Friction Loss in Pipe

Flow

INSTRUCTED BY: Mr. H Rathnasuriya

NAME V.W.MEEMADUMA

INDEX NUMBER 090325G

COURSE: MPR

GROUP: B3

DATE OF PER: 2010.08.03

DATE OF SUB: 2010.08.17

1.0 Introduction

Energy Loses Occur in pipe flow due to frictional resistance at the pipe surface. Such head losses are

known as frictional resistance head losses. It is important to determine frictional head losses in many

pipe flow problems.

Objectives

To verify that the friction factor in pipe flow varies as expressed in the Darcy-Weisbach and Hagen-

Poiseuille equations for a

(a) Small diameter pipe (3 mm)

(b) Commercially used PVC pipe

(c) Commercially used Galvanized Iron (GI) pipe

Theory

The frictional head loss (hf) depends on the type of flow, which can be laminar or turbulent. In laminar

flow, fluid flows in layers with orderly movement of fluid particles while in Turbulent flow fluid particles

move in a disorderly manner, as shown in Figure below.

Whether the flow is laminar or turbulent is decided by a non-dimensional Reynold’s number Re which is

expressed as

Re =

Where = Fluid density, v = Flow Velocity, D = pipe diameter, = Fluid viscousity

In pipes, the flow is laminar when Re < 2000 and turbulent when Re > 4000 with flow transition taking

place when 2000 < Re < 4000

Various scientists had a need to evaluate the frictional head loss for a given pipe flow. As a result of this,

certain formulae were created, some experimentally while others theoretically. From these formulae

two equations for the two separate flow states of turbulent and laminar are used commonly by

engineers to model pipe systems today.

For turbulent flow hf is given by the Darcy-Weisbach equation,

hf =

where = friction factor, L = pipe length and g = Accelaration due to gravity

For Laminar Flow hf is determined by the Hagen-Poiseuille Equation,

hf =

If the Hagen-Poiseuille Equation is expressed in the form of the Darcy-Weisbach equation, an equivalent

friction factor can be defined for laminar flow so that

hf =

=

yielding =

Apart from these equations, some other empirical equations are used occasionally

Eg: The Hazen-Williams formula

hf =

here C is a dimensional constant dependent on the pipe material and diameter and having values

between 75-150.

In both these cases, the friction factor can be found using several different methods.

1. Applying the Colebrook-White equation

The general form of the Colebrook-White equation is as follows

Where k = surface roughness of the pipe, D = diameter of pipe and = friction factor

Here = f(( ) therefore it is solved by iterative methods

However at lower Re values (Re 4000)

<<<

Then at lower Re values (Re )

0 Therefore

These are known as Prandtl and Von Karmann equations.

2. Using the Moody Diagram

The Variation of with the relative roughness

and Re values are graphically expressed in the Moody

diagram. This diagram has been obtained through a various number of experimental data and any pipe

obeying normal frictional flows will have values within the chart in the respected areas ( turbulent or

laminar). This method is rather easier and less time consuming than solving the above mentioned

equations.

3. Using Wallingford charts or tables

The Darcy-Weisbach equation and the Colebrook-White equation have been graphically represented in

“charts for the hydraulic design of channels and pipes” and have been tabularly represented in “tables

for the hydraulic design of channels and pipes” which have been published by the Hydraulic research

station, Wallingford, UK. Thus the name Wallingford charts and Wallingford tables being given to them.

These provide yet another convenient method for engineers to obtain various properties for a pipe flow,

not only the friction factor but also the required pipe diameter for a certain flow rate or the velocity in a

pipe for a particular roughness value hence eliminating the need to be involved in tedious sums using

the Colebrook-White equation.

Apparatus

1. Pipe Friction Apparatus 1 (for pipe with small diameter)

2. Pipe Friction Apparatus 2 (For larger diameter pipes)

3. Stop Watch

4. Measuring Vessel

5. Ruler/Measuring Tape

Methodology

For horizontal pipe of uniform diameter, hf ( frictional head loss) can be expressed as

hf =

Where P1 and P2 are the pressures at sections (1) and (2) respectively, as shown in the above diagram,

which can be measured by the piezometers or the differential manometer.

V can be expressed as

V =

in which flow rate = Q =

where is the volume of outflow in a time

Re can be calculated by the equation given earlier and therefore

can be calculated using the Darcy-Weisbach equation and the Darce-Weisbach equivalent for the

Hagen-Poiseuille equation.

hf =

and Re =

(where V =

)

then, hf =

and Re =

2.0 Procedure

Fix the apparatus as shown in the above diagrams for the two pipe cases.

Once a specific flow rate is set by the water pump do not adjust the pump, only adjust the flow

rate through the control valve at the down stream end.

