h16 manual (pg1-pg24)losses in piping

H16Losses in Piping

Systems

PE/djb/0501

iCONTENTSSection Page

1 INTRODUCTION 1-1Description of the Apparatus 1-1

2 THEORY 2-1Head Loss 2-1

Head Loss in Straight Pipes 2-1Head Loss due to Sudden Changes in Area of Flow 2-1Head Loss due to Bends 2-2Head Loss due to Valves 2-2

Principles of Pressure Loss Measurement 2-2Principles of Pressure Loss Measurement 2-2

3 INSTRUCTIONS FOR USE 3-1Filling the Mercury Manometer 3-1Experimental Procedure 3-1

4 TYPICAL SET OF RESULTS AND CALCULATIONS 4-1Results 4-1Identification of Manometer Tubes and Components 4-1Experiment 1: Straight Pipe Loss 4-2Experiment 2: Sudden Expansion 4-4Experiment 3: Sudden Contraction 4-6Experiment 4: Bends 4-8Experiment 5: Valves 4-9

5 GENERAL REVIEW OF THE EQUIPMENT AND RESULTS 5-1

6 H16p ROUGH PIPE ASSEMBLY 6-1Installation 6-1Dimensions 6-2Range of Experiments 6-2Theory 6-4

Flow Rate 6-4Experimental Procedure 6-4Typical Test Results 6-4

TQ Losses in Piping Systems

ii

1

SECTION 1 INTRODUCTION

One of the most common problems in fluid mechanics isthe estimation of pressure loss. This apparatus enablespressure loss measurements to be made on several smallbore pipe circuit components, typical of those found inhousehold central heating installations. This apparatus isdesigned for use with the TQ Hydraulic Bench H1,although the equipment may be supplied from anothersource, providing it has an accurate means of mass flowrate measurement. All reference to the bench in thismanual refers directly to the TQ Hydraulic Bench.

Description of Apparatus

The apparatus shown diagrammatically in Figure 1.1,consists of two separate hydraulic circuits; one painteddark blue, one painted light blue, each one containing anumber of pipe system components. Both circuits aresupplied with water from the same hydraulic bench. Thecomponents in each of the circuits are as detailed atFigure 1.1.

In all cases (except the gate and globe valves), thepressure change across each of the components ismeasured by a pair of pressurised piezometer tubes. Inthe case of the valves, pressure measurement is made byU-tube Manometers containing mercury.

Figure 1.1 Arrangement of the apparatus

Dark Blue Circuit Light Blue Circuit

A) Straight pipe 13.7 mm bore E) Sudden expansion - 13.6 mm / 26.2 mmB) 90 Sharp bend (mitre); F) Sudden contraction - 26.2 mm / 13.6 mmC) Proprietary 90 elbow G) Smooth 90 bend 50.8 mm radiusD) Gate valve H) Smooth 90 bend 100 mm radius

J) Smooth 90 bend 152 mm radiusK) Globe ValveL) Straight Pipe 26.4mm


Page 1-2

1

SECTION 2 THEORY

Figure 2.1

For an incompressible fluid flowing through a pipe thefollowing equations apply:

Q V A V A= =1 1 2 2 (Continuity)

Zpg

Vg

ZPg

V h1 1 12

22

22

1 22+ + = + + +

L (Bernoulli)

Notation:Q Volumetric flow rate (m3/s);V Mean velocity (m/s);A Cross sectional area (m2);z Height above datum (m);p Static pressure (N/m2);hL Head loss (m); Density (kg/m3);g Acceleration due to gravity (9.81 m/s2).

Head Loss

The head loss in a pipe circuit falls into two categories:

a) That due to viscous resistance extending throughoutthe total length of the circuit

b) That due to localised effects such as valves, suddenchanges in area of flow and bends.

The overall head loss is a combination of both thesecategories. Because of mutual interference betweenneighbouring components in a complex circuit the totalhead loss may differ from that estimated from the lossesdue to the individual components considered inisolation.

