 0.5-2.0
Table 4.1 Flow regimes
4.7 Baker Plot for a Two-Phase Flow Regime CorrelationTwo-phasehorizontalflowregimesarebasedontheBakerChartforvapour-liquidnon-flashingflowthrough•circular ducts (pipe).It is further assumed that the line pressure drop is less than 10% of the absolute pressure to support the use of •asinglevapourdensityandflowregimefortheentireline.Violationofthisassumptionrequiresthelinetobe broken into a number of segments which individually have pressure drops less than 10% of the segment absolute pressure.Eachflowregimehasanindividualpressuredropcorrelation.Thepressuredropsforstratified,plug,slug,and•annularflowregimesarebasedoncorrelationsbyBaker.
and
where isthesurfacetensionoftheliquid.TheBakermapinfig.4.8indicatesthatthemostcommonflowregimesingeothermalpipelinesareannularflowandwavyflow.It’sunlikelythattheBakermapisunderestimatingthe gravity force in larger pipes.
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Fig. 4.8 Baker plot
Slip velocity: Slip velocity is the velocity difference between the gas and liquid phase velocities.•
4.8 Pressure Drop Calculation for Gas-Liquid SystemsThis is the most effective method developed by Lockhart and Martinelli.
Step 1: CalculateX,theMartinellitwo-phaseflowmodulus.
Where,
= pressure drop per ∆ ofpipe,onlyliquidbeingassumedtoflowthroughthepipe,psi/100ft
= pressure drop per ∆ ofpipe,onlyliquidbeingassumedtoflowthroughthepipe,psi/100ft
Step 2: Calculatetwophaseflowmodulus.Φ = a
Whereaandbareempiricalconstantsfordifferentflowregimes.
Annular Flow:Φ = a
Where,a= 4.8 0.3125db=0.343-0.021d
where, d=inside pipe diameter, in (If d>10in, set d=10 in the correlation)
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Bubbleflow:Φ =
Stratifiedflow:Φ =
Slugflow:Φ =
Plugflow:Φ =
Step 3:
Two phase pressure drop
∆ Phaseflowpressuredropper100ftofpipe,psi/100ftEffect of static head:Thecontributionofstaticheadlossescanbesignificantintwo-phaseflowsystems.
∆P static = pressure difference due to elevation difference, psiZ static = elevation difference in ft
= average density of two phase mixture (ib/ft3)
Note:Steamcondensateinreturnlinesflashingintosteam•Two-phase feed lines entering distillation columns•Process plant refrigeration returns lines•
4.9 Mitigating ErosionDependingupontheflowregime,theliquidinatwo-phaseflowsystemcanbeacceleratedtovelocitiesapproachingor exceeding vapour velocities. In some cases these velocities are higher than desirable for a process piping system. Suchhighvelocitiescancauseaphenomenonknownas“erosioncorrosion”inequipmentandpipingsystems.
There are no general correlations that predict the rate of erosion corrosion in piping systems, but Coulson has proposed an index based on velocity head to determine the range of mixture densities and velocities below which erosion corrosion should not occur. The index takes the form
≤ 10.000
If the product of mixture density ρ and mixture velocity is below 10,000, erosion corrosion should not be a problem. Mixture density is calculated by:
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And mixture velocity ( um) is calculated by:
= + = mean velocity, ft/s
Where,
=superficiallineargasvelocity,ft/s
=superficiallinearliquidvelocity,ft/s
=gasmassflowrate,lb/h
=liquidmassflowrate,lb/h
Example:A6-inchschedule,40pipeshasatwo-phasemixtureflowingthroughit.Theflowrateanddensityofeachphaseare as follows:
Liquid Vapour
Massflowratelb/h 7200 21,600
Density lb/ft3 58 0.7
Determinewhetherthetwo-phaseflowwillexperienceerosioncorrosion.
Solution:Mixture density = 0.930 lb/ft• 3
Given that the pipe cross-sectional area is 0.20 ft• 2,thesuperficialliquidvelocityiscalculatedtobe0.172ftsandthesuperficialgasvelocityis42.86fts.The mean velocity = 43.03 ft/s•
The index calculated •
It is less than 10,000. Hence erosion corrosion is not expected to be a problem.•
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SummaryPipelinescarryingtwo-phasefluids(Liquidandgas)arecalledtwo-phaseflow.Theanalysisoftwo-phaseflow•pipingismorecomplexandlessunderstoodthanthatofincompressibleorcompressiblefluidflow.Both gases and vapours correlate similarly in two-phase systems except for certain conditions of continuous •vapourcondensationorliquidflashingintheflowingsystem.Annularflowoccursatrelativelylowergasvelocitiesthandispersedflow.Theliquidphaseformsanannulus•aboutthecircumferenceofthepipewiththegasflowingthroughthecentralcore.Stratifiedflowoccursonlyinhorizontalpipeswhenthegasphasevelocityisnotgreatenoughtomaintainan•annulus of liquid about the circumference on the pipe. Slugflowischaracterisedbyanintermittentpatternofalternatingliquidphasesandgasphasesalongthelength•of the line. Plugflowoccurswhentheliquidphaseformsanearlycontinuousphasewithlargeelongatedbubbleplugsof•gas located within the liquid phase.Slip velocity is the velocity difference between the gas and liquid phase velocities.•
ReferencesTwo Phase flows and Practice• , Available at: <http://www.wlv.com/products/databook/db3/data/db3ch12.pdf>. [Accessed 18 April 2011].Michael L. Corradini, Available at: <http://wins.engr.wisc.edu/teaching/mpfBook/node1.html>. [Accessed 18 •April 2011].Ahmed. W. H., • Innovative Techniques for Two-Phase Flow Measurements, Available at: <http://www.benthamscience.com/eeng/samples/eeng%201-1/Ahmed.pdf>.[Accessed 18 April 2011].
Recommended ReadingMamoru Ishii, Takashi Hibiki., 2010. • Thermo-Fluid Dynamics of Two-Phase Flow, 2nd ed., Springer.Kleinstreuer C., 2003. • Two-phase flow: theory and applications., Taylor & Francis.Azbel. D., 1981. • Two-phase flows in chemical engineering, Cambridge University Press.
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Self Assessment
Theanalysisof___________phaseflowpipingismorecomplexandlessunderstoodthanthatofincompressible1. orcompressiblefluidflow.
twoa. threeb. four c. singled.
Both gases and _______________ correlate similarly in two-phase systems.2. liquidsa. solidsb. slurriesc. vapoursd.
______________flowoccursatrelativelylowergasvelocitiesthandispersedflow.3. Stratifieda. Annularb. Slugc. Plugd.
_________________flowoccursonlyinhorizontalpipeswhenthegasphasevelocityisnotgreatenoughto4. maintain an annulus of liquid about the circumference on the pipe.
Stratifieda. Annularb. Slugc. Plugd.
________________ is characterised by an intermittent pattern of alternating liquid phases and gas phases along 5. the length of the line.
Stratifieda. Annularb. Slugc. Plugd.
Which of the following is true?6. Pipelinescarryingtwo-phasefluids(Liquidandgas)arecalleddouble-phaseflow.a. Pipelinescarryingtwo-phasefluids(Liquidandgas)arecalledduo-phaseflow.b. Pipelinescarryingtwo-phasefluids(Liquidandgas)arecalleddual-phaseflow.c. Pipelinescarryingtwo-phasefluids(Liquidandgas)arecalledtwo-phaseflow.d.
Which of the following is true?7. Dispersedflowisalsoreferredtoassprayormistflow.a. Annularflowisalsoreferredtoassprayormistflow.b. Stratifiedflowisalsoreferredtoassprayormistflow.c. Slugflowisalsoreferredtoassprayormistflow.d.
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Which of the following is false?8. Annularflowoccursatrelativelylowergasvelocitiesthandispersedflow.a. Annularflowoccursatrelativelyhighergasvelocitiesthandispersedflow.b. Dependingupontheflowregime,theliquidinatwo-phaseflowsystemcanbeacceleratedtovelocitiesc. approaching or exceeding vapour velocities.Plugflowoccurswhentheliquidphaseformsanearlycontinuousphasewithlargeelongatedbubbleplugsd. of gas located within the liquid phase.
Which of the following is false?9. Wavyflowisformedclosetothetransitionpointwherestratifiedflowcanbetransformedintoslugflowa. with a further increase in gas velocity.Wavyflowisformedclosetothetransitionpointwherestratifiedflowcanbetransformedintoslugflowb. with a further decrease in gas velocity.Stratifiedflowoccursonlyinhorizontalpipeswhenthegasphasevelocityisnotgreatenoughtomaintainc. an annulus of liquid about the circumference on the pipe. Theliquiddropletvelocityapproachesthegasphasevelocityinthisflowregimebecausethedropletterminald. velocity is negligible and the slip velocity approaches zero.
Which of the following is false?10. Slip velocity is the velocity difference between the gas and slurry phase velocities.a. Slip velocity is the velocity difference between the gas and liquid phase velocities.b. Bubbleorfrothflowliketheplugflow,hasadominantliquidphase,buttheliquidphaseinbubbleflowisc. atahighervelocitythantheliquidphaseinplugflow.Slugflowischaracterizedbyanintermittentpatternofalternatingliquidphasesandgasphasesalongthed. length of the line.
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Chapter V
Pipeline Networks
Aim
The aim of this chapter is to:
understand pipe line network analysis•
study head balancing•
learn colour coding of pipelines•
illustrate meter working•
Objectives
The objectives of this chapter are to:
explainfiguringflowrate•
definecriticalflow•
list types of pressure taps•
Learning outcome
At the end of this chapter, you will be able to:
recognise practices followed for provision of ground colour and colour bands •
identify vena contract taps•
classifyorificeselectionguidelines•
understandorificechoices•
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76
5.1 Introduction In the process industry, networks of somewhat different kind are encountered in relation to the closed loop utility circulationsystemsviz.,coolingwater,refrigeratedbrineandthermicfluidsystems.Thedistributionoffluidflowindifferentloopsofthenetworkisdictatedbyprocessrequirementsasincaseofutilities(water,brine,thermicfluid)orbystatutoryregulationsasinthecaseofthefirewaterdistributionsystemforfireprotection.
Pipingnetworksareencounteredinfireprotectionsystemswhereinringmainshavetobeinstalledtodeliver•water at different locations. Withaviewtodefinethescopeofthispresentation,schematicdiagramsforthenetworksreferredtoearlierare•shown in Fig. 6.1.
Fig. 5.1 Typical network for cooling water distribution(Source: http://lh6.ggpht.com/__lmqvG9CeQs/SjP0iD86hLI/AAAAAAAAB5A/gEDobO02mK8/Typicalnetwork
forcoolingwaterdistrib%5B1%5D.jpg)
5.2 Network Analysis The sizes of individual pipelines or branches, which constitute the network, are governed by one or more of the following considerations.
Fluid required •Fluidpressurerequiredataspecificlocation(suchasequipmentinletorfarthesthydrant)•Economic pipe velocity/diameter•Maximum and minimum operating conditions •
Thefactthatfluidflowandpressuredropsufferedbyfluidareinterrelatedisunderstood.Hence,changeinflowconditionofonebranchaffectstheflowandpressureinotherbranchesofthenetwork.Itisacommonexperiencethatflowinthefartherbranchmayreducewhentheflowthroughthennearerbranchincreases.Theanalysisofanetworkunderdifferentconditionsoftotalflowthroughthenetworkthereforeisusefulinunderstandingflowbehaviour through different branches.
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5.2.1 Principles of Network Analysis InanetworkwheretwopipelinebranchesareavailablefortheflowoffluidfrompointAtoB,theheaddifference(pressure drop) between these two points is the same irrespective of the route. The pressure drop, in turn, varies withtheflow.Therefore,inconformitywiththepressuredropbehaviour(samepressuredropirrespectiveoftheroute),theflowthroughthebranchofferinglesserresistanceismore.
Whenconsideredfromthepointofviewofpressuredropduetofluidfriction,theflowthroughthetwobranches•would adjust such that frictional pressure drop (friction head loss) would be the same in both the branches. DarcyofFanningequationgivestherelationshipbetweenfrictionheadloss(h)andflow(Q)aswellasbranch•parameters equivalent length (Le) and pipe diameter (d). Equivalent length (Le) takes into account pressure dropthroughthestraightpipeaswellasfittingsinthebranches.The primary form of the Darcy/fanning equation is,•
...................................(1)
(U- Velocity, ff-fanning friction factor)Considering Q = UA, A= , equation (1) takes the following form(Q-Volumetricflow,aflowarea)
..................................(2)
Considering the following units:Q in /sLe and d in mg=9.81m/ , in m/cEquation (2) would reduce to:
................................(3)
This shows, the relationship between h and Q is non-linear (apparently parabolic).•Another reason for the non-linear relationship is that the fanning friction factor (ff) decreases with an increase •in Q in a manner such that ff is approximately proportional to .The analysis of the network, therefore, needs iterative calculations (trial-error method). The iterative calculation •procedure used is commonly known as the Hardy Cross method. Themethodisbasedonmakingatrialguessforthevalueofflowineachbranchofthenetwork.Thetrial•guessesareimprovedbyemployingcorrectionsuntilthepressuredropcriteriaaresatisfied.Thisapproachisalso referred to as head balancing.
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5.2.2 Head Balancing Consider a typical network shown below:
Fig. 5.2 Typical network
LetQrandQlbefirstassumedvaluesofflowinright(1-2-4)andleft(1-3-4)branchesrespectivelyandlet and be corresponding correct values. Therefore,
Qr1= Qr + dQ and Ql1= Ql dQ
Where, dQ is error in assumed values
(Note: Q = Qr + Ql = + )
can be expressed in the form
hf = ………………..(4)
(From comparison with equation (3), and n=2)
If Hazen Williams form of equation is used; hf = head loss f = friction factor l = length of pipe q = discharged = diameter
K = Constant X Le and n = 1.85 (C Hazen William constant, typically C = 140 (for smooth, new, uncoated steel pipe)
Theflowintherespectivebrancheswouldbesuchthat
h ( 1-2-4 ) = h ( 1-3-4 )
Using the form of equation h1 = KQn and noting that , , and may not be the same,
Since r = Qr + dQ and Q l l = QI -dQ, using the binomial expansion and neglecting higher powers of dQ, the following expression is obtained.