First compare manometer readings at minimum and maximum output flow rates in pipes and

divide the difference in readings by the number of records to be taken in order to approximate a

periodical change in pressures to obtain flow rate values.

Obtain steady flow rates for different manometer readings and record them.

For each flow the outflow in a time is measured three times for an average value to be taken for

better accuracy of experimental values.

Measure the length of Pipe.

Record the diameter of the pipe.

Special considerations to be taken when handling the pipe of small diameter

Special care should be taken to observe that the manometric liquid and piezometric liquids do

not mix.

Also the dropping of the piezometric liquid level inside the pipe should be avoided.

To obtain a larger range or readings the internal pressure of the piezometric apparatus can be

increased by using a bicycle pump, but attention should be paid to the piezometric levels to

ensure none of the above mentioned occurs.

3.0 Calculations

PVC Pipe

Length (m) = 6.16

Diameter (m) = 0.016

a1x10-

3(m)

a2x10-

3(m)

deltaVx10-

6(m3) t1 t2 t3

Qx10-

6(m3/s)

hfx10-

3(m)

lambdax10

9 Re

21.9 7 10940 27.17 26.82 27.06 404.9352252 187.74

2.35637E-

12 36224.79

19.9 8.5 10940 31.76 31.87 31.92 343.4850863 143.64

2.50563E-

12 30727.57

19 9.4 10940 35.36 35.13 35.3 310.2372625 120.96

2.58649E-

12 27753.28

17.5 10.5 4790 19.13 19.16 18.81 251.6637478 88.2

2.86606E-

12 22513.4

16.7 11.4 4790 22.34 22.65 22.41 213.2047478 66.78

3.0235E-

12 19072.92

16 11.9 4790 26.34 26.76 26.99 179.423149 51.66

3.30259E-

12 16050.88

15.4 12.5 4790 32.16 32.06 32.13 149.1437468 36.54

3.38077E-

12 13342.14

14.8 12.9 4790 40.95 41.25 42.33 115.393881 23.94

3.70012E-

12 10322.93

14.3 13.2 4790 58.89 59 58.42 81.50416879 13.86

4.29399E-

12 7291.22

GI Pipe

Length (m) = 6.16

Diameter (m) = 0.0185

a1x10-

3(m)

a2x10-

3(m)

deltaVx10-

6(m3) t1 t2 t3

Qx10-

6(m3/s)

hfx10-

3(m)

lambdax10

9 Re

26.3 24.3 4790 61.75 61.49 61.24 77.89462272 25.2

1.76645E-

11 6026.652

28.2 22.5 4790 36.39 35.68 36.16 132.7727987 71.82

1.73278E-

11 10272.54

29.3 21.4 4790 30.6 30.99 29.89 157.0835155 99.54

1.71574E-

11 12153.44

30.5 20.3 4790 26.8 27.14 27.05 177.4293123 128.52

1.73635E-

11 13727.58

32.5 18.4 4790 22.24 22.86 22.62 212.1972829 177.66

1.67813E-

11 16417.55

34.1 16.8 4790 20.61 20.37 20.91 232.1861367 217.98

1.71973E-

11 17964.08

36 15 4790 18.75 18.33 18.29 259.5268196 264.6

1.67087E-

11 20079.41

37.7 13.6 10940 39.09 38.99 39.09 280.1058291 303.66

1.64611E-

11 21671.59

39 12.5 10940 36.95 37.38 37.59 293.2451751 333.9

1.65147E-

11 22688.17

40.5 11 10940 35.3 34.69 33.67 316.6120008 371.7

1.57708E-

11 24496.05

42.5 9.5 10940 15.02 15.27 14.91 726.1061947 415.8

3.35429E-

12 56178.32

a1x10-

3(m)

a2x10-

3(m)

deltaVx10-

6(m3) t1 t2 t3

Qx10-

6(m3/s)

hfx10-

3(m)