Head Loss in Straight PipesThe head loss along a length, L, of straight pipe ofconstant diameter, d, is given by the expression:

h f LVgdL

=

42

2

where f is a dimension constant which is a function ofthe Reynolds number of the flow and the roughness ofthe internal surface of the pipe.

Head Loss due to Sudden Changes in Area ofFlow

i) Sudden ExpansionThe head loss at a sudden expansion is given by theexpression:

( )h V VgL

=

1 22

2

Figure 2.2 Expanding pipe

ii) Sudden Contraction

Figure 2.3 Contracting pipe

The head loss at a sudden contraction is given by theexpression:

h KVgL

=22

2

where K is a dimension coefficient which dependsupon the area ratio as shown in Table 2.1. This tablecan be found in most good textbooks on fluidmechanics.

A2/A1 K

0 0.500.1 0.460.2 0.410.3 0.360.4 0.300.6 0.180.8 0.061.0 0

Table 2.1 Loss coefficients for suddencontractions


Page 2-2

Head Loss due to BendsThe head loss due to a bend is given by the expression:

h K VgB

B=

2

2

where K is a dimensionless coefficient which dependsupon the bend radius/pipe radius ratio and the angle ofthe bend.

NOTEThe loss given by this expression is not the totalloss caused by the bend but the excess loss abovethat which would be caused by a straight pipeequal in length to the length of the pipe axis.

See Figure 4.5, which shows a graph of typical losscoefficients.

Head Loss due to ValvesThe head loss due to a valve is given by the expression:

h KVgL

+2

2

where the value of K depends upon the type of valve andthe degrees of opening. Table 2.2 gives typical values ofloss coefficients for gate and globe valves.

Globe valve, fully open 10.0Gate valve, fully open 0.2Gate valve, half open 5.6

Table 2.2

Principles of Pressure Loss Measurement

Figure 2.4 Pressurised piezometer tubes tomeasure pressure loss between two points atdifferent elevations

Considering Figure 2.4, apply Bernoullis equationbetween 1 and 2:

zpg

Vg

pg

Vg

h+ + = + +1 12

2 22

2 2 L

(2-1)but:

V V1 2=(2-2)

Therefore

( )h z p pgL

= +1 2

(2-3)

Consider piezometer tubes:

( )[ ]p p g z x y= + +1 (2-4)

also

p p gy= 2 (2-5)

giving:

( )x z

p pg

= +1 2

(2-6)

Figure 2.5 U-tube containing mercury used tomeasure pressure loss across valves

Consider Figure 2.5; since 1 and 2 have the sameelevation and pipe diameter:

p pg

h1 2 =H O

L2

(2-7)Consider the U-tube. Pressure in both limbs of U-tubeare equal at level 00. Therefore equating pressure at 00:


Page 2-3

( )p g x y g x p g y2 1 1 1 + = H O Hg H O2 2(2-8)

giving:

( )p p xg1 2 = Hg H O2(2-9)

hence:

( )p pg

x s1 2 1 = H O2

(2-10)

Considering Equations (2-6) and (2-10) and taking thespecific gravity of mercury as 13.6:

h xL = 12 6.(2-11)


Page 2-4

1

SECTION 3 INSTRUCTIONS FOR USE

1. Connect the hydraulic bench supply to the inlet ofthe apparatus, directing the outlet hose into thehydraulic bench weighing tank.

2. Close globe valve, open gate valve and admit waterto the Dark Blue circuit, starting the pump andopening the outlet valve on the hydraulic bench.

3. Allow water to flow for two to three minutes.4. Close gate valve and manipulate all trapped air into

air space in piezometer tubes. Check that allpiezometer tubes indicate zero pressure difference.

5. Open the gate valve and by manipulating bleedscrews on the U-tube, fill both limbs with waterensuring that no air remains.