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Another form of the above equation, which is convenient for calculations is as follows:
Where,
a= ( + )And
b= ( + )
In a more generalised form, the above equation can be written as,
In calculating the numerator for the above equation, due attention needs to be paid to the sign convention. The •signofflow(andcorrespondinglythesignfor ) around the network loop in a clockwise direction is taken as positive and in an anticlockwise direction the sign is taken as negative. Inthisspecificexample,forthepurposeofcalculations,• (1-2-4) n would be positive while (1-3-4) would be negative.The value of dQ obtained from the above equation is applied to the assumed value and resulting value of Q •obtained is used for the next trial. The procedure is repeated with successive values of Q obtained till the required convergence is obtained in the •values of h (1-2-4) and h (1-3-4) (percentage deviation within 5%). A numerically dated example is given in fig.5.3.
Fig. 5.3 Typical network
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Table 5.1 (a) Quantity balancing
Table 5.1 (b) Quantity balancing
5.2.3 Quantity Balancing Quantity balancing is another method of analyzing piping network. This method is more convenient for analysing interconnectedreservoirseachatdifferentelevations.Intheheadbalancingmethod(discussedearlier),theflowineachbranch isassumed. In thequantitybalancingmethod,headofa junction isassumedtodetermineflow(quantity) in each branch.
Qr = Qr + dQ Q1 = Q1 – dQ0.01624347 0.033756530.01557331 0.034426690.01556541 0.034434590.01556541 0.034434590.01556541 0.034434590.01556541 0.034434590.01556541 0.034434590.01556541 0.03443459
a – headloss (1-2-4)b – headloss (1-3-4)
Qr Ql aQrK(1-2-4)
bQp (K1-3-4) a/Qr b/Ql N-a-b D-2
(a/Qr+b/Ql)a-|b|/a % deviation
dQ 7/8
1 2 3 4 5 6 7 8
(3-4) 2(5+6)
0.01 0.04 0.716 2.3408 71.6 58.52 -1.6248 26024 -226.9273743 0.006243
0.016243 0.033757 1.8891677 1.6670936 116.30323 49.38581 0.222074 331.3780695 11.75512972 -0.00067
0.015573 0.034427 1.7365013 1.7339428 111.50493 50.36624 0.002559 323.7423425 0.14733589 -7.9E-06
0.015565 0.034435 1.7347393 1.7347389 111.44834 50.37781 3.56E-7 323.6522951 2.05117E-05 -1.1E-09
0.015565 0.034435 1.7347391 1.7347391 111.44834 50.37781 6.44E-15 323.6522826 3.71197E-13 -2E-17
0.015565 0.034435 1.7347391 1.7347391 111.44834 50.37781 2.22E16 323.6522826 1.27999E-14 -6.9E-19
0.015565 0.034435 1.7347391 1.7347391 111.44834 50.37781 2.22E16 323.6522826 1.27999E -6.9E-19
0.015565 0.034435 1.7347391 1.7347391 111.44834 50.37781 2.22E16 323.6522826 1.27999E -6.9E-19
0.015565 0.034435 1.7347391 1.7347391 111.44834 50.37781 2.22E16 323.6522826 1.27999E -6.9E-19
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The comparison of two methods can be seen below.
Head balancing Quantity balancingAssumeflow(Q)ineachbranch. Assume elevation of junction.
Basedonassumedvaluesofflow,itcalculatesfrictional head loss in each branch.
Thismethodfindstheheadavailableforflowfromeach reservoir.
Head loss in each branch calculates dQ/dQ and represents correction to be applied to the assumed valueofflow.(Q)
ItcalculatesflowsatjunctionsfromeachreservoirandnetflowdQ.
Apply correction dQ to previously assumed value offlow(Q).Itfindsnewvalueofflow(Q+dQ)andusesnewvalueofflowtodeterminedQ
UsesdQandQ/hforeachflowpathandcalculatedH. dH represents correction to be applied to assumed H (elevation of junction)
Repeats the procedure till dQ becomes very small and nearly zero.
ApplycorrectiondHtofindnewvalueofHandrepeat procedure using new value of H.
Another test for coverage is that head loss hf = K in each ( % deviation – 5 – 10 %)
Repeats till dH becomes very small and nearly zero.
Table 5.2 Comparison between head and quantity balancing
Equation for dQ for head balancing is derived and discussed earlier. TheequationfordHquantitybalancingisdiscussedbelow.(Referfigure5.3)
Let,Hj -assumed head at junction and Hj -correct head at junction
Therefore dH Hj j
Where,dH correction; to be applied to assumed value Hj Forpipe1,availableheadforflow=HAHjForm equation (4) HA Hj = Q (A)K1constantforpipe1,Ql,flowthroughpipe1Andequation(A)andequation(B)andonfurthersimplification,
Similarly, nd Q2=dH (Q1/hf1) =
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82
5.2.4 The Calculation Procedure Based on Equation (C)
Assume head at junction (Hj) ------------- see note 1 •Calculatetheheadavailableforflowi.e.,•
Pipe1HAHj,Pipe2HBHj,Pipe3HjHc(referfigure6.3) �
Using hf = K• calculateflowthroughpipesi.e.,Pipe 1 � Q1,Pipe 2 � Q2,Pipe 3 � Q3.
Evaluate • , , Q3 , ( hf1 = HA Hj ) EvaluatedQ,takingflowintojunctionaspositiveandflowoutofjunctionasnegative•Evaluate dH ( Using eqn C ) •Use new value of Hj = Hj + dH •Repeat steps a to g till dH becomes very small, nearly zero. •
Note 1: The assumed head Hj is not an elevation of the function taking into consideration the head loss due to friction. Figure 5.3 also gives a numerically solved example using the method of quantity balancing.
5.3 Equivalent Length (Le) Using the form of equation h1 = K one of the parameters constituting constant (K) is the equivalent length (Le). In computation, Le rather than length of only straight pipe (L) in the branch is required to be used due to fact that fluidsufferspressurelossduetoflowthroughstraightpipelengthaswellasflowthroughfittingssuchbend,tee,value, etc.
Therearetwowaysofcomputingpressuredropthroughfittingsasrepresentedbyfollowingequations:
or
Where,DPPressuredropsacrossfittingsinm/c.ThenumericalvalueofKintheformerequationisdecidedbythetypeoffitting.Table5.3showssometypicalKvalueisgiven.
In the latter equation Le is the equivalent length of a straight pipe accounting for pressure loss, which is the same asthatofthefitting.
On comparing the two equations, It could be seen that,
Le
A typical chart used for estimating Le values is given below in table 5.4.
As such in each branch K in the equation hf = KQ depends on Le and Le in turn includes length of straight pipe as wellasequivalentlengthofallfittingsinthebranch.(ItmaybenotedthatKintheequationhf=KQnandKforfittingspressuredroparedifferent.ThenomenclatureofKvalueforfittingsiswidelyusedandhencethesamehasbeen retained here).
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Use of software tool for network analysis: Due to the nature of iterative calculations involved, network analysis is substantially aided by software tools. Some software tools are available under the proprietary names of Engineers Aide, Pipenet. (It is understood that use of PipenetforanalysisoffirewaterdistributionnetworkisacceptabletoTAC.)
Some of the important features and/or advantages of the software tools are seen as below: Preparation of network schematic diagram •High speed of iterative calculations till desired convergence is achieved •Quickassessmentofeffectofchangesandmodificationsonflowsthroughbranchesofnetwork•Facilityofpipelinesizingforgivenflow•Libraryoffluidproperties•Regression of data for H Q curve for the pump •LibraryofKvalues(forpressurecropacrossfittings)•Facility for computing friction factor (ff) for any Reynolds Number (Re) and using the same in the network •analysisNetwork analysis under transient conditions and for pressure surges•Analysisforflowthroughsprinklers•
LR Bend 0.6 Non – Return Valve (open) 2.5
U Bend 2.2 Gate Valve (open) Globe Valve (open)
0.19 10.00
Table 5.3 Some typical K value for friction head loss through fitting
Size Swing Check Valve Full Open
Gate Valve Half Open
Globe Valve Full Open L R Bend
50 NB 4.0. m 9.1 m 15.1. m 1.0 m
80 NB 6.1 m 15.2 m 24.4 m 1.8 m
Table 5.4 Some typical equivalent length (Le) for fittings
5.4 Restriction Orifice Theflowintwodifferentbrancheswouldgetequallydividedifresistanceofbothbranchesisthesame.Theresistanceofabranchcanbeincreasedbyintroducingtherestrictionorifice.
Referfigure5.3, K1-2-4=K12+K24=7160
And K 134 = K13 + K34 = 272 + 1190 = 1462
Ifflowthrough1-2-4and1-3-4aretobeequal,K134=7160,i.e.,K134istobeincreasedby5698(7160-1462),equivalent to 3.561 mWC
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Pressuredropacrossorificeplateisgivenby:
Note:Sinceβ=Do/Dp
βXDp=Do
Do-diaoforifice Dp-IDofpipe
Bisanimportantparameter,whichgovernspermanentpressureloss.Equationgivenforpressuredropacrossorificeplatecanbeusedtodeterminethesizeoftheorificetobeinstalled.
Note 1:Hazen-William equation
-friction head loss in ftL-length in ft C-Constant, dimensionless C = 140-new steel pipe C = 100-riveted pipe d -pipe ID in inch Q-in gpm
Note 2: Theequationisbasedonturbulentflowcondition,viscosityofwater=1.3.cp,theequationisapplicableessentiallyfor water.
5.5 Colour Coding of Pipelines Identificationandcolourcodingforthepipelinesisessentialtoavoidpotentialhazardsandaccidents.Givingacolour code and maintaining the uniformity for colour coding in industrial piping will eliminate accidental chances and reduce operational errors. Moreover, it enhances the safety aspects. Many companies and local regulations have prepared the standards for colour coding of the pipelines.
Examples: IS: 2379 BS: 1710 ANSI A 13.1
Colourcodingorthecolouringschemeistoknow,identifywhichfluidisflowinginsidethepipelines.Thiscanbeapplicable to building piping, process piping, industrial piping, chemical or process plants. Complete piping systems includingvalvesandfittingsaretobepaintedaccordingly.Further,paintsandpaintshadesselectedshouldconformto the governing standard prior to provision.
5.5.1 Colour Coding to Pipelines (Ground Colour and Colour Bands) Lineidentificationisdonebygivingabaseorgroundcolourtopipelinesbasedonfluidflowing.Furthercolourbandsareprovidedaccordingly.Thebase/groundcolourgivesthebasicnatureoftheflowingfluid(i.e.water,air,gases etc.). Typically ground colours are provided on the full pipe section or minimum 300 mm length portion or by attaching the label.
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Ground colour Fluid flow inside the pipe
Green Water
Sky Blue Air
Yellow Gases
Aluminium Steam
Table 5.5 Colour coding to pipelines
Over and above the base colour or ground colour of the pipeline, colour bands are provided to differentiate and identifytheapplicationofthebasicfluid.Example:
Fluid: Water Ground colour code: Green Cooling water: Sea green (ground colour) and application is for cooling. •Hence, a further colour band of French blue is provided. Fluid: Air Ground colour code: Sky blue Plant air: Sky blue (ground colour) and application is for supplying •the plant air. Hence, a further colour band of silver grey is provided.
5.5.2 Colour Bands As stated earlier, colour bands in single or double over the ground colour on the pipeline, and the ground colour on the entire or partial length of the pipeline is provided. These colour bands are provided at suitable locations such as:
At the beginning and termination points •For yard piping around 50 to 60 m distances •Atchangeinflowdirectionpointsandflowdiversionlocations•At locations where the pipe enters the building or exits from the building•
5.5.3 Typical Practices Followed for Provision of Ground Colour and Colour Bands on the Pipe Lines
Pipe Dia. Ground colour
Colour band
D
Fig. 5.4 Typical colour band
If colour bands are provided over the ground colour, then the ground colour should extend on both sides of the •colour bands. When double colour bands exist on the pipeline, then a proportional width of 4:1 to the next colour band is •provided. Minimum colour band width is 25 mm. •Generally below 80 NB piping width of the colour band is 25 mm. •
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86
For piping 100 NB to 150 NB width of the colour band is 50 mm. •Valves and piping accessories to be painted with the same colour as that of the pipe ground colour. •For insulated pipes, non-ferrous pipes, S.S. pipe ground colour to be given for minimum 1.5 m length. •For non-insulated piping above 100• oC, generally colour bands are not provided (only ground colour Aluminium isprovided).IfbandsaretobeprovidedthentheyshouldbeofTeflontape.Further,flowdirectionandarrowsmustbemarkedatsuitableintervalsalongtheline.Forthelinecarryingfluid,•thefluidnameshouldbewritteninthewhiteboxonthegroundcolourprovidedfortheline.Arrow sizes, dimensions differ with w.r.t. company standards.•
70
100
20
25
Fig. 5.5 Lettering size
Example: Below 200 NB line arrow dimensions are given below:
Letteringsizeforfluidnameisalsobasedonthepipediameter.•
Examples: 100 NB Pipe ---------------Legend Size is 30 mm 50 NB Pipe -----------------Legend Size is 25 mm 200 NB Pipe ---------------Legend Size is 50 mm
Visibility of Marking: It should be such that the operator can see if it is at the normal height. If lines are above •the operator’s head (may be along the roof, or side wall or through the rack), then the lettering is to be done below or towards the bottom side of the pipe. Lighting provided in the plant should not affect the colour and shades in terms of visibility particularly at •night. For closed circuit lines other than direction ‘F’ for flow and ‘R’ for return to be written for better •understanding. Lines carrying hazardous materials have a panel of colour with dots, strips; crosses are marked based on the •practices.
87
Fig. 5.6 Visibility of marking
Finally, uniformity for colour coding on pipelines will lead to better safety, less human errors.
5.6 Restriction Orifice Sizing Theseflowmeterscansuccessfullymonitorawidevarietyoffluidsunderdiverseconditionsifyouselecttherightorificeshapeandthetypeofpressuretaps.
Fig. 5.7 The orifice meter measures pressure e.g., at point a and b determines the flow rate
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88
To control an industrial process, it is essential to know the amount of material entering and leaving key process •steps.Tomonitorthis,theengineercanchoosefromawidevarietyofflowmeters.Despitethiswealthofchoice,simpleorificemetersareoftenselectedbecauseoftheirlowcost,compactness,•andsuitabilityforawiderangeofflowrates.
Here,wewillexplorehowsuchmeterswork,howtochoosetherighttypeoforifice,andtheappropriatepressuretaps.
5.6.1 How the Meters Work TheunderlyingprinciplebehindanorificemeterisBernoulli’senergyequationforstreamlineflowwhichstatesthatwhenaflowiscontractedorexpanded,thetotalenergyofthefluidremainsconstant.
