Losses in Piping

5/22/2018 Losses in Piping

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H16Losses in Piping

Systems

PE/djb/0501


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i

CONTENTSSection Page

1 INTRODUCTION 1-1

Description of the Apparatus 1-1

2 THEORY 2-1

Head Loss 2-1Head Loss in Straight Pipes 2-1

Head Loss due to Sudden Changes in Area of Flow 2-1

Head Loss due to Bends 2-2

Head Loss due to Valves 2-2

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

3 INSTRUCTIONS FOR USE 3-1

Filling the Mercury Manometer 3-1

Experimental Procedure 3-1

4 TYPICAL SET OF RESULTS AND CALCULATIONS 4-1

Results 4-1Identification of Manometer Tubes and Components 4-1Experiment 1: Straight Pipe Loss 4-2

Experiment 2: Sudden Expansion 4-4

Experiment 3: Sudden Contraction 4-6

Experiment 4: Bends 4-8

Experiment 5: Valves 4-9

5 GENERAL REVIEW OF THE EQUIPMENT AND RESULTS 5-1

6 H16p ROUGH PIPE ASSEMBLY 6-1

Installation 6-1

Dimensions 6-2

Range of Experiments 6-2

Theory 6-4

Flow Rate 6-4

Experimental Procedure 6-4

Typical Test Results 6-4


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TQ Losses in Piping Systems

ii


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Page 1-1

SECTION 1 INTRODUCTION

One of the most common problems in fluid mechanics is

the estimation of pressure loss. This apparatus enables

pressure loss measurements to be made on several small

bore pipe circuit components, typical of those found in

household central heating installations. This apparatus isdesigned for use with the TQ Hydraulic Bench H1,

although the equipment may be supplied from another

source, providing it has an accurate means of mass flow

rate measurement. All reference to the bench in this

manual 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 painted

dark blue, one painted light blue, each one containing anumber of pipe system components. Both circuits are

supplied with water from the same hydraulic bench. The

components in each of the circuits are as detailed at

Figure 1.1.

In all cases (except the gate and globe valves), the

pressure change across each of the components is

measured by a pair of pressurised piezometer tubes. In

the case of the valves, pressure measurement is made by

U-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 mm

B) 90Sharp bend (mitre); F) Sudden contraction - 26.2 mm / 13.6 mmC) Proprietary 90elbow G) Smooth 90bend 50.8 mm radiusD) Gate valve H) Smooth 90bend 100 mm radius

J) Smooth 90bend 152 mm radiusK) Globe Valve

L) Straight Pipe 26.4mm


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Page 1-2


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Page 2-1

SECTION 2 THEORY

Figure 2.1

For an incompressible fluid flowing through a pipe the

following equations apply:

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

Z p

g

V

gZ

P

gV 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/s

2).

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 these

categories. Because of mutual interference between

neighbouring components in a complex circuit the total

head loss may differ from that estimated from the losses

due to the individual components considered in

isolation.

Head Loss in Straight PipesThe head loss along a length, L, of straight pipe of

constant diameter, d, is given by the expression:

h f LV

gdL =

4

2

2

where f is a dimension constant which is a function of

the Reynolds number of the flow and the roughness of

the internal surface of the pipe.

Head Loss due to Sudden Changes in Area ofFlow

i) Sudden Expansion

The head loss at a sudden expansion is given by the

expression:

( )h

V V

gL =

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 the

expression:

h KV

gL =

22

2

where K is a dimension coefficient which depends

upon the area ratio as shown in Table 2.1. This table

can be found in most good textbooks on fluid

mechanics.

A2/A1 K

0 0.50

0.1 0.46

0.2 0.41

0.3 0.36

0.4 0.30

0.6 0.18

0.8 0.06

1.0 0

Table 2.1 Loss coefficients for sudden

contractions


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Page 2-2

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

h K V

gB

B=2

2

where K is a dimensionless coefficient which depends

upon the bend radius/pipe radius ratio and the angle of

the bend.

NOTE

The loss given by this expression is not the total

loss caused by the bend but the excess loss above

that which would be caused by a straight pipe

equal in length to the length of the pipe axis.

See Figure 4.5, which shows a graph of typical loss

coefficients.

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

h KV

gL +

2

2

where the value of Kdepends upon the type of valve and

the degrees of opening. Table 2.2 gives typical values of

loss coefficients for gate and globe valves.

Globe valve, fully open 10.0

Gate valve, fully open 0.2

Gate 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:

z p

g

V

g

p

g

V

gh+ + = + +1 1

22 2

2

2 2 L

(2-1)

but:

V V1 2=

(2-2)

Therefore

( )h z

p p

gL = +

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 p

g= +

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 same

elevation and pipe diameter:

p p

gh1 2

=

H OL

2

(2-7)

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


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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 p

gx s1 2 1

=

H O2(2-10)

Considering Equations (2-6) and (2-10) and taking the

specific gravity of mercury as 13.6:

h xL = 12 6.