6. Close gate valve, open globe valve and repeat theabove procedure for the Light Blue circuit.

Both circuits are now ready for measurements.The datum position of the piezometer can be

adjusted to any desired position either by pumping airinto the manifold with the hand pump supplied, or bygently allowing air to escape through the manifoldvalve. Ensure that there are no water locks in thesemanifolds as these will tend to suppress the head ofwater recorded and so provide incorrect readings.

Filling the Mercury Manometers

ImportantMercury and its vapour are poisonous andshould be treated with great care. Any localregulations regarding the handling and use ofmercury should be strictly adhered to.

Due to regulations concerning the transport of mercury,TQ Ltd are unable to supply this item. To fill themercury manometers, it is recommended that a suitablesyringe and catheter tube are used (not supplied) and themercury acquired locally. Approximately 1Kg ofMercury is sufficient.

Remove any items of gold or silver jewellery.Unscrew the two caps at the top of the manometer.

Thread a suitable catheter tube into the manometer tube,ensuring the catheter tube end touches the end of themanometer column. Fill a syringe with 10 ml of mercuryand connect to the catheter tube. Slowly fill themanometer using the syringe, and as the mercury fillsthe columns, withdraw the tube ensuring there are no airbubbles left. The optimum level for the mercury is400 mm from the bottom of the U-tube.

When the manometer has the correct amount ofmercury in it, water should be added to thereservoir, covering the mercury and preventingvapour from escaping into the air.

Figure 7 Filling the manometers

Unscrew the caps at the top of the manometer to purgeany trapped air. Replace caps immediately.

Experimental Procedure

The following procedure assumes that pressure lossmeasurements are to be made on all the circuitcomponents.

Open fully the water control valve on the hydraulicbench. With the globe valve closed, open the gate valvefully to obtain maximum flow through the Dark Bluecircuit. Record the readings on the piezometer tubesand the U-tube. Collect a sufficient quantity of water inthe weigh tank to ensure that the weighing takes placeover a minimum period of 60 seconds.

Repeat the above procedure for a total of tendifferent flow rates, obtained by closing the gate valve,equally spaced over the full flow range.

With an accurate thermometer, record the watertemperature in the sump tank of the bench each time areading is taken.

Close the gate valve, open the globe and repeat theexperiment procedure for the Light Blue circuit.

Before switching off the pump, close both the globevalve and the gate valve. This procedure prevents airgaining access to the system and so saves time insubsequent setting up.


Page 3-2

1

SECTION 4 TYPICAL SET OF RESULTS AND CALCULATIONS

Results

Basic DataPipe diameter (internal) 13.7 mmPipe diameter [between sudden expansion(internal) and contraction] 26.4 mm

Pipe material Copper tubeDistance between pressure tappings forstraight pipe and bend experiments 0.914 m

Table 4.1

Bend Radii90 Elbow (mitre) 090 Proprietary elbow 12.7 mm90 Smooth bend 50.8 mm90 Smooth bend 100 mm90 smooth bend 152 mm

Table 4.2

Identification of Manometer Tubes andComponents

Manometer tube number Unit

1 Proprietary elbow bend23 Straight pipe45 Mitre bend67 Expansion89 Contraction1011 152 mm bend1213 100 mm bend1415 50.8 mm bend16

Table 4.3


Page 4-2

Experiment 1: Straight Pipe Loss

The object of this experiment is to obtain the followingrelationships:

a) Head loss as a function of volume flow rate;b) Friction Factor as a function of Reynolds number.

Specimen CalculationsFrom Table 4.4, test number 1

Mass flow rate = 18/63 = 0.286 kg/s

Head loss = 0.332 m water

Volume flow rate (Q) = Mass flow rate/density=

0 286103.

= 286 106 m3/s

Area of flow (A) = 4

1372 . = 147.3 mm2

Mean velocity (V) = QA

= 286 10

147 3 10

6

6

.