During contraction, kinetic energy increases and potential energy decreases, whereas potential energy increases •at thecostofkineticenergy inexpansion.Achange inpotentialenergy is reflected in thechangeofstaticpressure. Reductionofthecross-sectionoftheflowingstreamwhilepassingthroughanorificeincreasesitsvelocityhead•at the expense of its pressure head. Bernoulli’s equation, thus, provides a basis for correlating the increase in velocityheadwiththedecreaseinthepressurehead.Duetothesharpnessofthedownstreamsideoftheorificeplate,itformsafree-flowingjetinthedownstreamfluid,asshowninfigure5.1.Thepointofminimumareaoftheflowstream,thevenacontracta,islocatedatapositionalongthepipethat•dependsontheflowrate.Minimumpressureisobservedatthevenacontractsposition.Pressuretaps(theproperpositioning of which will be discussed later) at the upstream and downstream sides allow the measurement of thedifferentialpressureacrosstheorifice.
5.6.2 Orifice Choices The type of orifices can be classified by their geometry. Each has advantages, disadvantages, and typicalapplications.
Fig. 5.8 Orifice shapes
89
Circular cross sectionItisthefunctionthatreturnsthe‘ThickEdgedOrificeGeometry’foracircularcrosssectionoftheorifice.Inputs
Type Name Default Description
Diameter diameter Innerdiameterofcircularorifice[m]
Diameter venaDiameter Diameter of vena contraction [m]
Length venaLength Length of vena contraction [m]
Outputs
Type Name Description
Geometry geometry Geometryofcircularthickedgedorifice
Rectangular cross sectionItisthefunctionthatreturnsthe‘ThickEdgedOrificeGeometry’forarectangularcrosssectionoftheorifice.Inputs
Type Name Default DescriptionLength width Innerwidthofrectangularorifice[m]Length height Innerheightofrectangularorifice[m]Length venaWidth Width of vena contraction [m]Length venaHeight Height of vena contraction [m]Length venaLength Length of vena contraction [m]
Outputs
Type Name Description
Geometry geometry Geometryofcircularthickedgedorifice
General cross sectionItisthefunctionthatreturnsthe‘ThickEdgedOrificeGeometry’forageneralcrosssectionoftheorifice.
InputsType Name Default Description
Area crossArea Inner cross sectional area [m2]
Length perimeter Inner perimeter [m]
Area venaCrossArea Cross sectional area of vena contraction [m2]
Length venaPerimeter Perimeter of vena contraction [m]
Length venaLength Length of vena contraction [m]
Outputs
Type Name Description
Geometry geometry Geometryofcircularthickedgedorifice
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5.6.3 Concentric Thisiscommonlyusedinthechemicalprocessindustries(CPI).Theconcentricorificeplateisaflatmetalsheetwithacircularhole.Itisinstalledinthepipelinewiththeholeororificeconcentrictothepipe(seeFigure5.2).
Asquareorsharpedgedorificeisaclean-cutholewithstraightwallsperpendiculartotheplate’sface.Erosion•orotherdamagetotheinletshapecanmakesuchorificesunsuitableforsomeflowmeasurements.Toavoiddamagetoorificeedges,theycanbemadeconicalorroundedontheupstreamsideoftheplate.•Thesevariants arecalledconical-edgedandquadrant-edgedorifices, respectively.Theyprovidea constant•dischargecoefficientevenatalowReynoldsnumber.Concentricorificesareusefulforcleanliquids,gases,andlow-velocityvapours.•
5.6.4 Eccentric and SegmentalThese are frequently used for gas metering when there is a possibility that entrained liquids or solids would otherwise accumulateinfrontofaconcentriccircularorifice.Suchabuild-upcanbeavoidediftheopeningisplacedonthelower or upper side of the pipe.
Forliquidflowwithentrainedgas,theopeningisplacedontheupperside.Insuchsituations,thepressuretaps•should be located on the opposite sides of the pipe from the opening. If the upper or lower segment of the pipe is blocked by a plate with a straight square edge, then the wall of the •pipeactsasaboundaryoftheorificeresultinginanincreaseofthedischargeororificecoefficient.Insomeofthecommerciallyavailablesegmentalorifices,theplatecanberaisedorloweredlikeagate,thus•eliminatingtheneedtochangetheorificeplate.
5.6.5 Annular This orifice consists of a dish supported concentrically in a pipe sectionby supporting spiders.Upstreamanddownstream pressures are transmitted through the central shaft to a differential pressure transmitter through the centralshafttoadifferentialpressuretransmitter.TheflowcoefficientisconstantaboveapipeReynoldsnumberof 10,000.
Anannularorificeprovidesfreedrainageforheavymaterialsatthebottomofthepipewhileallowinggasor•vapours to pass along the top of the pipe. Suchorificesareusedforgasmeteringwhenthereisapossibilityofentrainedliquidsorsolidsandforliquid•metering with entrained gases present in small concentrations. They avoid the problem of dirt build-up in front ofanorificeinliquidstreamsandofliquidbuild-upinamostgasstream.Theirdisadvantagesarelackofavailablestandardequations,anddependenceonpipedimensionstodefineflow•area,whichisamoreseriousdrawbackatahighratiooforificetopipelinediameter(b>0.9).
5.6.6 Integral Forverysmallpipesizes,anorificecanbeinstalledintegrallywithadifferentialpressuretransmitter.Thispro-videsacompactinstallationwithanaccuracyof2¬5%.Suchacombinationisusedparticularlyforflowstudies.
5.7 Types of Pressure Taps Anyrestrictionintheflowpipecausesadropofpressure,thatis,thedownstreampressurelowersbyanamountequaltothepressuredropduetotherestriction.Incaseoforifices,thedropinpressurevariesfromthelocationoftheorificeplatetothedownstreamsideuntiltheflowbecomesfullydeveloped.Thepressuredropisatitsmaximumatthevenacontract.Tapsareusedtosensethepressureandtheyareclassifiedbasedontheirlocation.
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5.7.1 Corner Taps Inthisarrangement,openingsforthepressuretapsarelocatedintheupstreamanddownstreamflangesholdingtheorificeplate.
Fig. 5.9 Orifice meter with corner
Theseopeningsshouldbeascloseaspossibletotheorificeplate.They,however,aresusceptibletodirtfreezing•and clogging with hydrates. Theyaremoreaffectedbyupstreamdisturbancesandgenerallyarelessreliablethanflangeorvenacontracta•taps.
5.7.2 Radius Taps Here,pressuretapsarelocated1pipediameterupstreamand½diameterdownstreamfromtheorificeplate(seeFigure 5.10). This arrangement is best from a practical standpoint because the downstream pressure tap is located ataboutthemeanpositionofthevenacontract,andtheupstreamtapissufficientlyfarupstreamtobeunaffectedbydistortionoftheflowintheimmediatevicinityoftheorifice.(Inpractice,theupstreamtapcanbeasfaras2pipe diameters from the plate without affecting the results.)
5.7.3 Pipe Taps In this, holes for the pressure taps are located 2 ½ pipe diameters upstream and 8 pipe diameters downstream from theorificeplate(seeFigure5.4).Boththetapsarelocatedintheregionofthefullydevelopedflow.Thus,theygivethetotalpressurelossduetotheorificeandareusefulfordeterminingtheoverallpressurelossesinthepipeline.
5.7.4 Flange Taps Thisdesignplacesonepressuretaphole1inchupstreamandtheother1inchdown-streamfromtheorificeplate.Beingcloselylocatedtothefaceoftheflange,theyareaccessibleforinspection.Duetosymmetry,theycanbeusedtomeasureflowineitherdirection.Theyshouldnotbeusedinpipesizeslessthan2incheswheretheratioishigh, because the downstream tap is located in a highly unstable pressure region.
5.7.5 Vena Contracta Taps Here,theupstreampressuretapis2½pipediametersfromtheorificeplateandthedownstreamtapislocatedattheposition of minimum pressure, the vena contracta. Theoretically these taps should be best as pressure is minimum at thispointandthedropinpressureforfluidpassingthroughtheorificeshouldbemaximum.Butapracticalproblem,suchasthechangeofpositionofthevenacontractawithflowrate,limitsthesuitabilityofthesetypesoftaps.
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5.8 Orifice Selection Guidelines TheCPIdealswithinnumerabletypesoffluidstreamsforinstance,cleanliquids,wetsteam,andliquidscontainingsolidparticles.Thenatureof the streamdetermines the suitabilityof thevarious typesoforifices.Letusnowsummarisethetypeandselectionoforifice.
Flowofcleanliquids,gases,andlow-velocityvapoursisbestmeasuredbyconcentricorifices.•ForReynolds number lower than 10,000, install square-edged orifices.AtReynolds numbers lower than•10,000,howeverthedischargecoefficientofsquare-edgedorificeschangeappreciablywitheitherflowrateorviscosity. Forthisreason,eitherquadrantorconical-edgedorificesarepreferred.Quadrant-edgedorificesarerelatively•immunetotheeffectsofcorrosion,erosion,andthedepositofsolidsatthesurfaceoftheorifice.
r. r.
Fig. 5.10 Orifice meter with corner taps
Granular solids inaflowingfluid, condensate in steam,orvapourorgas ina liquid,generallydonotuse•concentricorificesbecausetheprojectingrimsoftheorificeformsadamandtheseforeignmaterialsbuild-upintheapproachpipeattheplate,causingachangeinthedistributionofflow.Todealwithgranularsolidsandcondensate,installaneccentricorsegmentalorificeplatewiththeholeatthe•bottomofthehorizontalpipetopermitthefreepassageofthosematerials.Iftheorificecanbelocatedinaverticalrunwiththeflowinadownwarddirection,however,thentheconcentricorificeispreferredbecauseofitsbetterdischargecoefficientaccuracy.Whenliquidscontaininggasorvapourmustbemeasuredinahorizontalpipe,useasegmentalorificewiththe•openingatthetopofthepipe.Forthesefluids,however,ifsuitablelocationsareavailableinverticalpipeswiththeflowinanupwarddirection,concentricorificesarepreferredforgreateraccuracy.Segmentalorificeplatesshouldnotbeusedtomeasureliquidscontainingsolidsthataresicklyorthathavea•densitysimilartotheliquids.Thisdesignisaffectedbydepositsonthefaceoredgeoftheorificeinthesamewayastheconcentricorifice.Iffluidstreamscontainbothheavymaterialsandgasorvapourintheliquid,annularorificesarerecommended.Insmallerlinesizes,itisimpracticaltoinstallthedownstreamvenacontractatapwhenusingaconcentricorifice,•becauseofinterferenceoftheflangehub.Both,thesegmentalandeccentricorificeplates,havevenacontractalocationfartherdownstreamthantheconcentricorificeplate.Inmanycases,thisdifferenceisjustsufficienttomakeuseofvenacontracttapsfeasible,andsothealternativeorificesshouldbeselected.
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Table 5.6 Orifice coefficient for different types of pressure taps
Table 5.7 Expansion factors for different tap positions
5.9 Figuring Flow Rate Theoretically,themass-flowrateofanincompressiblefluidflowingthroughapipelinewithasharpedgedconcentricorificemeterisgivenby:
.......................................(1)
where is a velocity correction factor (1)
Type of Tap Orifice Coefficient at Infinite Reynolds Number,
Corner Flange
2in.≤dp≤2.3in.
dp≥2.3in.
Radius
Pipe (1
)
Expansion Factor Upstream measurement
or
Downstream measurement
where
Forcorner,flangsandradiustaps
For pipe taps
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Duetothepermanentlossofenergyexperiencedbytheflowingfluid,alesserflowrateisactuallyobservedintheorificeflowmeter.Acorrectionfactor,calledthecoefficientofdischargeororificecoefficient,isintroduced,andisdefinedas:C=truefluidflowrate/thetheoreticalfluidflowrate......(2)
Hencethetruefluidflowrateforincompressiblefluidsisgivenby:q = C x q ................. (3)
TheorificecoefficientdependsonthetypeofpressuretapandtheReynoldsnumberofflowingfluid,per:
................. (4)WhereCxisthevalueoftheorificecoefficientattheinfiniteReynoldsnumberforthespecifictypeoftap;theequations to calculate C are given in Table 6.1.
Compressiblefluidslosemoreenergyoncontractionandexpansionthanincompressibleones.Thus,theirtruemassflowrateislessthanthetheoreticallyevaluatedviaequation3andanexpansionfactormustbeused:
Y=truemass-flowrateofcompressiblefluid/flowratecalculatedbyequation3.........................(5)
The expansion factor also depends on the type of pressure taps being used (as shown in Table 6.2).
Hence,thetruemassflowrateofacompressiblefluidisgivenby:
........................(6)
5.10 Critical Flow Whenthevelocityofthefluidpassingthroughtheorificereachesthespeedofsoundattheupstreamtemperature,itiscalledthecriticalflowcondition(seetable5.3).Atthiscondition,orificeswithwell-roundedentrancesexhibitamaximumflowindependentofthedownstreampressure.Thistheoreticallyisgivenby(2):
........................(7)
Incontrast,thesquare-edgedorificesgenerallyusedinthepipingsystempermitincreasesflowevenasthedownstreampressureisreducedbelowthecriticalvalue.Hence,thetrueflowratethroughasharp-edgedconcentricorificeis:
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........................(8)
Where the velocity correction factor and k is is theflowcoefficient,which depends on the ratio ofdownstream to upstream pressure (that is, p
2 lp ).
The regression result for experimentally obtained values of K vs. ( plp ) for air is given by:
5.10.1 Computer ProgramAcomputerprogramcalled‘KORIFICE’isdevelopedforthecalculationoftheflowratethroughsquareedgedconcentricorificesusingdifferenttypesofpressuretaps.Italsoincludessub-programforsizingoforificesandfindingthepressuredropacrossorifices.
Basicinputdatarequiredtorunthisprogramarediameteroftheorificeandpipeincomparableunits,physical•propertiesofthefluid,upstreamanddownstreamfluidpressures,andsoon.Theprogramissuitableforincompressibleandcompressiblefluidsatbothnormalandcriticalflowconditions.•An example of the input data required to run the program and output result for the supplied data are presented in Table 5.8.
Input dataViscosityoffluid,µ 0.0219 cpDensityoffluid 0.0996 lb/
Upstreamfluidpressure,P1 25.33 psiaDownstreamfluidpressure,P2 20.18 psiaUpstreamfluidtemperature,T1 685 RSpecificheatratio,k(= / ) 1.4Molecularweightoffluid,mw 29
Diameter of pipeline 1.39 in.