lambdax10

9 Re

390 355 100 76.97 76.92 76.84 1.300221038 35

1.16077E-

10 620.3493

393 347 100 52.94 52.91 53.07 1.88774226 46

7.23745E-

11 900.6619

398 339 100 41.59 42.08 41.91 2.388915432 59

5.79647E-

11 1139.777

402 326 100 32.39 32.7 32.38 3.077870114 76

4.49807E-

11 1468.485

412 311 200 48.77 48.82 48.71 4.101161996 101

3.36683E-

11 1956.708

455 257 200 38.23 38.75 39.22 5.163511188 198

4.16378E-

11 2463.566

493 211 200 31.86 32.05 32.13 6.247396918 282

4.05102E-

11 2980.699

410 37 250 34.46 34.11 34.34 7.287921485 373

3.93745E-

11 3477.145

494 38 300 35.98 35.93 34.99 8.419083255 456

3.60702E-

11 4016.834

528 15 300 33.13 32.42 33.15 9.118541033 513

3.45923E-

11 4350.553

274 317 400 43.22 43.61 42.89 9.250693802 541.8

3.5498E-

11 4413.604

272 319 400 42.25 42.38 43.45 9.369144285 592.2

3.78253E-

11 4470.118

272 319 400 40.51 41.11 41.31 9.761652973 592.2

3.48446E-

11 4657.388

271 320 400 39.27 39.35 40.21 10.09845998 617.4

3.39445E-

11 4818.082

268 322 400 37.7 37.2 37.52 10.67425725 680.4

3.34813E-

11 5092.801

266 324 400 37.82 36.66 36.74 10.78942636 730.8

3.51978E-

11 5147.75

264 326 500 44.83 45.19 45.03 11.10699741 781.2

3.55044E-

11 5299.266

4.0 Discussion

Significance of Frictional Head loss in the analysis of pipe flow

Analysis of pipe flow deals with the characteristics of fluid flowing within a pipe. The flow rate between

points of the pipe, the velocity of the fluid, etc… In an ideal pipe having no head loss one could simply

find all above mentioned factors if the necessary data about the pipe was given, since the Head

differences at two points would be the same. However if there were to be some limiting force against

the flow of the water, the analysis of the flow would not be as straight forward. As there is no ideal pipe

in practical applications there will always exist a frictional head loss, no matter how minimal it maybe,

affecting the fluid flow in the pipe.

More accurately there will be two types of head loss, frictional and local, but in civil engineering

applications where we deal with considerably larger pipes with a small number of bends the local losses

reduce to something comparatively negligible. Hence the frictional head loss becomes the major

component. Therefore it is vital that frictional head loss be taken into account when analysing pipe

flows.

Smooth Turbulent Flow

If the Renault Number in a fluid undergoing turbulent flow is close to the value 4000 then it is knows as

a smooth turbulent flow.

Rough Turbulent Flow

If the Renault Number in a fluid undergoing turbulent flow is very high then it is knows as a rough

turbulent flow.

Transitional Turbulent Flow

Transitional turbulent flow is a region in between the smooth turbulent flow and rough turbulent flow

having fluid with a moderate Renault number.

Hydraulically Smooth Pipes

If the Flow rate inside a pipe can produce a laminar flow then the pipe is said to be a hydraulically

smooth pipe. Concrete, Cast iron, Copper and Glass all produce smooth pipes. The surface roughness

plays a major role in deciding the flow rate at which turbulent flow occurs. Therefore a material with

higher surface roughness can cause turbulent flows at lower flow rates.

Hydraulically Rough Pipes

The flow rate in a pipe producing turbulent flow is said to be a hydraulically rough pipe. The surface

roughness values of these pipes are considerably higher, which causes the flow rate to be turbulent at a

lower flow rate than a smooth pipe having identical dimensions.

Behaviour of friction factor and Moody Diagram

For low Re values the fluid remains laminar. Therefore the relationship between the friction factor and

the Re number is = (64/Re) while for turbulent flows the relationship becomes much more

complicated. Hence the curvatures in the Moody diagram.

Effect of Aging of pipes and friction factor

Aging of a pipe is its prolonged usage. As a pipe is used for a long time, if improperly maintained the

interior will be encrusted with scale, dirt, tubercules or other foreign matter. This causes an increase in

roughness value of the pipe but comparatively the diameter of the pipe is considered as unchanged.

Therefore the relative roughness of the pipe will increase. According to the Moody diagram this increase

in relative roughness will cause an increase in the friction factor as well. ( some studies have shown a 4

inch diameter steel pipe undergoing a 20% increase in friction factor after its roughness was increased

by twice the value from 3 years usage).

Local Losses and their significance in engineering applications

Apart from the Frictional Head losses, Local Head losses ( minor head losses) are incurred at pipe bends,

junctions and valves. These losses occur due to eddy formation generated by the fluid at the fitting. For

cases where pipes are shorter the local losses could be higher than the frictional head loss, therefore it

is important to consider this in such situations or there would be an error in any assumption made

about the flow system.

Local head loss can be expressed in the form hl =kl

Where kl = constant for a particular fitting

An expression can be derived for kl in terms of the area of the pipe.

The types of local losses are

1. Sudden Contraction

2. Sudden Expansion

3. Head Losses due to Bending

4. Losses due to pipe junctions

5.0 References

Flows of fluids through valves, fittings and Pipes. Crane (p12)

Hydraulics in Civil and Environmental Engineering, Taylor & Francis, 2004, (p112)