= 1.94 m/s

Reynolds number (Re) = V d

For water at 23C = 9.40 197 m2/s

Therefore,

Re = 194 13 7 10

9 40 10

3

7. .

.

= 2.83 104

Friction Factor (f ) = h gdLV

L 24 2

f = 0 332 2 9 81 13 7 104 914 10 194

3

3 2. . .

.

= 0.0065

Figure 4.1 shows the head loss - volume flow raterelationship plotted as a graph of log hL against log Q.

The graph shows that the relationship is of the formhL Qn with n = 1.73. This value is close to thenormally accepted range of 1.75 to 2.00 for turbulentflow. The lower value n is found as in this apparatus, incomparatively smooth pipes at comparatively lowReynolds number.

Figure 4.2 shows the Friction Factor - Reynoldsnumber relationship plotted as a graph of friction factoragainst Reynolds number.

The graph also shows for comparison therelationship circulated from Blasiuss equation forhydraulically smooth pipes.

Blasiuss equation:

f = 0 07851 4.

Re in the range 10 104 5<


Page 4-3

Figure 4.1 Head loss versus volume flow rate

Figure 4.2 Friction factor versus Reynolds number


Page 4-4

Experiment 2: Sudden Expansion

The object of this experiment is to compare themeasured head rise across a sudden expansion with therise calculated on the assumption of:

a) No head loss;b) Head loss given by the expression:

( )h V VgL

=1 2

2

2

Testnumber

Time to collect 18 kgwater

Piezometer tube readings (cm) water U-tube(cm) Hg

(s) 7 8 9 10 11 Globe valve11 73.2 38.7 43.5 42.5 12.1 38.3 37.4 20.2*12 76.8 39.2 43.5 42.5 22.1 38.5 38.5 19.013 82.6 39.1 43.0 42.2 24.5 38.3 40.2 17.414 95.4 39.4 42.0 41.5 28.5 38.3 43.0 14.715 102.6 39.7 42.2 41.7 30.2 38.0 44.0 13.616 130.8 40.0 41.5 41.1 33.8 37.3 46.5 11.717 144.6 40.4 41.5 41.2 35.2 37.5 47.5 10.118 176.9 40.7 41.4 41.2 37.0 37.3 49.1 8.619 220.8 41.0 41.5 41.4 38.6 37.4 50.2 7.520 227.8 41.2 41.6 41.6 39.6 37.5 51.4 6.5

Table 4.2(a) Experimental results for light blue circuit

Testnumber

Time to collect 18 kgwater

Piezometer tube readings (cm) water U-tube(cm) Hg

(s) 12 13 14 15 16 Globe valve11 73.2 12.1 35.0 7.2 32.1 3.8 37.4 20.2*12 76.8 14.1 34.9 9.7 32.5 6.0 38.5 19.013 82.6 17.0 34.9 12.6 31.6 8.6 40.2 17.414 95.4 22.0 34.5 17.6 31.5 13.7 43.0 14.715 102.6 23.6 34.2 19.4 30.7 15.2 44.0 13.616 130.8 28.0 33.4 23.7 29.6 19.5 46.5 11.717 144.6 29.7 33.4 25.5 29.8 21.4 47.5 10.118 176.9 31.9 33.2 27.7 29.4 23.5 49.1 8.619 220.8 33.6 33.3 39.4 29.5 25.4 50.2 7.520 227.8 35.0 33.4 30.9 29.5 26.8 51.4 6.5

Table 4.2(b) Experimental results for light blue circuit (continued)

Specimen Calculation

From Table 4.2 test number 11measured head rise = 48 mm.

a) Assuming no head loss

( )h h

V V

g2 122

22

2 =

(Bernoulli)

since

A V A V1 1 2 2= (Continuity)

( )( )h h V

A A

g2 1 12 1 2

21

2 =

( )=

Vd d

g12 2

41

2

( )1

From the table,

V QA1 1

=

=

18

732 10 147 3 103 6. .