Table 5.8 (a) Flow rate of compressible fluids under normal flow conditions
Type of taps Flow rate, lb/s Reynolds number Orifice coefficient
Corner 0.1345 s101,188 0.60694
Flange 0.1344 101,113 0.60649
Radius 0.1347 101,339 0.60788
Pipe 0.1627 122,404 0.73444
From KORIFICE computer programmer
Table 5.8 (b) Output data
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5.11 Restriction Orifices to Maintain Required Flow Rates Thesedevicescanprotectequipment,ensuresafety,andboostprocessperformance.Arestrictionorifice(RO)isanothernameforanorificeplate,thatis,aplatewithaconcentricholeinit,insertedinbetweentwoflangesinapipe.Thereducedcross-sectionalareaoftheROlowersthedownstreamflowrateasthepressuredropsacrosstheopening.
Therequireddownstreamflowrateandpressuredropmainlysetthesizeoftheorifice.Theauthorhaspresented•equationsfordeterminingflowandpressuredropforliquidsandgasesinanRO(1).Inthechemicalprocessindustries(CPI),ROsareusedtoreducefluidpressures,oftentokeepprocesseseither•stableor safeduring lowflows.Someof themore commonapplicationsofROswill bediscussed in thischapter.
5.11.1 Maintaining Minimum Flow in Pumps Centrifugalpumpscannotrundry,andmusthaveaminimumfluidflowtooperateproperlytoavoidcavitationsandsubsequent mechanical damage to the pump. Toprotectthepump,aminimumflowlinenormallyiscreatedleadingfromthepump’smaindischargelinebacktothesuctiontank.Sometimes,thislinealsofunctionsasare-circulationline(seefigure5.1).Usually,theminimumflowisconsideredtobe10-15%oftheratedcapacityofthepump.
This capacity meets the discharge pressure required to satisfy process requirements. •TheROcreatesapressuredropthatsetstheminimumflowlineforthepump.Thisorificeisalwayslocated•near the pump discharge. TheupstreampressureontheROisfixedbythedischargepressureofthepump;thedownstreampressureby•that is needed to attain the suction tank pressure. TheROissized,basedonthepressuredropacrosstheROandtheminimumspecifiedfluidflowrateofthe•pump.
5.11.2 Safely Operating Critical Processes Certaincriticalprocessesrequireminimumfluidflowforsafeoperationduringtheemergencyshutdownofaplant.For example, consider two-phase processes in which toxic gases, such as chlorine, are present.
Duringnormaloperationthechlorineisremovedsafelyfromtheprocessingunitwiththeflowingliquids.But•during an emergency shutdown, the chlorine is collected in the unit and its pipeline headers. Hence, a minimum fluidisrecommendedtoflushawaythecollectedgases.
To Processing unit
Centrifugalpump
RO
Minium - flowline
Fig. 5.11 An RO protects a centrifugal pump from cavitations
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OnesuchapplicationisshowninFig.5.12,wherethereactantfluidisfedtotheprocessingunitandtheform•rateisalwaysmaintainedbyusinganRO.Fornormaloperationoftheprocessingunit,flowiscontrolledbyafail-to-close (normally open) control value.
Fig. 5.12 An RO sets minimum flow for safe operation of critical processes
The upstream pressure on the RO is equal to the liquid head from the tank. The downstream pressure is set to •meet the pressure requirement of the processing unit. Again, the RO is sized, based on its differential pressure andtheminimumsafefluidflowrate.
5.11.3 Maintaining Pump Flow for Multiple Applications In some CPI plants, a single pump sometimes is used for multiple applications. For example, the same pump may feed raw material to two different processing units (A and B), working independently at different times. (see Fig. 5.13).
Fig. 5.13 RO arrangement for multiple flows
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Theflowandpressureheadrequirementofbothunitscouldbedifferent.Incertaincases,suchrequirements•are met by the proper selection of pump characteristics. In others, this is not possible, and additional pressure drop is required. Here, an RO is used. Table 5.1 shows how this situation might look like for processes A and B. The pump suits the requirements of •process A, but requires an additional pressure drop of 0.4 bar for process B. An RO placed in the discharge line feeding process B will meet the pressure requirement.
End of last cycleFilter
Start of next cycleFilter
Case 1: without RO Pressure Drop, bar 0.2 0.2 0.1 0.2 0.2 0.1Flow rate, m3/h 50 50 0 0* 33.3 66.7Deviation from normal 0 0 - - -33.4 +33.4flow,%
Case 2:with ROPressure drop, bar * 0.7 0.7 0.5 0.7 0.7 0.6Flow rate m3/h 50 50 0 0* 46.1 53.9Deviation from normal 0 0 - - -7.8 +7.8Flow, %
Basis: Total Fluid rate = 100 m3/hPressureDropacrossfilter=0.1barMaximumallowablepressuredropacrossfilter=0.2bar
*Thecloggedfilterisbackwashed.+TotalpressuredropacrossfilterandRO,ROdrop=0.5bar
A B C A B C
Table 5.9 (a) RO calculation
Note:CalculationsshowthatROsprovideanevenflowrateinparallelfiltration
Process Requirements Pumps supplies
Flow rate m3/h pressure
Differential bar m3/ in
Flow rate Pressure
Differential bar
Process A 5.0 2.0 5.0 2.0
Process B 3.0 1.8 3.0 2.2
Table 5.9 (b) An RO in the line to Process B meets pressure requirements
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5.11.4 Providing Adequate Agitation Air Distribution in Tanks In the CPI agitation, air is used for applications including the maintenance of homogeneous slurry in tanks, removing gases from the liquids and purifying waste water.
Normally, compressed air requirements at different units are met by a centrally located compressor and utility •stations at different units. The compressed air typically will be at a pressure of 2 bar. While this pressure may be suitable for some plant application, it is too high for agitation. The required agitation pressure depends on the liquid head in the tank. Again, a reduced pressure drop is created •in the agitation airline by inserting an RO before the tank. If a tank is large and requires several spargers, multiple airlines are drawn off the main header. Each line will have an RO in it to reduce the pressure, and will uniformly distribute the air.
Primary Sedimentation
Secondary Sedimentation
Trickling Filter (6-10
Arms) Dosage more than 10
MGAD
To Primary Tank
AERO-FILTER
To Digester
Sludge
Sludge to Digester
Recirculation
Fig. 5.14 Aero-filter(Source: http://t3.gstatic.com/images?q=tbn:ANd9GcS34Ob7ydar4_MRkhjIEjaUtlltgqraUQru51pswnjmvNtDV
TgX_w)
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SummaryIn the process industry, networks of somewhat different kind are encountered in relation to the closed loop utility •circulationsystemsviz.coolingwater,refrigeratedbrineandthermicfluidsystems.InanetworkwheretwopipelinebranchesareavailablefortheflowoffluidfrompointAtoB,theheaddifference•(pressure drop) between these two points is the same irrespective of the route. The pressure drop, in turn varies withtheflow.Quantity balancing is another method of analyzing piping network. This method is more convenient for analysing •interconnected reservoirs each at different elevations. Identificationandcolourcodingforthepipelinesisessentialtoavoidpotentialhazards,accidents.Givinga•colour code and maintaining the uniformity for colour coding in industrial piping will eliminate accidental chances, reduces operational errors.Furthercolourbandsareprovidedaccordingly.Thebase/groundcolourgivesthebasicnatureoftheflowing•fluid.Colour bands in single or double over the ground colour on the pipeline, and the ground colour on the entire or •partial length of the pipeline is provided.The type of orifices canbe classifiedby their geometry.Eachhas advantages, disadvantages, and typical•applications.Theconcentricorificeplateisaflatmetalsheetwithacircularhole.Itisinstalledinthepipelinewiththehole•ororificeconcentrictothepipe.Forverysmallpipesizes,anorificecanbeinstalledintegrallywithadifferentialpressuretransmitter.This•provides a compact installation with an accuracy of 2¬5%.Anyrestrictionintheflowpipecausesadropofpressurethatisthedownstreampressurelowersbyanamount•equal to the pressure drop due to the restriction.TheCPIdealswithinnumerabletypesoffluidstreamsforinstance,cleanliquids,wetsteam,andliquidscontaining•solidparticles.Thenatureofthestreamdeterminesthesuitabilityofthevarioustypesoforifices.Acomputerprogramcalled‘KORIFICE’isdevelopedforthecalculationoftheflowratethroughsquareedged•concentricorificesusingdifferenttypesofpressuretaps.Italsoincludessub-programforsizingoforificesandfindingthepressuredropacrossorifices.
ReferencesV & M Systems, 1992• , Pipe Network Fluid Flow Analysis Systems, [Online].Available at: < http://www.vmc.com.tw/english/prod_pn.htm#top>. [Accessed 13 June 2011].Dr. Swamee,P.k., Dr.Sharma,A.K., 2008, • Design of Water Supply Pipe Networks [Online]. Available at: <http://as.wiley.com/WileyCDA/WileyTitle/productCd-0470178523,descCd-description.html>. [Accessed 13 June 2011].
Recommended ReadingParisher, R., 1999, • Pipeline networks for fluids, 2nd ed., North-Holland.Bausbacher, E., 1996, • Pipeline Networks Rules of Thumb Handbook, 2nd ed., McGraw-Hill.Blevins, T. L., 1980, • Pipeline network construction, 3rd ed., Pergamon Press.
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Self Assessment
__________networksareencounteredinfireprotectionsystemswhereinringmainshavetobeinstalledto1. deliver water at different locations.
Pipinga. Coding b. Fluidc. Fluid pressure.d.
Identificationand_________forthepipelinesareessentialtoavoidpotentialhazards,accidents.2. line codinga. index codingb. colour codingc. string codingd.
___________or other damage to the inlet shape can make such orifices unsuitable for some flow 3. measurements.
Erosiona. Rustb. Electric shockc. Vibrations d.
___________ofthecross-sectionoftheflowingstreaminpassingthroughanorificeincreasesitsvelocityhead4. at the expense of its pressure head.
Increasea. Reductionb. Removalc. Doubling d.
Thetypeoforificescanbeclassifiedbytheir_________.5. geometrya. sizeb. numberc. segmentsd.
Which of the following true?6. Segmentalorificeplatesshouldbeusedtomeasureliquidscontainingsolidsthataresicklyorthathaveaa. density similar to the liquids.Segmentalorificeplatesshouldnotbeusedtomeasureliquidscontainingsolidsthataresicklyorthathaveb. a density similar to the liquids.Segmentalorificeplatesshouldnotbeusedtomeasureliquidscontainingsolidsthataresicklyorthathavec. a density similar to the solids.Segmentalorificeplatesshouldnotbeusedtomeasuresolidscontainingliquidsthataresicklyorthathaved. a density similar to the liquids.
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Which of the following true?7. The downstream pressure on the RO is equal to the liquid head from the tank.a. The downstream pressure on the RO is not equal to the liquid head from the tank.b. The upstream pressure on the RO is not equal to the liquid head from the tank.c. The upstream pressure on the RO is equal to the liquid head from the tank.d.
Which of the following false?8. The downstream pressure is set to meet the pressure requirement of the processing unit.a. The downstream pressure is set to meet the vibration requirement of the processing unit.b. To control an industrial process, it is essential to know the amount of material entering and leaving key c. process steps.Theflowintwodifferentbrancheswouldgetequallydividedifresistanceofbothbranchesisthesame.d.
Which of the following true?9. Quality balancing is another method of analyzing piping network.a. Quantitybalancingisanothermethodofanalyzingfluidhandling.b. Quantity balancing is another method of analyzing piping network.c. Quantity balancing is another method of analyzing coding.d.
Which of the following false?10. Colourcodingorthecolouringschemeistoknow,identifywhichfluidisflowinginsidethepipelines.a. Intheheadbalancingmethod(discussedearlier),theflowinonebranchwasassumed.b. The change in flow condition of one branch affects the flow and pressure in other branches of thec. network.Thetrialguessesareimprovedbyemployingcorrectionsuntilthepressuredropcriteriaaresatisfied.d.
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Chapter VI
Fluid Flow Theory and Practices
Aim
The aim of this chapter is to:
explain velocity constraints•
discuss Reynolds number•
recognise friction factors•
Objectives
The objectives of this chapter are to:
explaintubingandotherflowconduits•
illustrategravityflow•
listthetypesoffluids•
Learning outcome
At the end of this chapter, you will be able to:
identify roughness (• )
classify the rule of fours for pressure drop •
understand economic velocity for line sizing•
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6.1 IntroductionOne of the process engineer’s most important tasks in the design of a facility is the sizing of the pipes and ducts that connect equipment or pipes with other equipment, pipes or boundary points. Standard commercial pipe sizes were originallydefinedbytheAmericanStandardsAssociation(ASA)nowknownastheAmericanNationalStandardsInstitute (ANSI). These commercial sizes are known as iron pipe sizes (IPS). For 1-through 12inch pipe, the OD is somewhat above the nominal size; i.e., an 8-inch pipe has an OD of 8.625 inch. However, at diameters of 14-inch and larger, the OD is equal to the nominal size of the pipe.
The ASA also established several categories of pipe according to the pressure service to which a pipe may be subjected.Thesearetermed“Schedules”(Sch),andtheyarelistedasSch10,Sch20,Sch30,Sch40,Sch60,Sch80, Sch 100, Sch120, Sch 140, and Sch 160. The OD for each nominal size is the same for all schedules. As would be expected, the wall thickness for a given schedule increases with the nominal size of the pipe.
6.2 Schedule Number The relationship between pressure, schedule, corrosion allowance and wall thickness are expressed by the •following equations:
Schedule number = 1000 P/S And t = (P/S × d/2) + C
Where, P = maximum internal working pressure; psig S = allowable working stress at design temperature, psig t = pipe thickness, in d = outside pipe diameter, in C = corrosion allowance, in
Corrosion allowances are not normally used in association with stainless steel or alloy piping since these materials •are chosen for their resistance to corrosion.
6.3 Tubing and Other Flow Conduits Tubingandotherflowconduitsaredescribedasunder:
Tubing has mechanical characteristics, different from those of pipe and can sometimes be used in place of it •to great advantage. Itisespeciallyusefulforrunsof1-inchdiameterandlesswhentheflexibilityoftubingcomparedwiththe•greater rigidity of pipe is desired. Tubing is normally available in nominal sizes from 1/8 to 12 inches diameter and is used for applications such •as reactor coils and heating coils in small vessels or large storage tanks. A very important use for tubes is in heat exchangers. In this case, the OD of the tube is the same as its nominal •size. The wall thicknesses are set by the standards of the Tubular Exchanger Manufacturers Association (TEMA) •in Birmingham wire gauge units, a scale originally developed for wire diameters and also used for sheet metal thickness.