(2-11)


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Page 2-4


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Page 3-1

SECTION 3 INSTRUCTIONS FOR USE

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

hydraulic bench weighing tank.

2. Close globe valve, open gate valve and admit waterto the Dark Blue circuit, starting the pump and

opening 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 all

piezometer tubes indicate zero pressure difference.

5. Open the gate valve and by manipulating bleedscrews on the U-tube, fill both limbs with water

ensuring 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 air

into the manifold with the hand pump supplied, or by

gently allowing air to escape through the manifold

valve. Ensure that there are no water locks in these

manifolds as these will tend to suppress the head of

water recorded and so provide incorrect readings.

Filling the Mercury Manometers

Important

Mercury and its vapour are poisonous and

should be treated with great care. Any local

regulations regarding the handling and use of

mercury should be strictly adhered to.

Due to regulations concerning the transport of mercury,

TQ Ltd are unable to supply this item. To fill the

mercury manometers, it is recommended that a suitable

syringe and catheter tube are used (not supplied) and the

mercury acquired locally. Approximately 1Kg of

Mercury 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 the

manometer column. Fill a syringe with 10 ml of mercury

and connect to the catheter tube. Slowly fill the

manometer using the syringe, and as the mercury fills

the columns, withdraw the tube ensuring there are no air

bubbles left. The optimum level for the mercury is

400 mm from the bottom of the U-tube.

When the manometer has the correct amount of

mercury in it, water should be added to thereservoir, covering the mercury and preventing

vapour from escaping into the air.

Figure 7 Filling the manometers

Unscrew the caps at the top of the manometer to purge

any trapped air. Replace caps immediately.

Experimental Procedure

The following procedure assumes that pressure loss

measurements are to be made on all the circuit

components.

Open fully the water control valve on the hydraulic

bench. With the globe valve closed, open the gate valve

fully to obtain maximum flow through the Dark Blue

circuit. Record the readings on the piezometer tubes

and the U-tube. Collect a sufficient quantity of water in

the weigh tank to ensure that the weighing takes place

over a minimum period of 60 seconds.

Repeat the above procedure for a total of ten

different flow rates, obtained by closing the gate valve,

equally spaced over the full flow range.

With an accurate thermometer, record the water

temperature in the sump tank of the bench each time a

reading is taken.

Close the gate valve, open the globe and repeat the

experiment procedure for the Light Blue circuit.

Before switching off the pump, close both the globe

valve and the gate valve. This procedure prevents air

gaining access to the system and so saves time in

subsequent setting up.


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Page 3-2


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Page 4-1

SECTION 4 TYPICAL SET OF RESULTS AND CALCULATIONS

Results

Basic Data

Pipe diameter (internal) 13.7 mm

Pipe diameter [between sudden expansion

(internal) and contraction]26.4 mm

Pipe material Copper tube

Distance between pressure tappings for

straight pipe and bend experiments0.914 m

Table 4.1

Bend Radii

90Elbow (mitre) 0

90Proprietary elbow 12.7 mm

90Smooth bend 50.8 mm

90Smooth bend 100 mm

90smooth bend 152 mm

Table 4.2

Identification of Manometer Tubes andComponents

Manometer tube number Unit

1 Proprietary elbow bend

2

3 Straight pipe

4

5 Mitre bend

6

7 Expansion

8

9 Contraction

10

11 152 mm bend

12

13 100 mm bend

14

15 50.8 mm bend

16

Table 4.3


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Page 4-2

Experiment 1: Straight Pipe Loss

The object of this experiment is to obtain the following

relationships:

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

=0286

103.

= 286 106 m3/s

Area of flow (A) = 4

1372 . = 147.3 mm2

Mean velocity (V) =Q

A

=286 10

147 3 10

6

6

.

= 1.94 m/s

Reynolds number (Re) = Vd

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 gd

LV

L 2

4 2

f =0 332 2 9 81 137 10

4 914 10 194

3

3 2

. . .

.

= 0.0065

Figure 4.1 shows the head loss - volume flow rate

relationship plotted as a graph of log hLagainst log Q.

The graph shows that the relationship is of the form

hL Qn with n = 1.73. This value is close to the

normally accepted range of 1.75 to 2.00 for turbulent

flow. The lower value n is found as in this apparatus, in

comparatively smooth pipes at comparatively low

Reynolds number.

Figure 4.2 shows the Friction Factor - Reynolds

number relationship plotted as a graph of friction factor

against Reynolds number.

