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 HagenPoiseuille 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 h f is determined by the Hagen-Poiseuille Equation, hf =
If the Hagen-Poiseuille Equation is expressed in the form of t he Darcy-Weisbach equation, an equivalent friction factor can be defined for laminar flow so that
h = = yielding = f
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
<<<
Then at lower Re values (Re
0 Therefore
4000)
)
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, h f ( 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.
h = and Re = (where V = ) then, h = and Re = f
f
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 a1x10-
a2x10-
deltaVx10-
3(m)
3(m)
6(m3)
t1
t2
t3
Qx10-
hfx10-
lambdax10
6(m3/s)
3(m)
9
Re
2.35637E21.9
7
10940
27.17
26.82
27.06
404.9352252
187.74
12
36224.79
2.50563E19.9
8.5
10940
31.76
31.87
31.92
343.4850863
143.64
12
30727.57
2.58649E19
9.4
10940
35.36
35.13
35.3
310.2372625
120.96
12
27753.28
2.86606E17.5
10.5
4790
19.13
19.16
18.81
251.6637478
88.2
12
22513.4
3.0235E16.7
11.4
4790
22.34
22.65
22.41
213.2047478
66.78
12
19072.92
3.30259E16
11.9
4790
26.34
26.76
26.99
179.423149
51.66
12
16050.88
3.38077E15.4
12.5
4790
32.16
32.06
32.13
149.1437468
36.54
12
13342.14
3.70012E14.8
12.9
4790
40.95
41.25
42.33
115.393881
23.94
12
10322.93
4.29399E14.3
13.2
Length (m) = 6.16 Diameter (m) = 0.016
4790
58.89
59
58.42
81.50416879
13.86
12
7291.22
GI Pipe a1x10-
a2x10-
deltaVx10-
3(m)
3(m)
6(m3)
t1
t2
t3
Qx10-
hfx10-
lambdax10
6(m3/s)
3(m)
9
Re
1.76645E26.3
24.3
4790
61.75
61.49
61.24
77.89462272
25.2
11
6026.652
1.73278E28.2
22.5
4790
36.39
35.68
36.16
132.7727987
71.82
11
10272.54
1.71574E29.3
21.4
4790
30.6
30.99
29.89
157.0835155
99.54
11
12153.44
1.73635E30.5
20.3
4790
26.8
27.14
27.05
177.4293123
128.52
11
13727.58
1.67813E32.5
18.4
4790
22.24
22.86
22.62
212.1972829
177.66
11
16417.55
1.71973E34.1
16.8
4790
20.61
20.37
20.91
232.1861367
217.98
11
17964.08
1.67087E36
15
4790
18.75
18.33
18.29
259.5268196
264.6
11
20079.41
1.64611E37.7
13.6
10940
39.09
38.99
39.09
280.1058291
303.66
11
21671.59
1.65147E39
12.5
10940
36.95
37.38
37.59
293.2451751
333.9
11
22688.17
1.57708E40.5
11
10940
35.3
34.69
33.67
316.6120008
371.7
11
24496.05
3.35429E42.5
9.5
Length (m) = 6.16 Diameter (m) = 0.0185
10940
15.02
15.27
14.91
726.1061947
415.8
12
56178.32
a1x10-
a2x10-
deltaVx10-
3(m)
3(m)
6(m3)
t1
t2
t3
Qx10-
hfx10-
lambdax10
6(m3/s)
3(m)
9
Re
1.16077E390
355
100
76.97
76.92
76.84
1.300221038
35
10
620.3493
7.23745E393
347
100
52.94
52.91
53.07
1.88774226
46
11
900.6619
5.79647E398
339
100
41.59
42.08
41.91
2.388915432
59
11
1139.777
4.49807E402
326
100
32.39
32.7
32.38
3.077870114
76
11
1468.485
3.36683E412
311
200
48.77
48.82
48.71
4.101161996
101
11
1956.708
4.16378E455
257
200
38.23
38.75
39.22
5.163511188
198
11
2463.566
4.05102E493
211
200
31.86
32.05
32.13
6.247396918
282
11
2980.699
3.93745E410
37
250
34.46
34.11
34.34
7.287921485
373
11
3477.145
3.60702E494
38
300
35.98
35.93
34.99
8.419083255
456
11
4016.834
3.45923E528
15
300
33.13
32.42
33.15
9.118541033
513
11
4350.553
3.5498E274
317
400
43.22
43.61
42.89
9.250693802
541.8
11
4413.604
3.78253E272
319
400
42.25
42.38
43.45
9.369144285
592.2
11
4470.118
3.48446E272
319
400
40.51
41.11
41.31
9.761652973
592.2
11
4657.388
3.39445E271
320
400
39.27
39.35
40.21
10.09845998
617.4
11
4818.082
3.34813E268
322
400
37.7
37.2
37.52
10.67425725
680.4
11
5092.801
3.51978E266
324
400
37.82
36.66
36.74
10.78942636
730.8
11
5147.75
3.55044E264
326
500
44.83
45.19
45.03
11.10699741
781.2
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 thi s 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 h l =kl
Where kl = constant for a particular fitting An expression can be derived for k l 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)