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6.4 Velocity Constraints Following are the various factors for velocity constraints:
Theexistenceofvelocityconstraintsonfluidsflowinginpipesmustalwaysbekeptinmind.•Eachtypeofflowhasitsownpeculiaranddistinctvelocitylimitsbeyondwhichitshouldnotbedesigned.•Single phase liquids such as water, hydrocarbons, solutions and others can cause water hammer or erosion of •thepipingifvelocitiesaresufficientlygreat.
“Waterhammer”isthetermgiventotheforcessetup,shouldthevelocityoftheflowingmediabechangedsuddenly.At higher velocities, the forces can be destructive enough to damage piping or supports.
A rough thumb rule, based on engineering experience, for use with water in metallic pipes which are of 3 inches diameter and greater and are in continuous service is that the velocity in feet per second should not exceed about 4 plus one-half of the nominal diameter in inches. i.e., 4 + d/2. Thus, the velocity in a 3 inches pipe should normally be kept below 51/2 ft/s, and the velocity in a 16-inch line could be as great as 12 ft/s, in the absence of other constraints. In no case should a pumped liquid velocity be allowed to exceed 14 to 17 ft/s. Below 3 inch diameter, velocities of 5 ft/s are acceptable for liquids.
6.5 Gravity FlowBesidesinducedflowsbymeansofpumps,compressors,orvacuumdevices, therecanbegravityfloworflowcaused solely by differences in elevation or static pressure between two points in the system. In these cases, the total pressure or friction loss cannot be greater than the static head or pressure differential.
Apipeofsufficiently largediametermustbechosen tomaintain the friction lossata reasonablevaluefor therequiredflow.Aproperlysizeddiameteralsopreventsahighentrancelossorbuild-upofliquidduetoconstrictionabove the inlet to the piping system.
6.6 ViscosityAnimportantphysicalpropertyofafluidthatinfluencesthetypeofflowpattern,whichwillbedevelopedinaconduitand,thus,thefrictionlossisthefluid’sviscosity.
Area A
Area AForce F
d
u = 0
Fig. 6.1 Viscosity
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ExperimentalresultsshowthatforallNewtonianfluids,theslopeofthevelocitydistributionlinei.e.,u/d,correlateswell with and are proportional to the shear rate or stress, i.e.,
The proportionality factor between the two elements is termed as the dynamic or absolute viscosity • such that
Fluid Handling =
Most absolute viscosities are commonly referred to in terms of centipoises (cp), or one hundredth of poise (P), •the metric unit for viscosity. Frequently,measurementsofviscosityaremadewhenthefluidisflowing.Theresultsoobtainedistermedthe•“kinematic”viscosityz.
In the metric system, kinematic viscosity is measured in square centimetres per second, or stokes (St). It is obtained bydividingtheabsoluteviscosityinpoisesbythespecificgravitysofthefluid.Similarly,centipoisesdividedbythespecificgravityiscalledcentistokes(cSt).
6.7 Viscosity ClassificationAllgasesandthegreatmajorityofliquidsareknownastrue,simple,orNewtonianfluids.•Thecriterionforthisclassificationisthattheviscosityofthefluidisapointfunctionofitstemperatureand•pressure only and that it is not affected by the type or amplitude of motion to which it may be subjected or by time. Thus, for a Newtonian liquid, when temperature and pressure remain constant:•
The viscosity or ratio of shear stress to shear rate is a constant for all shear rates. �There is no shear rate only when there is no shear stress. �The viscosity does not change with time. �
Non-Newtonian liquids obviously deviate from Newtonian ones in which they do not follow one or more of •these criteria.
6.8 Types of FluidsFluid can be divided into the following categories:
6.8.1 Newtonian FluidsPlasticsubstanceshavedefiniteyieldstrengthanddonotflowuntilacertaindegreeofshearstresshasbeenapplied.Example: Oil paints
F/A
u/d F/Au/d
Fig. 6.2 Newtonian fluids (a)
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6.8.2 Bingham Plastic Fluids
F/A
u/d F/Au/d
Fig. 6.3 Bingham plastic fluids (b)
6.8.3 Dilatants FluidsDilatantfluidsexhibitanincreaseofviscositywithanincreasingrateofstress.Example:Concentratedsuspensionsof titanium dioxide particles in water.
F/A
u/d u/d F/A
Fig. 6.4 Dilatants fluids (c)
6.8.4 Pseudoplastic FluidsThe viscosity of a Pseudoplastic material decreases with the increase in shear stress. Example: Many solutions of highmolecularweightindustrialpolymersinorganicsolventsbelongtothisclassification.
F/A
u/d u/d F/A
Fig. 6.5 Pseudoplastic fluids (d)
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6.8.5 Thixotropic FluidsThixotropy is the property, exhibited by certain gels and emulsions of becoming more liquid when stirred or shakeni.e.,thestructureofthefluidchangeswithtime.Example:Manydrillingmuds,greasesandinksfallintothis category.
F/A
u/d u/d F/A
θ
θ
θ
θ
θ
Fig. 6.6 Thixotropic fluids (e)
6.8.6 Rheopectic Fluids Theviscosityofrheopecticfluidsisalsoafunctionoftimeandthemannerinwhichtheshearstresswasapplied.Their viscosities remain constant at a given instant of time but are dependent on time. Example: Gelatins.
F/A
u/d u/d F/A
Fig. 6.7 Rheopectic fluids
6.9 Reynolds NumberItexpressestheratioofinertiaforcesofamovingfluidtoitsviscousforcesandwasdevelopedinthelate1800’sbyOsborneReynolds,anEnglishscientist,whowasoneoftheearlierinvestigatorsintothenatureoffluidflow.
Re = Dimensionless number (Reynolds’s number) D = ID of pipe
u = mean liner velocity, ft/h
=fluiddensity,lb/ft3
= absolute viscosity , lbm/(ft – h) Laminar region: Re < 2100 (Independent of /D), = Roughness of pipe
D = ID of pipe/D = Dimensionless
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Critical region: Re 2100 4000 (Independent of /D)Transient + Turbulent : Re + 4000 (Depends on /D)
6.10 Velocity HeadAsignificantconceptinallsituationsinvolvingfluidflowisthatof“velocityhead”.h = u2/2g,where,h=velocityhead,ftfluid,u = mean linear velocity, ft/sg = dimensional constant, 32.17 (lbm/lbf) (ft/s2)
6.11 Friction FactorsThe friction that is developed in a section of a conduit is a function of many variables, some of which are •interrelated. They are:
Mean linear velocity and density or their product, mass velocity. �Pipe diameter or hydraulic radius �Viscosity l �Roughness of conduit �Length of Pipe �
F=frictionloss,ftfluid,f=Moodyfrictionfactor,L=Equivalentlengthofconduit,ft,D=Equivalentdiameterofconduit (ft), u= velocity (ft/s), g = dimensional constant, 32.17 (lbm / lbf) (ft/s2).
6.12 Roughness (ϵ) Roughness is a measure of the height of regular protrusions or unevenness, which extend from the surface of •theconduittodisturbfluidflow.These protrusions can range from 0.001 to 0.01 ft (0.305 to 3.05 mm) for concrete pipe, 0.0005 ft (0.15 mm) •for galvanised -iron pipe, and 0.00015 ft (0.05 mm) for commercial steel pipe. The least roughness is given as 0.000005 ft (1.5n m m) for smooth brass, lead, glass, or some lined pipe. •
6.13 Laminar Flow Friction
TransitionandturbulentflowfrictionfactorsCriticalregion:2-4timesofLaminarflowfrictionfactorTransition and turbulent: Transition: f = 0.316 / (Re) 1/4
(for )
for all Re
Rough turbulent:
/8, shear stress at boundary
= shear stress at distance r from boundary
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6.14 Steps in Line SizingAssume pipe ID say‘d’•Ascertaindensityandviscosityaswellasnatureoffluid(Newtonian/nonNewtonian)•Determine Re•Find • or Use Darcy equation, determine DP•IfDPcalculatedisnotwithin+/-5%ofspecifiedDP,assumenewpipeID•Repeat the procedure till the required convergence is achieved.•When convergence is achieved, select standard pipe ID nearest to and higher than the calculated pipe ID.•
6.15 Newtonian and Non-Newtonian Fluids DP (CGS System)Independent of case.
Newtonian
Q = cm3/s (Flow rate)
L = cm (Length of pipe)R = cm (Radius of pipe)
= dynes/cm2
Non-Newtonian n = Flow behaviour index
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SummaryStandardcommercialpipesizeswereoriginallydefinedbytheAmericanStandardsAssociation(ASA)now•known as the American National Standards Institute (ANSI). Tubing has mechanical characteristics, different from those of pipe and can sometimes be used in place of it •to great advantage. “Waterhammer”isthetermgiventotheforcessetup,shouldthevelocityoftheflowingmediabechanged•suddenly. Besidesinducedflowsbymeansofpumps,compressors,orvacuumdevices,therecanbegravityfloworflow•caused solely by differences in elevation or static pressure between two points in the system. Animportantphysicalpropertyofafluidthatinfluencesthetypeofflowpattern,whichwillbedevelopedina•conduitand,thus,thefrictionloss,isthefluid’sviscosity.Most absolute viscosities are commonly referred to in terms of centipoises (cp), or one hundredth of poise (P), •the metric unit for viscosity. In the metric system, kinematic viscosity is measured in square centimetres per second, or stokes (St).•The viscosity of a Pseudoplastic material decreases with the increase in shear stress.•Roughness is a measure of the height of regular protrusions or unevenness, which extend from the surface of •theconduittodisturbfluidflow.
ReferencesSubramanian, • R.S., Non-Newtonian Flows [Online] Available at: <http://web2.clarkson.edu/projects/subramanian/ch301/notes/nonnewtonian.pdf >. [Accessed 7 April 2011].Rashaida. A., • Flow of a non-Newtonian Bingham plastic fluid over a rotating disk [Online] Available at: <http://www.collectionscanada.gc.ca/obj/s4/f2/dsk3/SSU/TC-SSU-08172005120844.pdf>. [Accessed 7 April 2011].Velocity and pressure drop in pipes• [Online]Availableat:<http://4wings.com/lib/files/velocity_and_pressure_drop_in_pipes.pdf>. [Accessed 7 April 2011].Cornflour, Water and Speakers Non Newtonian Expt 2007,• puddyman, Available at: <http://www.youtube.com/watch?v=GU3fOeDctbY&feature=related>. [Accessed 8 June 2011].King, H.W., Brater, E.F., 1976. • Handbook of Hydraulics, 6th ed., McGraw Hill Book Comnay, New York. Shapiro, A.H., 1953. • The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. I, The Ronald Press Company, New York.
Recommended ReadingDennis Siginer, A., Daniel De Kee and Chhabra, R. P., 1999. • Advances in the Flow and Rheology of Non-Newtonian Fluids, Volume 1. , Elsevier.Böhme Gert., 1987. • Non-Newtonian fluid mechanics, North-Holland.Michel Saad, A., 1993. • Compressible fluid flow, 2nd ed, Prentice Hall.
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Self Assessment
What is Standard Commercial Pipe Size known as?1. copper pipe sizea. steel pipe sizeb. digital pipe sizec. iron pipe sized.
One of the process engineer’s most important tasks in the design of a facility is the ______________of the 2. pipes.
sizinga. cleaningb. cuttingc. breaking d.
Where is the important use of tube made?3. Heat exchangera. Heat transformerb. Heat converterc. Heat changerd.
__________has mechanical characteristics, different from those of pipe.4. Tubing a. Pipingb. Fluidc. Roped.
Theexistenceof________constraintsonfluidsflowinginpipesmustalwaysbekeptinmind.5. fluidflowa. velocityb. sizingc. viscosityd.
Which of the following is true?6. Corrosion allowances are normally used in association with stainless steel or alloy piping.a. Corrosion allowances are not normally used in association with stainless steel or alloy piping.b. Corrosion allowances are normally used in association with alloy piping.c. Corrosion allowances are normally used in association with stainless steel.d.
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Which of the following is true?7. Single phase liquids such as water, hydrocarbons, solutions and others can cause water hammer or erosion a. of the piping.Double phase liquids such as water, hydrocarbons, solutions and others can cause water hammer or erosion b. of the piping.Quarter phase liquids such as water, hydrocarbons, solutions and others can cause water hammer or erosion c. of the piping.Half phase liquids such as water, hydrocarbons, solutions and others can cause water hammer or erosion d. of the piping.
Which of the following is true?8. Apipeofsufficientlysmalldiametermustbechosentomaintainthefrictionlossatareasonablevaluefora. therequiredflow.Apipeofsufficientlymediumdiametermustbechosentomaintainthefrictionlossatareasonablevalueb. fortherequiredflow.Apipeofsufficientlylargediametermustbechosentomaintainthefrictionlossatareasonablevalueforc. therequiredflow.Apipeofsufficientlylargeradiusmustbechosentomaintainthefrictionlossatareasonablevalueforthed. requiredflow.
All gases and the great majority of liquids are known as _________________.9. Newtonianfluidsa. non-Newtonianfluidsb. velocityc. viscosityd.
Theviscosityof_________fluids is alsoa functionof timeand themanner inwhich the shear stresswas10. applied
Newtoniana. rheopecticb. non-Newtonianc. compressiblefluidd.
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Chapter VII
Fluid Piping Systems
Aim
The aim of this chapter is to:
explain pressure drop•
elaborate about valves •
discuss piping system design•
Objectives
The objectives of this chapter are to:
explain steam distribution•
illustrate energy consideration•
list the types of valves•
Learning outcome
At the end of this chapter, you will be able to:
recognise thermal insulation •
identify heat loss from pipe surfaces•
describe economic thickness of insulation•
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7.1 IntroductionSelection of piping system is an important aspect of system design in any energy consuming system. The selection issuessuchasmaterialofpipe,configuration,diameter,insulationetc.havetheirownimpactontheoverallenergyconsumption of the system. Piping is one of those few systems when oversized, will generally save energy; unlike for a motor or a pump.
PipingsystemdesigninhugeindustrialintricatelikeRefineries,Petrochemicals,FertilizerPlantsetcaredonenowa day with the help of design software. It is the relatively small and medium users who generally do not have access to design tools; use various thumb rules for selecting size of pipes in industries. These methods of piping design are basedoneither“workedbefore”or“educatedestimates”.
7.2 Pressure Drop in Components in Pipe SystemsMinor head loss in pipe systems can be expressed as:
Where,
= minor head loss (m)
k=minorlosscoefficientu=flowvelocity(m/s)g= acceleration of gravity (m/s2)Minorlosscoefficientsforsomeofthemostcommonusedcomponentsinpipeandtubesystemsaregivenintablebelow.