The graph also shows for comparison the

relationship circulated from Blasiuss equation for

hydraulically smooth pipes.

Blasiuss equation:

f =0 0785

1 4

.

Rein the range 10 104 5<


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Page 4-3

Figure 4.1 Head loss versus volume flow rate

Figure 4.2 Friction factor versus Reynolds number


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Page 4-4

Experiment 2: Sudden Expansion

The object of this experiment is to compare the

measured head rise across a sudden expansion with the

rise calculated on the assumption of:

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

( )h

V V

gL =

1 2

2

2

Test

number

Time to collect 18 kg

water

Piezometer tube readings (cm) water U-tube

(cm) Hg

(s) 7 8 9 10 11 Globe valve

11 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 19.0

13 82.6 39.1 43.0 42.2 24.5 38.3 40.2 17.4

14 95.4 39.4 42.0 41.5 28.5 38.3 43.0 14.7

15 102.6 39.7 42.2 41.7 30.2 38.0 44.0 13.6

16 130.8 40.0 41.5 41.1 33.8 37.3 46.5 11.7

17 144.6 40.4 41.5 41.2 35.2 37.5 47.5 10.1

18 176.9 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 7.5

20 227.8 41.2 41.6 41.6 39.6 37.5 51.4 6.5

Table 4.2(a) Experimental results for light blue circuit

Test

number

Time to collect 18 kg

water

Piezometer tube readings (cm) water U-tube

(cm) Hg

(s) 12 13 14 15 16 Globe valve

11 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 19.0

13 82.6 17.0 34.9 12.6 31.6 8.6 40.2 17.4

14 95.4 22.0 34.5 17.6 31.5 13.7 43.0 14.7

15 102.6 23.6 34.2 19.4 30.7 15.2 44.0 13.6

16 130.8 28.0 33.4 23.7 29.6 19.5 46.5 11.7

17 144.6 29.7 33.4 25.5 29.8 21.4 47.5 10.1

18 176.9 31.9 33.2 27.7 29.4 23.5 49.1 8.6

19 220.8 33.6 33.3 39.4 29.5 25.4 50.2 7.5

20 227.8 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 1

22

22

2 =

(Bernoulli)

since

A V A V1 1 2 2= (Continuity)

( )( )h h V A Ag2 1 12 1 2

2

1

2 =

( )=

V

d d

g

12 2

41

2

( )1

From the table,

V Q

A1

1

=

=

18

732 10 147 3 103 6

. .

= 167. m / s

therefore

( )( )h h2 1 24

1671 137 26 4

2 9 81 =

.

. .

. = 0.132 m


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Page 4-5

Therefore head rise across the sudden expansion

assuming no head loss is 132 mm water.

b) Assuming

( )h

V V

gL =

1 22

2

( )h h

V V

g h2 1

12

22

2 =

L (Bernoulli)

( ) ( )=

V V

g

V V

g

12

22

1 2

2

2 2

or rearranging and inserting values of d1= 13.7 mm

and d2= 26.4 mm, this reduces to

h h V

g2 1

120396

2 =

.

which when

V1 167= . m / s

gives

h h2 1 00562 = . m

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

water.

Figure 4.3 shows the full set of results for this

experiment plotted as a graph of measured head rise

against calculated head rise.

Comparison with the dashed line on the graph shows

clearly that the head rise across the sudden expansion is

given more accurately by the assumption of a simple

head loss expansion, rather than by the assumption of no

head loss.

Figure 4.3 Head rise across a sudden enlargement


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Page 4-6

Experiment 3: Sudden Contraction

The object of this experiment is to compare the

measured fall in head across a sudden contraction with

the fall calculated in the assumption of:

a) No head loss,

b) Head loss given by the expression:

h KV

gL =

2

2


From table 4.2 test number 11 measured head fall =

221 mm water.

a) Assuming no head loss: combining Bernoullis

equation and the continuity equation gives:

( )( )h h Vd d

g2 1 2

22 1

41

2 =

/

= 0.927V

g

22

2

Which when

V2 = 1.67 m/s

gives

h1 h2 = 0.132 m

Therefore head fall across the sudden contraction

assuming no head loss is 132 mm water.

b) Assuming

h KV

gL =

22

2

( )h h V

d d

g h2 1 2

2 2 1

41

2 =

+

/

L

( )

( )=

+

Vd d

g KV g22 2 1

4

22

1

2 2

/

/

From Table 2.1, when:

A

A

2

1

0 27= .

K = 0.376

giving:

h h V

g

V

g1 2

22

22

09272

03762

= +. .

= 13032

22

. V

g

Which when:

V2 = 1.67 m/s

gives:

h1 h2 = 0.185 m

Therefore head fall across the sudden contraction

assuming loss coefficient of 0.376 is 18.5 cm water.