= 167. m / s

therefore

( )( )h h2 1

2

4

1671 13 7 26 4

2 9 81 =

.

. .

.

= 0.132 m


Page 4-5

Therefore head rise across the sudden expansionassuming no head loss is 132 mm water.

b) Assuming

( )h V VgL

=

1 22

2

( )h h

V V

g h2 112

22

2 =

L (Bernoulli)

( ) ( )=

V V

gV V

g12

22

1 22

2 2or rearranging and inserting values of d1 = 13.7 mmand d2 = 26.4 mm, this reduces to

h h Vg2 1

120 396

2 =

.

which when

V1 167= . m / s

gives

h h2 1 0 0562 = . m

Therefore head rise across the sudden expansionassuming the simple expression for head loss is 56 mmwater.

Figure 4.3 shows the full set of results for thisexperiment plotted as a graph of measured head riseagainst calculated head rise.

Comparison with the dashed line on the graph showsclearly that the head rise across the sudden expansion isgiven more accurately by the assumption of a simplehead loss expansion, rather than by the assumption of nohead loss.

Figure 4.3 Head rise across a sudden enlargement


Page 4-6

Experiment 3: Sudden Contraction

The object of this experiment is to compare themeasured fall in head across a sudden contraction withthe fall calculated in the assumption of:

a) No head loss,b) Head loss given by the expression:

h KVgL

=

2

2


From table 4.2 test number 11 measured head fall =221 mm water.

a) Assuming no head loss: combining Bernoullisequation and the continuity equation gives:

( )( )h h V

d d

g2 1 22 2 1

41

2 =

/

= 0.927 Vg22

2

Which when

V2 = 1.67 m/s

gives

h1 h2 = 0.132 m

Therefore head fall across the sudden contractionassuming no head loss is 132 mm water.

b) Assuming

h KVgL

=22

2

( )h h V d dg h2 1 2

2 2 141

2 =

+

/

L

( )( )=

+

V

d dg KV g

22 2 1

4

22

1

2 2

/

/

From Table 2.1, when:

AA

2

10 27= .

K = 0.376

giving:

h h Vg

Vg1 2

22

22

0 9272

0 3762

= +. .

= 13032

22

.

Vg

Which when:

V2 = 1.67 m/s

gives:

h1 h2 = 0.185 m

Therefore head fall across the sudden contractionassuming loss coefficient of 0.376 is 18.5 cm water.

Figure 4.4 shows the full set of results for thisexperiment plotted as a graph of measured head fallagainst calculated head fall.

The graph shows that the actual fall in head isgreater than predicted by the accepted value of losscoefficient for this particular area ratio. The actual valueof loss coefficient can be obtained as follows:

Let hm = measured fall in head and K = actual losscoefficient, then:

h Vg

K Vgm

= +0 927

2 2

2 2.

hence

= Khg

V2 0 927

22 .

which when V2 = 1.67 m/s gives K = 0.63


Page 4-7

Figure 4.4 Head decrease across a sudden contraction


Page 4-8

Experiment 4: Bends

The purpose here is to measure the loss coefficient forfive bends. There is some confusion over terminology,which should be noted; there are the total bend losses(KL hL)and those due solely to bend geometry, ignoringfrictional losses (KB, hB).

K gVB

=

22

(Total measured head loss straight line loss)i.e.

K gV

=

22

(Head gradient for bend - k head gradient for straightpipe)

Where k = 1 for KB

k rL

= 12

For either, h K Vg

=

2

2

Plotted on Figure 4.5 are experimental results for KB andKL for the five types of bends and also some tabulateddata for KL. The last was obtained from Handbook ofFluid Mechanics by VL Streeter. It should be notedthough, that these results are by no means universallyaccepted and other sources give different values.Further, the experiment assumes that the head loss isindependent of Reynolds number and this is not exactlycorrect.

Is the form of KB what you would expect? Doesputting vanes in an elbow have any effect? Which doyou consider more useful to measure, KL or KB?