Type of Component or Fitting Minor Loss CoefficientK
Flanged Tee, Line Flow 0.2
Threaded Tees, Line Flow 0.9
Flanged Tees, Branched Flow 1.0
Threaded Tees, Branched Flow 2.0
Threaded Union 0.08
Flanged Regular 900 Elbows 0.3
Threaded Regular 900 Elbows 1.5
Threaded Regular 450 Elbows 0.4
Flanged Long Radius 90o Elbows 0.2
Threaded Long Radius 90o Elbows 0.7
Flanged Long Radius 45o Elbows 0.2
Flanged 180o Return Bends 0.2
Threaded 180o Return Bends 1.5
Fully Open Globe Valve 10
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Fully Open Angle Valve 2
Fully Open Gate Valve 0.15
1/4 Closed Gate Valve 0.26
1/2 Closed Gate Valve 2.1
3/4 Closed Gate Valve 17
Forward Flow Swing Check Valve 2
Fully Open Ball Valve 0.05
1/3 Closed Ball Valve 5.5
2/3 Closed Ball Valve 200
Table 7.1 Minor loss coefficients
7.3 ValvesValvesseparate,changeandmanagefluidflowinapipingsystem.Valvescanbeoperatedmanuallywithlevers•and gear operators or remotely with electric, pneumatic, electro-pneumatic, and electrohydraulic powered actuators. Manually operated valves are typically used where operation is rare and/or a power source is not available. •Powered actuators allow valves to be operated automatically by a control system and distantly with push button •stations. Valveautomationbringsmomentousadvantagestoaplantintheareasofprocessquality,efficiency,safety,•and productivity.Types of valves and their features are summarised below.•
7.3.1 Gate Valves
It has a sliding disc (gate) that gives mutually into and out of the valve port. •Gate valves are an ultimate isolation valve for high pressure drop and high temperature applications where •operation is irregular. Manual operation is accomplished through a multi rotational hand wheel gear stream assembly.•Multi rotational electric actuators are typically required to mechanize gate valves, however long stroke pneumatic •and electro-hydraulic actuators are also available.
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Fig. 7.1 Gate valve
Recommended uses:•Fully open/closed, non-throttling �Infrequent operation �Minimalfluidtrappinginline �
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Applications• : Oil, gas, air, slurries, heavy liquids, steam, non-condensing gases, and corrosive liquids
Advantages• High capacity �Tight shutoff �Low cost �Littleresistancetoflow �
Disadvantages•Poor control � Cavitate at low pressure drops �Cannot be used for throttling �
7.3.2 Globe Valves
It has a conical plug, which gives mutually into and out of the valve port. Globe valves are idyllic for shutoff •as well as for controlling service in high pressure drop and high temperature applications. Available in globe, angle, and y-pattern designs. •Manual operation is accomplished by a multi-turn hand wheel assembly.•Multiturn electric actuators are typically required to automate globe valves. However, linear stroke pneumatic •and electrohydraulic actuators are also available.
Steam
Bonnet
Disc
Wheel
Fig. 7.2 Globe valve
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Recommended uses•Throttlingservice/flowregulation �Frequent operation �
Applications •Liquids �Vapours �Gases �Corrosive substances �Slurries �
Advantages •Efficientthrottling �Accurateflowcontrol �Available in multiple ports �
Disadvantages•High pressure drop �More expensive than other valves �
7.3.3 Ball Valves
Ball Valves were a welcome support to the process industry. •They provide tight shutoff and high capacity with just a quarter-turn to operate. Ball valves are now more •common in 1/4”-6” sizes.Ball valves can be easily activated with pneumatic and electric actuators.•
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Handle with Arrow•Indicatesflowdirection•allowsquickoperationtoopenandclose
Panel Mounting Nut•alloweasyinstallation
Variety of end Connections•Includefraction/metric VE-locktubefitting,NPTfemale, ISO female threads
Body pattern•Isavailableinstraightandangle•isavailablein3-wayand4-way
Orifice•Isoptimizeddesignfor
minimum pressure drop
Integral Ball Steam•Ismechanisedfromonepiece•isbestsuitedtoencapsulateballseats
Metal Supports •preventcoldflowof PTFEintoOrifice
Packing Bolt•allowseasypacking
adjustment with valves in-line
PTFE packing•issupportedbytop
and bottom glands
Encapsulating ball seats•Virtuallyallownodeedvolume•areuniformlyforcedtoformtight
seals against ball and body cavity
Fig. 7.3 Ball valve(Source: http://t1.gstatic.com/images?q=tbn:ANd9GcTp9-PcnNlvqXmFCEbrZKnYiiqeirtowLKBJiKFuT2ORXJ
HXIdR)
Recommended uses•Fully open/closed, limited-throttling �Highertemperaturefluids �
Applications• Most liquids �high temperatures �slurries �
Advantages •Low cost �High capacity �Tight sealing with low torque �
Disadvantages•Poor throttling characteristics �Prone to cavitations �Low leakage and maintenance �
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7.3.4 Butterfly Valve
Butterflyvalvesarecommonlyusedascontrolvalvesinapplicationswherethepressuredropsrequiredofthe•valvesarerelativelylow.Butterflyvalvescanbeusedinapplicationsaseithershutoffvalves(on/offservice)orascontrollingvalves(forfloworpressurecontrol).Likeshutoffvalves,butterflyvalvesofferadmirableperformancewithintherangeoftheirpressurerating.•Typical useswould include isolation of equipment, fill/drain systems, and bypass systems and other like•applicationswheretheonlycriterionforcontroloftheflow/pressureisthatitbeonoroff.Althoughbutterflyvalveshaveonlyalimitedabilitytocontrolpressureorflow,theyhavebeenwidelyusedas•control valves because of the economics involved. Thecontrolcapabilitiesofabutterflyvalve• canalsobesignificantlyimprovedbycombiningitwithanoperatorand electronic control package.
Lever
Disc
Fig. 7.4 Butterfly valve
Recommended uses•Fully open/closed or throttling services �Frequent operation �Minimalfluidtrappinginline �
Applications •Liquids �gases �slurries �liquids with suspended solids �
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Advantages •Low cost and maintainance �High capacity �Goodflowcontrol �Low pressure drop �
Disadvantages•High torque required for control �Pronetocavitationsatlowerflows �
7.4 Piping System DesignThere are two basic systems for distribution system:
A single line from the supply to the point(s) of usage, also known as radial system.•Ring main system, where supply to the end use is taken from a closed loop header. The loop design allows •airflowintwodirectionstoapointofuse.Thiscancuttheoverallpipelengthtoapointinhalfthatreducespressure drop. It also means that a large volume user of compressed air in a system may not starve users downstream since they can draw air from another direction. In many cases a balance line is also recommended whichprovidesanothersourceofair.Reducingthevelocityoftheairflowthroughthecompressedairpipingsystemisanotherbenefitoftheloopdesign.Thisreducesthevelocity,whichreducesthefrictionagainstthepipe walls and reduces pressure drop.
Plate 5
PIPE GUIDE
EXPANSION JOINTS
SOLID FOUNDATION
TEE SUPPORT ANCHOR TO BASE
ELBOW SUPPORT
ANCHOR TO BASE
Fig. 7.5 Types of piping layout(Source: http://t2.gstatic.com/images?q=tbn:ANd9GcR9SYqE-aUStGmQG_IajObO8U9h3G_
vmIE2Xj1ffIwCFbsaETBwRA)
7.5 Steam DistributionThe objective of the steam distribution system is to supply steam at the correct pressure to the point of use. •It follows; therefore, that pressure drop through the distribution system is an important feature.•One of the most important decisions in the design of a steam system is the selection of the generating, distribution, •and utilisation pressures.The piping system distributes the steam, returns the condensate, and removes air and non-condensable gases. •
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In steam heating systems, it is important that the piping system distribute steam, not only at full design load, •but also at partial loads and excess loads that can occur on system warm-up.When the system is warming up, the load on the steam mains and returns can exceed the maximum operating •load for the coldest design day, even in moderate weather. This load comes from raising the temperature of the piping to the steam temperature and the building to the •indoor design temperature.
7.6 Energy ConsiderationsSteam and condensate piping system have a great impact on energy usage. •Proper sizing of system components such as traps, control valves, and pipes has a tremendous effect on the •efficienciesofthesystem.Condensate is a by-product of a steam system and must always be removed from the system as soon as it •accumulates, because steam moves rapidly in mains and supply piping, and if condensate accumulates to the point where the steam can push a slug of it, serious damage can occur from the resulting water hammer. Pipe insulationalsohasatremendouseffectonsystemenergyefficiency.All steam and condensate piping should be insulated. It may also be economically wise to save the sensible heat •ofthecondensateforboilerwatermake-upsystemsoperationalefficiency.Oversized pipe work means:•
Pipes,valves,fittings,etc.willbemoreexpensivethannecessary. �Higher installation costs will be incurred, including support work, insulation, etc. �For steam pipes a greater volume of condensate will be formed due to the greater heat loss. �
This, in turn, means that either:•more steam trapping is required �wet steam is delivered to the point of use �
Undersized pipe work means:•A lower pressure may only be available at the point of use. �This may hinder equipment performance due to only lower pressure steam being available. �There is a risk of steam starvation. �There is a greater risk of erosion, water hammer and noise due to the inherent increase in steam velocity. �
7.7 Thermal InsulationThere are many reasons for insulating a pipeline, most important being the energy cost of not insulating the •pipe. Enough thermal insulation is essential for conserving both heat loss from hot surfaces of ovens/furnaces/piping •and heat gain in refrigeration systems. Inadequate thickness of insulation or fall of existing insulation can have a major impact on the energy •consumption. The material of insulation is also important to attain low thermal conductivity and also low thermal inertia.•The simplest method of evaluate whether to use 1” or 2” or 3” insulation is by comparing the cost of energy •losses with the cost of insulating the pipe. The insulation thickness, for which the total cost is minimum, is expressed as economic thickness. Refer to •fig.7.6.The curve representing the total cost reduces initially and after reaching the economic thickness equivalent to •the minimum cost, it increases.
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Fig. 7.6 Economic insulation thickness
7.8 Heat Losses from Pipe SurfacesHeat loss from 1/2” to 12” steel pipes at various temperature differences between pipe and air can be found in the table below.
Nominal bore Temperature Difference (0C)
(mm) (inch) 50 60 75 100 110 125 140 150 165 195 225 280
15 ½ 30 40 60 90 130 155 180 205 235 280 375 575
20 ¾ 35 50 70 110 160 190 220 255 290 370 465 660
25 1 40 60 90 130 200 235 275 305 355 455 565 815
32 1 ¼ 50 70 110 160 240 290 330 375 435 555 700 1000
40 1 ½ 55 80 120 180 270 320 375 420 485 625 790 1120
50 2 65 95 150 220 330 395 465 520 600 770 975 1390
65 2 ½ 80 120 170 260 390 465 540 615 715 910 1150 1650
80 3 100 140 210 300 470 560 650 740 860 1090 1380 1980
100 4 120 170 260 380 5850 700 820 925 1065 1370 1740 2520
150 6 170 250 370 540 815 970 1130 1290 1470 1910 2430 3500
200 8 220 320 470 690 1040 1240 1440 1650 1900 2440 3100 4430
250 10 270 390 570 835 1250 1510 1750 1995 2300 2980 3780 5600
300 12 315 460 670 980 1470 1760 2060 2340 2690 3370 4430 6450
Table 7.2 Heat loss from Fluid inside Pipe (W/m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ann
ual c
osts
, Rs
Insulation thickness in mm
Combined costs
Fuel cost due to loss
Depreciation cost of insulation
3
2
1
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The heat loss value must be corrected by the correction factor for certain applications:•
Application Correction FactorSingle pipe freely exposed 1.1More than one pipe freely exposed 1.0More than one pipe along the ceiling 0.65Single pipe along the skirting or riser 1.0More than one pipe along the skirting or riser 0.90Single pipe along ceiling 0.75
Table 7.3 Correction factor
7.9 Calculation of Insulation ThicknessThe most basic model for insulation on a pipe is shown below:
r1 shows the outside radius of the pipe. r2 shows the radius of the Pipe + insulation.•Heat loss from a surface is expressed as:•
H = h X A x (Th-Ta)
Where,h=Heattransfercoefficient,W/m2-KH = Heat loss, WattsTa = Average ambient temperature, KTs = Desired/actual insulation surface temperature, ºCTh=Hotsurfacetemperature(forhotfluidpiping),ºC&Coldsurfacetemperatureforcoldfluidspiping)
For Temperature to 2100F Above and Below ground
Hot Water CondensateChilled WaterFuel OilProcess Piping
Polyurethane Foam Insulation
Steel Carrier Pipe as specified
HDPE Jacket
Fig. 7.7 Insulated pipe section(Source: http://t2.gstatic.com/images?q=tbn:ANd9GcQ--XPx9vc89iorU2kc3pQF3ZQJizQqv0hdeelYIDVPRsFfozkwjQ)
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Forhorizontalpipes,heattransfercoefficientcanbecalculatedby:•h = (A + 0.005 (Th – Ta)) x 10 W/m2-KFor vertical pipes,h = (B + 0.009 (Th – Ta)) x 10 W/m2-KUsingthecoefficientsA,Basgivenbelow:•
Surface ε A B
Aluminum, bright rolled 0.05 0.25 0.27
Aluminum, oxidized 0.13 0.31 0.33
Steel 0.15 0.32 0.34
Galvanized steel metal 0.44 0.53 0.55
Non metallic surfaces 0.95 0.85 0.87
Table 7.4 Coefficients A, B for estimating ‘h’ (in W/m2-K)
Tm =
k = Thermal conductivity of insulation at mean temperature of Tm, W/m-Ctk = Thickness of insulation, mmr1 = Actual outer radius of pipe, mmr2 = (r1 + tk)
Rs = Surface thermal resistance = ºC-m2/W
Rl = Thermal resistance of insulation = ºC-m2/W
TheheatflowfromthepipesurfaceandtheambientcanbeexpressedasfollowsH=Heatflow,Watts
= =
From the above equation, and for desired Ts, Rl can be calculated. From Rl and known value of thermal conductivity k, thickness of insulation can be calculated.
Equivalent thickness of insulation for pipe,
7.10 Insulation MaterialInsulationmaterialsareclassifiedintoorganicandinorganictypes.•
Organic insulations are based on hydrocarbon polymers, which can be expanded to obtain high void structures. �Examples are thermocol (Expanded Polystyrene) and Poly Urethane Form (PUF). Inorganic insulation isbasedonSiliceous/Aluminous/Calciummaterials infibrous,granularorpowder �forms. Examples are Mineral, wool, Calcium silicate etc.