Figure 4.4 shows the full set of results for this

experiment plotted as a graph of measured head fall

against calculated head fall.

The graph shows that the actual fall in head is

greater than predicted by the accepted value of loss

coefficient for this particular area ratio. The actual value

of loss coefficient can be obtained as follows:

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

h V

g

K V

gm = +

0927

2 2

2 2

.

hence

= K hg

V

20927

22

.

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


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Page 4-7

Figure 4.4 Head decrease across a sudden contraction


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Page 4-8

Experiment 4: Bends

The purpose here is to measure the loss coefficient for

five bends. There is some confusion over terminology,

which should be noted; there are the total bend losses

(KLhL)and those due solely to bend geometry, ignoring

frictional losses (KB, hB).

K g

VB =

22

(Total measured head loss straight line loss)

i.e.

K g

V=

22

(Head gradient for bend - khead gradient for straightpipe)

Where k= 1 for KB

k r

L= 1

2

For either, h KV

g=

2

2

Plotted on Figure 4.5 are experimental results for KBand

KL for the five types of bends and also some tabulated

data for KL. The last was obtained from Handbook of

Fluid Mechanics by VL Streeter. It should be noted

though, that these results are by no means universallyaccepted and other sources give different values.

Further, the experiment assumes that the head loss is

independent of Reynolds number and this is not exactly

correct.

Is the form of KB what you would expect? Does

putting vanes in an elbow have any effect? Which do

you consider more useful to measure, KLor KB?

Figure 4.5 Graph of loss coefficient


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Page 4-9

Experiment 5: Valves

The object of this experiment is to determine the

relationship between loss coefficient and volume flow

rate for a globe type valve and a gate type valve.


h KV

gL =

2

2

Globe Valve

From 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 in

the form of a graph of loss coefficient against percent

volume flow.

Figure 4.6 Loss coefficient for globe and gate valves


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Page 4-8


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Page 5-1

SECTION 5 GENERAL REVIEW OF THE EQUIPMENT AND RESULTS

An attempt has been made in this apparatus to combine

a large number of pipe components into a manageable

and compact pipe system and so provide the student user

with the maximum scope for investigation. This is made

possible by using small bore pipe tubing. However, inpractice, so many restrictions, bends and the like may

never be encountered in such short pipe lengths. The

normally accepted design criteria of placing the

downstream pressure tapping 30 - 50 pipe diameters

away from the obstruction i.e. the 90bends, has beenadhered to. This ensures that this tapping is well away

from any disturbances due to the obstruction and in a

region where there is normal steady flow conditions.

Also sufficient pipe length has been left between each

component in the circuit, to obviate any adverse

influence neighbouring components may tend to have on

each other.Any discrepancies between actual experimental and

theoretical or published results may be attributed to

three 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, although

easily readable, are encountered on the smooth 90bends and sudden expansion. The results on these

components should therefore be taken with the utmost

care to obtain maximum accuracy from the equipment.

The results obtained however, are quite realistic as can

be seen from their comparison with published data, as

shown in Figure 4.6. Although there is wide divergence

even amongst published data, refer to page 472 of

Engineering Fluid Mechanics by Charles Jaeger and

published by Blackie and Son Ltd, it is interesting to

note that all curves seem to show a minimum value of

the loss coefficient Kwhere the ratio r/dis between 2

and 4. It is important to realise and remember

throughout the review of the results that all published

data have been obtained using much larger bore tubing(76 mm and above) and considering each component in

isolation and not in a compound circuit.

Normal manufacturing tolerances assume greater

importance when the physical scale is small. This effect

may be particularly noticeable in relation to the internal

finish of the tube near the pressure tappings. The utmost

care is taken during manufacturing to ensure a smooth

uninterrupted bore of the tube in the region of each

pressure tappings, to obtain maximum accuracy of

pressure reading.

Concerning again all published information relating

to pipe systems, the Reynolds numbers are large, in theregion of 1 105 and above. The maximum Reynoldsnumber obtained in these experiments, using the

hydraulic bench, H1, is 3 104 although this has notadversely affected the results. However. as previously

stated in the introduction to this manual, an alternative

source of supply (provided by the customer) could be

used if desired, to increase the flow rate. In this case an

alternative flowmeter would also be necessary.

The three factors discussed very briefly above are

offered as a guide to explain discrepancies between

experimental and published results, since in most cases

all three are involved, although much more personal

investigation is required by the student to obtain

maximum value from using this equipment.

In conclusion the general trends and magnitudes

obtained give a valuable indication of pressure loss from

the various components in the pipe system. The student

is therefore given a realistic appreciation of relating

experimental to theoretical or published information.


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Losses in Piping

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