Figure 4.5 Graph of loss coefficient


Page 4-9

Experiment 5: Valves

The object of this experiment is to determine therelationship between loss coefficient and volume flowrate for a globe type valve and a gate type valve.


h KVgL

=

2

2

Globe ValveFrom Table 4.2, test number 11.

Volume flow rate = 246 106m3/s (valve fully open);U-tube reading = 172 mm mercury.

Therefore hL = 172 12.6= 2.17 m water

Velocity (V) = 1.67 m/s

Giving K = 2.17 2 9.81/1.672= 15.3

Figure 4.6 shows the full set of results for both valves inthe form of a graph of loss coefficient against percentvolume flow.

Figure 4.6 Loss coefficient for globe and gate valves


Page 4-8

1

SECTION 5 GENERAL REVIEW OF THE EQUIPMENT AND RESULTS

An attempt has been made in this apparatus to combinea large number of pipe components into a manageableand compact pipe system and so provide the student userwith the maximum scope for investigation. This is madepossible by using small bore pipe tubing. However, inpractice, so many restrictions, bends and the like maynever be encountered in such short pipe lengths. Thenormally accepted design criteria of placing thedownstream pressure tapping 30 - 50 pipe diametersaway from the obstruction i.e. the 90 bends, has beenadhered to. This ensures that this tapping is well awayfrom any disturbances due to the obstruction and in aregion where there is normal steady flow conditions.Also sufficient pipe length has been left between eachcomponent in the circuit, to obviate any adverseinfluence neighbouring components may tend to have oneach other.

Any discrepancies between actual experimental andtheoretical or published results may be attributed tothree main factors:

a) Relatively small physical scale of the pipe work;b) Relatively small pressure differences in some cases;c) Low Reynolds numbers.

The relatively small pressure differences, althougheasily readable, are encountered on the smooth 90bends and sudden expansion. The results on thesecomponents should therefore be taken with the utmostcare to obtain maximum accuracy from the equipment.The results obtained however, are quite realistic as canbe seen from their comparison with published data, asshown in Figure 4.6. Although there is wide divergenceeven amongst published data, refer to page 472 ofEngineering Fluid Mechanics by Charles Jaeger andpublished by Blackie and Son Ltd, it is interesting to

note that all curves seem to show a minimum value ofthe loss coefficient K where the ratio r/d is between 2and 4. It is important to realise and rememberthroughout the review of the results that all publisheddata have been obtained using much larger bore tubing(76 mm and above) and considering each component inisolation and not in a compound circuit.

Normal manufacturing tolerances assume greaterimportance when the physical scale is small. This effectmay be particularly noticeable in relation to the internalfinish of the tube near the pressure tappings. The utmostcare is taken during manufacturing to ensure a smoothuninterrupted bore of the tube in the region of eachpressure tappings, to obtain maximum accuracy ofpressure reading.

Concerning again all published information relatingto pipe systems, the Reynolds numbers are large, in theregion of 1 105 and above. The maximum Reynoldsnumber obtained in these experiments, using thehydraulic bench, H1, is 3 104 although this has notadversely affected the results. However. as previouslystated in the introduction to this manual, an alternativesource of supply (provided by the customer) could beused if desired, to increase the flow rate. In this case analternative flowmeter would also be necessary.

The three factors discussed very briefly above areoffered as a guide to explain discrepancies betweenexperimental and published results, since in most casesall three are involved, although much more personalinvestigation is required by the student to obtainmaximum value from using this equipment.

In conclusion the general trends and magnitudesobtained give a valuable indication of pressure loss fromthe various components in the pipe system. The studentis therefore given a realistic appreciation of relatingexperimental to theoretical or published information.


Page 5-2

h16 manual (pg1-pg24)losses in piping

Documents

straight pipe loss

head lossthe head loss

overall head loss

pressure measurement

area of flow

globe valves

pipe thefollowing equations

tq hydraulic bench h1