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Properties of common insulating materials are as under:•Calcium Silicate: Used in industrial process plant piping where high service. temperature and compressive �strength is needed. Temperature ranges varies from 40°C to 950°C.Glassmineralwool:Theseareavailableinflexibleforms,rigidslabsandpreformedpipeworksections. �Good for thermal and acoustic insulation for heating and chilling system pipelines. Temperature range of application is –10 to 500°C.Thermocol: These are mainly used as cold insulation for piping and cold storage construction. �Expandednitrilerubber:Thisisaflexiblematerialthatformsaclosedcellintegralvapourbarrier.Originally �developed for condensation control in refrigeration pipe work and chilled water lines; now-a days also used for ducting insulation for air conditioning.Rock mineral wool: This is available in a range of forms from light weight rolled products to heavy rigid �slabs including preformed pipe sections. In addition to good thermal insulation properties, it can also provide acousticinsulationandisfireretardant.
The thermal conductivity• of a material is the heat loss per unit area per unit insulation thickness per unit temperature difference. The unit of measurement is W-m• 2/m°CorW-m/°C.The thermal conductivity ofmaterials increaseswithtemperature. Sothermalconductivityisalwaysspecifiedatthemeantemperature(meanofhotandcoldfacetemperatures)•of the insulation material.Thermal conductivities of typical hot and cold insulation materials are given below:•
Mean Temperature °C Calcium Silicate Resin bonded mineral wool
Ceramic Fiber Blan-kets
100 - 0.04 -200 0.07 0.06 0.06300 0.08 0.08 0.07400 0.08 0.11 0.09700 - - 0.171000 - - 0.26
Table 7.5 Thermal conductivity of hot insulation
Materials Thermal Conductivity W/m – 0CMineral or Glass Fiber Blanket 0.039
Board or SlabCellular Glass 0.058Cork Board 0.043Glass Fiber 0.036Expanded Polystyrene (smooth) – Thermocole 0.029Expanded Polystyrene (Cut Cell) – Thermocole 0.036Expanded Polyurethane 0.017Phenotherm (Trade Name) 0.018
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Loose FillPaper or Wood Pulp 0.039Sawdust or Shavings 0.065Minerals Wool (Rock, Glass, Slag) 0.039Wood Fiber (Soft) 0.043
Table 7.6 Specific thermal conductivity of materials for cold insulation
7.11 Economic Thickness of InsulationTo explain the concept of economic thickness of insulation, we will use an example. •
Consider an 8 bar steam pipeline of 6” dia having 50-meter length. We will evaluate the cost of energy losses �whenweuse1”,2”and3”insulationtofindoutthemosteconomicthickness.Astep-by-stepprocedureisgiven below:
Establish the bare pipe surface temperature, by measurement.1. Note the dimensions such as diameter, length & surface area of the pipe section under consideration.2. Assumeanaverageambienttemperature.Here,wehavetaken30°C.3. Since we are doing the calculations for commercially available insulation thickness, some trial and error 4. calculations will be required for deciding the surface temperature after putting insulation. To begin with assume avaluebetween55&65°C,whichisasafe,touchtemperature. Select an insulation material, with known thermal conductivity values in the mean insulation temperature range. 5. Herethemeantemperatureis111°C.andthevalueofk=0.044W/m2-°Cformineralwool.Calculatesurfaceheattransfercoefficientsofbareandinsulatedsurfaces.Calculatethethermalresistanceand6. thickness of insulation. Select r2 such that the equivalent thickness of insulation of pipe equals to the insulation thickness estimated in 7. step 6. From this value, calculate the radial thickness of pipe insulation = r2-r1. Adjust the desired surface temperature values so that the thickness of insulation is close to the standard value 8. of 1” (25.4 mm). Estimate the surface area of the pipe with different insulation thickness and calculate the total heat loss from 9. thesurfacesusingheattransfercoefficient,temperaturedifferencebetweenpipesurfaceandambient. Estimate the cost of energy losses in the 3 scenarios. Calculate the Net Present Value of the future energy costs 10. during an insulation life of typically 5 years.Find out the total cost of putting insulation on the pipe (material + labour cost)11. Calculate the total cost of energy costs and insulation for 3 situations.12. Insulation thickness corresponding to the lowest total cost will be the economic thickness of insulation.13.
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Insulation Thickness
Description Unit 1” 2” 3”
Length of pipe, L m 50 50 50
Bare pipe outer diameter, d1 mm 168 168 168
Bare pipe surface area, A m2 26.38 26.38 26.38
Ambient temperature, Ta: 0C 30 30 30
Bare pipe wall temperature, Th: 0C 160 160 160
Desired Wall Temperature With Insulation, Tc: 0C 62 48 43
Material of Insulation: Mineral Wool
Mean Temperature of Insulation, Tm = (Th+Tc)/2 0C 111 104 101.5
Ap. Conductivity of Insulation Material, k (from catalogue) W/m 0C 0.044 0.042 0.04
Surface Emissivity of Bare pipe: 0.95 0.95 0.95
Surface emissivity of insulation cladding (typically Al) 0.13 0.13 0.13
Table 7.7 Economic insulation thickness calculations
7.11.1 Calculations
SurfaceHeatTransferCoefficientofHotBareSurface,h:(0.85+ 0.005 (Th – Ta)) x 10 W/m2°C 15 15 15
SurfaceHeatTransferCoefficientAfterInsulation,h’=(0.31+ 0.005 (Tc – Ta)) x 10 W/m2°C 4.7 4 3.75
Thermal Resistance, Rth = (Th-Tc)/[h’x (Tc-Ta)] : °C-m2/W 0.7 1.6 2.4
Thickness of Insulation, t = k x Rth:(ifsurfacewasflat) mm 28.7 65.3 96.0
r1=outer diameter/2 = mm 84 84 84
teq = r2 x ln(r2/ r1) = ( select r2 so that teq = t) mm 28.7 65.3 106.3
Outer radius of insulation , r2= mm 109.2 135.9 161.9
Thickness of insulation mm 25.2 51.9 77.9
Insulated pipe Area , A : m2 34.29 42.66 50.85
Total Losses From Bare Surface, Q = h x A x (Th-Ta): kW 51.4 51.4 51.4
Total Loss From Insulated Surface, Q’ = h’ x A’ x (Tc-Ta) : kW 5.16 3.07 2.48
Power Saved by Providing Insulation, P = Q-Q’ : kW 46.3 48.4 49.0
Annual Working Hours, n : Hrs 8000 8000 8000
Energy Saving After Providing Insulation, E = P x n : kWH/year 370230 386892 391634
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7.11.2 Economics
Steam Costs, Rs/Kg 0.070 0.70 0.70
Heat Energy Costs, p: Rs./kWH 1.11 1.11 1.11
Annual Monetary Saving, S = E x p : Rs. 412708 431313 436599
Discount factor for calculating NPV of cost of energy loss % 15% 15% 15%
Cost of insulation (material + labour) Rs/m 450 700 1100
Total cost of insulation Rs/m 22500 35000 55000
Annual Cost of energy loss Rs/year 46000 27395 22109
NPV of annual cost of energy losses for 5 years Rs 154198 91832 74112
Total cost (insulation & NPV of heat loss) Rs 176698 126832 129112
Note: the total cost in lower when using 2” insulation, hence is the economic insulation thickness.•
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SummarySelection of piping system is an important aspect of system design in any energy consuming system.•Valvesisolate,switchandcontrolfluidflowinapipingsystem.•Manually operated valves are typically used where operation is infrequent and/or a power source is not •available. Gate valves are an ideal isolation valve for high pressure drop and high temperature applications where operation •is infrequent. A single line from the supply to the point(s) of usage, also known as radial system.•The objective of the steam distribution system is to supply steam at the correct pressure to the point of use. •All steam and condensate piping should be insulated.•Adequate thermal insulation is essential for preventing both heat loss from hot surfaces of ovens/furnaces/piping •and heat gain in refrigeration systems. Insulationmaterialsareclassifiedintoorganicandinorganictypes.•
ReferencesDevki Energy Consultancy Pvt. Ltd., 2006, • Best Practice Manual-Fluid Piping [Online] Available at :< http://www.energymanagertraining.com/CodesandManualsCD-5Dec%2006/BEST%20PRACTICE%20MANUAL-FLUID%20PIPING.pdf>. [Accessed 7 April 2011].Rashaida. A., • Flow of a non-Newtonian Bingham plastic fluid over a rotating disk [Online] Available at :< http://www.collectionscanada.gc.ca/obj/s4/f2/dsk3/SSU/TC-SSU-08172005120844.pdf>. [Accessed 7 April 2011].Velocity and pressure drop in pipes• [Online]Availableat:<http://4wings.com/lib/files/velocity_and_pressure_drop_in_pipes.pdf> [Accessed 7 April 2011].Fireman,• 2003,puddyman,Availableat:<http://www.tpub.com/fireman/69.htm>.[Accessed15June2011].
Recommended ReadingKing, R.P., 2002, • Introduction to Practical Fluid Flow, Butterworth-Heinemann.Granger, R.A., 1985, • fluid mechanics, Dover publication. Inc, United States of America.Michel Saad, A., 1993, • Compressible fluid flow, 2nd ed, Prentice Hall.Cengel, Y. A, Cimbala J, M., 2006, • Fluid Mechanics, Tata McGraw Hill, India.
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Self Assessment
_______ is one of those few systems when oversized, will generally save energy.1. Fluida. Piping b. Controllingc. Evaluatingd.
Which device allows valves to be operated automatically?2. Powered actuatorsa. Controllersb. Fluidc. Pipelined.
Which valve is an ultimate isolation valve for high pressure drop?3. Ball Valvea. Gate Valveb. Globe Valvec. ButterflyValved.
__________ are commonly used as control valves in applications where the pressure drops required of the 4. valves are relatively low.
Globe Valvea. Gate Valveb. ButterflyValvec. Ball Valved.
A single line from the supply to the point(s) of usage, also known as ___________.5. radial systema. ring main systemb. pressure drop systemc. piping system d.
The_____________allowsairflowintwodirectionstoapointofuse.6. pipe design a. loop designb. fluiddesignc. pipeline designd.
What is required to mechanise gate valve?7. Multi rotational electric actuatorsa. Single rotational electric actuatorsb. Bi- rotational electric actuatorsc. Hierarchical rotational electric actuatorsd.
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State which of the following is true.8. Globe valve has a square plug.a. Globe valve has a rectangular plug.b. Globe valve has a round plug.c. Globe valve has a conical plug.d.
State which of the following is true.9. Butterflyvalvesarecommonlyusedasdestructivevalvesinapplicationswherethepressuredropsrequireda. of the valves are relatively low.Butterflyvalvesarecommonlyusedascontrolvalvesinapplicationswherethepressuredropsrequiredofb. the valves are relatively high.Butterflyvalvesarecommonlyusedascontrolvalvesinapplicationswherethepressuredropsrequiredofc. the valves are relatively low.Butterflyvalvesarenotusedascontrolvalves inapplicationswhere thepressuredropsrequiredof thed. valves are relatively low.
The insulation thickness for which the total cost is minimum is expressed as _________ thickness.10. unwanteda. economicb. expansivec. measurabled.
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Case Study I
Refinery Leverages Ultrasonic Flowmeter for LNG Custody Transfer
Cameron Measurement Systems’ LNG meter, the Caldon eight-path LEFM 280CLT, has proven itself to be an important technology on the world stage. Several years ago, it was chosen over several other competitive technologies tobeusedatQatargas’sRasLaffanLNGrefinery,oneofthelargestintheworld.AgroupoftheLEFMmetershas been successfully operating at the facility since then, and several more are scheduled to be installed in the near future.
Natural gas can be transported by specially designed tankers when the gas has been converted into liquid form, knownasLiquefiedNaturalGas(LNG).LNGisprocessedfromnaturalgasbyremovingtheheaviercompoundsand unwanted gases, such as CO2 and H2S,beforecoolingtheremainingleangasdowntoatemperatureof161°C,at which point the gas will be in liquid form. LNG takes up around 1/600th the volume of natural gas, making it ideal for transportation over long distances by sea tanker. The liquid is kept cold by insulating the storage or transportation tanks,andalsobythe“boiloff,”whichremovesheatfromtheliquidandkeepsthetemperaturelow.
Cameron is one of the meters supplied for the Qatar Gas II project, one of the world’s largest LNG projects to date. Qatargas and sister company RasGas are expanding their capacities with the addition of four new trains. Cameron has supplied RasGas and Qatargas with a total of 22 LEFM 280CiLT eight-path meters in eight-inch and 10-inch sizes. This meter is installed, but the insulation has been removed. Since there is no ice on the meter, there is no LNGflowinginthelineandthemeterisatatmospherictemperature.
When transporting LNG by sea, the primary measurement of loading is by the ship’s tank gauging systems. Until now,ithasnotbeenthepracticetousedynamicflowmeasurementforLNGincustodytransfer,dueprimarilytothepotentialflashingofthegascausedbythepressuredropacrossthemeter.Thisalsoincludestheuseofflowconditioning devices normally associated with custody-transfer metering. In 2006, Caldon Ultrasonics was selected to take part in a study to determine the suitability of ultrasonic technology in LNG service. A Caldon eight-path LEFM 280CLT was tested along with two Coriolis meters from different manufacturers in an installation without theuseofaflowconditioningdeviceandwithpipeworkdesignedspecificallytogenerateasymmetricandswirlingflow.TheresultsshowedthattherewaslittletodifferentiatebetweentheultrasonicmeterandtheCoriolismetersintermsofperformance,buttheultrasonicmeter’sabilitytohandlenon-idealflowswithminimumpressuredropmadeitaparticularlygoodfitfortheexpansionprojectatRasLaffan,Qatar.
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Qatargas and sister company RasGas are expanding their production capacities with the addition of four new trains, each capable of producing 7.8 MTPA of LNG. The natural gas being fed to these new trains is from different customers. Rather than building dedicated storage tanks for each stream, the project decided upon a common storage tank area for each of these trains with dynamic measurement of the LNG both for production and inter-tank transfers to provide the operators with allocation and mass balance information. Cameron Caldon meter has supplied both Qatargas and RasGas a total of 22 LEFM 280CLT meters in eight-inch and ten-inch sizes. Of these 22, all but six are in operation with the remainder due to be commissioned later this year.
Questions:Write a short note on transport of natural gas.1. WhyusingdynamicflowmeasurementforLNGincustodytransferwasnotinpractice?2. What was the result of testing of a Caldon eight-path LEFM 280CLT along with two Coriolis meters from 3. different manufacturers in an installation?
