fluid flow in pipes - lecture 1

8/8/2019 Fluid Flow in Pipes - Lecture 1

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VE2400: Pipeflow - Lecture 1 09/04/200

School of Civil EngineeringFACULTY OF ENGINEERING

Fluid Flow in Pipes: Lecture 1

Dr Andrew Sleigh

Dr Ian Goodwill

CIVE2400: Fluid Mechanics

www.efm.leeds.ac.uk/CIVE/FluidsLevel2Fluid Mechanics: Pipe Flow Lecture 1

Fluid Flow in Pipes

Pressurised flow

Liquid or Gas

Above or below atmosphericpressure

No free surface

That is open channel flow

Real viscous fluid

Interacts with boundary

Fluid Mechanics: Pipe Flow Lecture 1 3

Resistance to flow

Flowing fluid

Shear stress where touches solid boundary

Both for pipes & open channels

Referred to as frictional resistance

Energy transfer between fluid and boundary

Experienced as a loss of energy in fluid

Energy loss at joints and junctions

Due to flow separation (a local frictioneffect)


This module:

Analysis of pipeline flow

How to quantify friction

What causes it

What is its magnitude

How significant it is

How to take account of friction

How to take account of other losses

Examples:

Pipes in series Pipes in parallel

Branched pipes (small networks)


Analysis of pipelines

Typical simple pipeline joining 2 reservoirs

Bernoulli

Constant22

22

Hzg

u

g

pz

g

u

g

pB

BBA

AA


Bernoulli Equation

Including losses

fexitLLentryLBBB

pumpAAA hhhhz

g

u

g

phz

g

u

g

pexpansion

22

22

Friction Loss


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Fluid Mechanics: Pipe Flow Lecture 1

pA = Atmospheric pressure

pB = Atmospheric pressure

uA = small (negligible)

uB = small (negligible)

fexitLLentryLBBB

pumpAAA hhhhz

g

u

g

phz

g

u

g

pexpansion

22

22

7

Bernoulli Equation (simplified)

fexitLLentryLpumpBA hhhhhzz expansionFluid Mechanics: Pipe Flow Lecture 1

Fluid flowing in pipe

Piezometer

Level rises

8

Pressure head

g

ph

Pressure Head


Fluid flowing in pipe

Piezometer &

L-shaped Piezometer

Levels rise

9

Velocity head

g

uh

2

2

Velocity Head

g

u

g

p

2

2

g

p


Shear stress on fluid

Newtons law of viscosity

Shear stress proportional to velocity gradient

Viscosity, , is the constant of proportionality

du

dy

du

dy


Laminar and turbulent flow

Flow can be either Laminar - low velocity

Turbulent high velocity (with a small transitional zone between)

Reynold' Number

Pipe flow nearly always turbulent

ududRe

Laminar flow: Re < 2000Transitional flow:2000 < Re < 4000

Turbulent flow: Re > 4000


Reynolds Number Calculation

Pipe diameter: 0.5m

Crude oil:Kinematic viscosity = 0.0000232 m/s

Water:

Dynamic viscosity = 8.90 104 Pas

What are the velocities when

Turbulent flow would be expected

to start?


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Reynolds Number Calculation

Crude oil:

Water:

ududRe

smu

u

/1784.01023.2

5.04000

5

smu

u

/007.0

108.90

5.010004000

4-


Pressure loss due to friction in pipes

Cylinder of fluid:

Driving force (due to pressure)

Driving force = upstream force downstream force

Driving force =

Direction of flow

w

w

Area A

Pressure p Pressure p - p

P = F/A

pA p p A p A pd

2

4



Retarding force (due to shear stress at wall)

Retarding force = shear stress x area acts

Retarding force =

Direction of flow

w

w

Area A


dLww =wallpipeofarea



Driving force = Retarding force

pressure loss in terms of Shear Stress at wall

Direction of flow

w

w

Area A


pd

dL

pL

d

w

w

2

4

4


Shear stress willchange with velocity

So shear stresschanges with Re

Laminar

Turbulent

17

Pressure loss velocity relationship

up


This graph is empirical

Obtained from experiment

We would like to knowThe relationship between

w and Pressure

Will not get a general expression

But we will see a method of estimating w

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Pressure loss shear stress relationship


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Todays lecture:

Fluid flow in pipes

Analysis of pipelines

Bernoulli Equation (revision)

Pressure loss / Wall Shear Stress andvelocity relationship

fluid flow in pipes - lecture 1

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