AnswersNatural gas can be transported by specially designed tankers when the gas has been converted into liquid form, 1. knownasLiquefiedNaturalGas(LNG).LNGisprocessedfromnaturalgasbyremovingtheheaviercompoundsand unwanted gases, such as CO2 and H2S, before cooling the remaining lean gas down to a temperature of 161°C,atwhichpointthegaswillbeinliquidform.LNGtakesuparound1/600th the volume of natural gas, making it ideal for transportation over long distances by sea tanker. The liquid is kept cold by insulating the storageortransportationtanks,andalsobythe“boiloff,”whichremovesheatfromtheliquidandkeepsthetemperature low.
DynamicflowmeasurementforLNGincustodytransferwasnotinpracticeduetothepotentialflashingofthe2. gas caused by the pressure drop across the meter.
A Caldon eight-path LEFM 280CLT was tested along with two Coriolis meters from different manufacturers 3. inaninstallationwithouttheuseofaflowconditioningdeviceandwithpipeworkdesignedspecificallytogenerateasymmetricandswirlingflow.Theresultsshowedthattherewaslittletodifferentiatebetweentheultrasonic meter and the Coriolis meters in terms of performance, but the ultrasonic meter’s ability to handle non-idealflowswithminimumpressuredropmadeitaparticularlygoodfitfortheexpansionprojectatRasLaffan, Qatar.
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Case Study II
Characterisation of Newtonian Fluid Flow in Variable Cross-Section Micro channels: With Application in Flow Regulation Devices
Presentstudyismotivatedbytheapplicationofvariablecross-sectionmicrochannelsinflowregulationdevicesin which variable-cross-section micro channel can be used to alter the shear rate and viscous dissipation of a non-Newtonianfluidalongthechannel.Duetotheavailablefabricationtechniques,awidevarietyofchannelcross-sectionshave been utilised. For instance, micro channels fabricated by the etching technique in silicon have trapezoidal or rectangular cross-sections depending on the orientation of the silicon crystal planes. Soft lithography and replica molding in poly (dimethylsiloxane) (PDMS) result in almost rectangular cross-sections. CO2 laser ablation in acrylic plastics (PMMA) and PDMS leads to triangular like cross-section with rounded corners. This indicates the need for abetterunderstandingoftheflowinvaryingcross-sectionmicrochannelswithvariouscross-sections.
Fig. 1 (a) Schematic illustration of a slowly-varying channel of arbitrary cross-section (b) A reference straight channel with the same cross-sectional shape
Thepressuredropofsinglephaseflowinslowlyvaryingchannelsofarbitrarycross-sectionshowninfig.1aisanalyticallyinvestigatedinthiswork.Thereferencestraightchannelshowninfig.1-bisusedtonormalisetheresults.Newtonianfluidwithconstantpropertiesisconsideredthroughoutouranalysisforthesakeofsimplicityand the effect of viscous heating is neglected. An approximate model for the pressure drop is developed. It has been shown that the total pressure drop and the axial velocity distribution are functions of both frictional and inertia forces for medium Reynolds numbers; while for thecreepingflow,i.e.,streamwiseperiodicgeometries,theeffectsoftheinertialforcescanbeneglected.Althoughthe proposed approach is general, compact relationships are proposed for common channel geometries including rectangular and trapezoidal cross-sections. Two typical wall shapes of stream wise periodic linear and hyperbolic
(b)
(a)
r0
r(x)
g(x)
τ(x)
dx
A(x)
A0
x
x
z
z
y
y
L
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contraction are studied as examples to demonstrate the validity of our model. Fig. 2 shows the geometrical parameters oflinearandhyperbolicwallprofiles.ForastreamwiseperiodicgeometryshowninFigure2-a,ourmodelshowsthattheinertialeffectcanbeeffectivelyneglectedandthefrictionaltermhassignificanteffectonthetotalpressurelossofthechannel.Forthehyperbolicconvergingchannel,showninfig.2-b,theinertialtermissignificantandisa function of inlet and outlet cross-sectional area, a0/L and the Reynolds number.
Fig. 2 Studied wall geometries (a) Stream wise periodic geometry with linear wall and
(b) Hyperbolic contraction
To validate the proposed relationships, an independent numerical study is performed. Commercial mesh generator software, Gambit, is used to generate the numerical domain and a CFD solver, Fluent, is used for the simulation of laminarflow.Pressuredropdataobtainedfromthenumericalsimulationiscomparedagainstthatofcalculatedfromthecompactrelationships.Fig.3showsatypicalvelocitydistributionindifferenceplanesalongtheflowdirectionforcreepingflow.ItcanbeobservedthatforlowReynoldsnumbers,thevelocitydistributionresemblesfullydevelopedflowinastraightchannelofrectangularcross-section.Ourresultsshowthatthemaximumpressuregradientoccursatthesmallestcross-section,i.e.,thechannelthroat.Moreover,flowreversalisobservedwhenthechannelcross-sectionincreasesalongtheflowdirection(adivergingchannel)orwhentheReynoldsnumberincreases.Effectofwallprofileontheshearrateisalsoinvestigatedanditisshownthatbychangingthewallprofile;localshearrateat each axial location can be assigned.
ZY X
Fig. 3 Typical velocity distribution in difference planes along the flow direction for creeping flow
Questions:Whatistheresultofapplicationofvariablecross-sectionmicrochannelsinflowregulationdevices?1. How local shear rate at each axial location can be assigned?2. WriteanoteonNewtonianfluid.3.
L δ
(a) (b)
a0 a0aminamax amax
flow
L
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Case Study III
Particles from Piping Pose Pump Problems
RECSolarGradeSiliconLLCistheworld’sfirstdedicatedproducerofpolycrystallinesiliconformakingsolarpanels. In early 2009 the company’s plant at Moses Lake, Wash., started experiencing premature failures of its magnetic-drive pumps. The failures were blamed on ferrous metal (black powder) contamination in the piping system delivering trichlorosilane and dichlorosilane chemicals. Black powder buildup was evident (Figure 1).Each magnetic drive pump handled approximately 900 gpm of trichlorosilane and dichlorosilane supplied by 10-in.-diameter carbon steel pipe. Black powder contamination originated from corrosion and erosion of the pipelines. Someofthefineferrouspowdercouldgetmagneticallytrappedintheimpellerdrive,causingprematurewearofthejournal bearings, internal shaft, impeller and magnet carrier. The material also could compromise product purity.
Fig. 1 Black powder buildupMagnetic-drivepumpcomponentsshowedsignificantdepositsoffineferrousmaterial.
Black powder ranges from 100 microns or more to sub-micron in size and typically contains 80% ferrous metals, 16%–18% silica, with the remainder other minerals. REC Solar Grade Silicon is hardly alone in having to contend withthematerial.Blackpowdercausesmanycostlyproblemsintheprocessingandrefiningindustries--suchasproduct degradation and premature wear of rotating equipment (pumps, turbine and compressor components, etc.). Italsoafflictspipelines;fluidinthepipelinepicksupmetalcontaminants,whichthenactlikesandpapertocreatemoreferrousparticulate.“Wehaveseensituationswherethereissomuchblackpowderinalinethattraditionalfiltersbecomeclogged,pipelineflowis reducedandmetersbecomeplugged thereby increasingdowntimeandreducing production values,” notes Roger Simonson, president of One Eye Industries, Calgary, AB.
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The plant contacted One Eye Industries, which recommended and supplied three magnetic-separator basket strainers for installation immediately ahead of the pumps. These strainers feature oversized housings to allow maximum exposureoftheirpatentedmagnetictechnology.Thedesignensuresefficientcontaminationremovalfromhighflowandviscousfluidswithminimalflowrestriction.OneEyeIndustriesistheonlycompanythatcurrentlyemploysthis type of magnetic technology for contamination removal. The basket strainers are inexpensive and typically pay for themselves in a month.
Fig. 2 Effective removalThe magnetic separators captured a substantial amount of contamination in just three days.
In just three days, the magnetic separators eliminated the majority of ferrous and non-ferrous contamination from thechemicalstream(figure2).“Uponopening thebasketstrainerwewerequiteamazed tosee theamountofcontamination trapped by the magnetic separators -- not only did [they] remove ferrous material but we also noticed non-ferrous material captured by the magnetic separators,” says Michael A. VanDeVanter, reliability engineer at the Moses Lake plant. Figure 3 shows the non-ferrous contamination, which is trapped on the magnetic separators by static adhesion. Flow inside the pipeline creates a static charge on the non-ferrous materials. When exposed totheseparator’spowerfulmagneticfields,theyarepulledoutofthefluidandtrappedonthemagneticseparatorelement.
Tofurtherevaluateefficiencyofthemagneticseparators,fluidsamplesweretakenupstreamanddownstreamofastrainer.Analysisshowedsubstantialremovalofferrousmaterialandasignificantreductioninchromium,nickeland iron.
Despite contamination removal, pump failures continued. This led to identifying that a seal within the drives was inadequatefortheapplication.Becausethepumpswerestillunderwarranty,thevendornowisworkingtofindasuitable replacement.
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Fig. 3 Non-ferrous contaminationFlow inside pipeline creates a static charge on non-ferrous materials, which then are trapped on magnetic
separator by static adhesion.
However, ferrous contamination certainly remains an issue — because of concerns about serious wear on magnetic-drive components and purity problems for the chemical within the production process. So, the Moses Lake plant continues to rely on the strainers. The plant cleans them monthly.
(Source: Rob Albee, One Eye Industries. Available at: <http://www.chemicalprocessing.com/articles/2010/036.html> [Accessed 9 May 2011])
Questions:What was the main behind premature failures of magnetic-drive pumps at REC Solar Grade Silicon LLC?1. What One Eye Industries recommended for overcoming the problem of failures of magnetic-drive pumps?2. Considering the situation, what piping material would you recommend to avoid future problems?3.
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Bibliography
ReferencesAhmed, W. H., • Innovative Techniques for Two-Phase Flow Measurements, [Online] Available at: http://www.benthamscience.com/eeng/samples/eeng%201-1/Ahmed.pdf> [Accessed 18tApril 2011]. Antaki, G. A., 2003. • Piping and pipeline engineering: design, construction, maintenance, integrity, and repair, Marcel Dekker, pp. 38-46.Chhabra, R. P., & Richardson, J. F., 2008. • Non-Newtonian flow and applied rheology: engineering applications, 2nd ed., Butterworth-Heinemann, pp. 1-14, 18-37. Corradini, M. L., Available at: <http://wins.engr.wisc.edu/teaching/mpfBook/node1.html>. [Accessed 18th •April 2011].Ferry, J. D., 1980. • Viscoelastic properties of polymers, 3rd ed., John Wiley and Sons, pp. 315-320.Fluid piping systems & insulation• , Available at: <http://www.energymanagertraining.com/bee_draft_codes/best_practices_manual-PIPING.pdf>. [Accessed 12 April 2011].Mo Mohitpour, Hossein Golshan, Matthew Alan Murray, 2007, • Pipeline design & construction: a practical approach, 3rd ed., ASME Press, pp. 23-32.Paco Axel Lagerstrom, 1996, • Laminar flow theory, Princeton University Press, pp. 45-62.R. Shankar Subramanian, • Non-Newtonian Flows [Online] Available at: <http://web2.clarkson.edu/projects/subramanian/ch301/notes/nonnewtonian.pdf>. [Accessed 7 April 2011].Rashaida,• A. A., Flow of a non-Newtonian Bingham plastic fluid over a rotating disk, Available at: http://www.collectionscanada.gc.ca/obj/s4/f2/dsk3/SSU/TC-SSU-08172005120844.pdf>. [Accessed 7 April 2011]Two Phase flows and Practice• , Available at: <http://www.wlv.com/products/databook/db3/data/db3ch12.pdf>. [Accessed18 April 2011].Velocity and pressure drop in pipes• ,Availableathttp://4wings.com/lib/files/velocity_and_pressure_drop_in_pipes.pdf> [Accessed 7 April 2011].
Recommended ReadingAzbel, D., 1981. • Two-phase flows in chemical engineering, Cambridge University Press.Bausbacher, E, 1996. • Pipeline Networks Rules of Thumb Handbook, 2nd ed., McGraw-Hill.Beaumont, J. P., 2008. • Runner and Gating Design Handbook: Tools for Successful Injection Molding, 2nd ed.Blevins, T. L., 1980. • Pipeline network construction, 3rd ed., Pergamon Press.Böhme Gert, 1987, • Non-Newtonian fluid mechanics, North-Holland.Constantine Dafermos, Ericksen, L., Kinderlehrer, D., 1987. • Amorphous Polymers and Non-Newtonian Fluids, 1st ed., Springer.Dennis Siginer A., Daniel De Kee and Chhabra R. P., 1999, • Advances in the Flow and Rheology of Non-Newtonian Fluids, Volume 1, Elsevier.Jack Evett, 1989. • 500 Solved Problems In Fluid Mechanics and Hydraulics, 1st ed., McGraw-Hill.Kleinstreuer C, 2003. • Two-phase flow: theory and applications., Taylor & Francis.Mamoru Ishii, Takashi Hibiki, 2010. • Thermo-Fluid Dynamics of Two-Phase Flow, 2nd ed., Springer.McAllister, E. W., 2009. • Pipeline Rules of Thumb Handbook, A Manual of Quick, Accurate Solutions to Everyday Pipeline Engineering Problems, 7th ed., Gulf Professional Publishing.Michel Saad A., 1993. • Compressible fluid flow, 2nd ed, Prentice Hall.Murray, A., 2007. • Pipeline Sizing Construction: A Practical Approach, (Pipelines and Pressure Vessels), 3rd ed., ASME Press.Parisher R, 1990, • Pipeline networks for fluids, 2nd ed., North-Holland.Schowalter, W.R., 1978. • Mechanics of Non-Newtonian Fluids, 1st ed., Pergamon Press.
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Self Assessment Answers
Chapter Ia1. b2. b3. d4. d5. c6. c7. b8. c9. c10.
Chapter IIa1. a2. b3. a4. a5. c6. b7. a8. b9. a10.
Chapter IIIa1. a2. c3. a4. b5. c6. b7. a8. d9. c10.
Chapter IVa1. d2. b3. a4. c5. d6. a7. b8. b9. a10.
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Chapter Va1. c2. a3. b4. a5. b6. d7. b8. c9. b10.
Chapter VId1. a2. a3. a4. b5. b6. a7. c8. a9. b10.
Chapter VIIb1. a2. b3. c4. a5. b6. a7. d8. c9. b10.