FRICTION COEFFICIENT IN PIPES
Table of Contents Table of Figures ....................................................................................................................................... 3 Theory ..................................................................................................................................................... 4
Objectives ............................................................................................................................................... 5 Apparatus............................................................................................................................................... 5 Procedure............................................................................................................................................... 6 Results .................................................................................................................................................... 7 Experimental Results ........................................................................................................................... 7 Copper 26mm .................................................................................................................................. 7 Copper 16mm .................................................................................................................................. 7 Galvanized Steel, 16 mm .................................................................................................................. 7 Conversions ......................................................................................................................................... 8 Flow Rates ....................................................................................................................................... 8 Diameters ........................................................................................................................................ 8 Height Readings ............................................................................................................................... 8 Calculations ......................................................................................................................................... 9 Velocity ........................................................................................................................................... 9 Formula for head loss: ..................................................................................................................... 9 Reynold’s Number ......................................................................................................................... 10 Haaland’s Equation ........................................................................................................................ 11
Calculated Results .......................................................................................................................... 11
Discussion ............................................................................................................................................ 13 Limitations: ........................................................................................................................................... 15 Source of Error ...................................................................................................................................... 15 Conclusions ........................................................................................................................................... 16
References............................................................................................................................................ 16
Figure 1: Diagram Showing Sketch of Apparatus Used for Studying Friction Coefficient in Pipes ...... 6 Figure 2: Table Showing the Upstream and Downstream Values of Copper 26 mm Pipe .......................... 7 Figure 3: Table Showing the Upstream and Downstrea m Values for Copper 16 mm Pipe ......................... 7 Figure 4: Table Showing The Upstream and Downstream Values of Galvanized Steel 16 mm Pipe ........... 7 Figure 5: Table Showing Copper 26 mm Converted SI unit Values ............................................................ 8 Figure 6: Table Showing Copper 16 mm Converted SI Units Values .......................................................... 8 Figure 7: Table Showing 16 m Galvanized Steel SI Unit Values ................................................................. 9 Figure 8: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Copper 26 mm Pipe ............................................................................................................................... 11 Figure 9: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Copper 16 mm Pipe ............................................................................................................................... 11 Figure 10: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Galvanized Steel 16 mm Pipe ................................................................................................................. 12 Figure 11: Graph Comparing Darcy's C oefficient vs. Reynold's number for Varying Flows in Three Different Pipes ..................................................................................................................................................... 12 Figure 12: Graph Comparing Darcy's Coefficient Obtained from Darcy's Equation and Haaland's Equation for a Flow Rate of 500L/h for Three Different Pipes ............................................................................... 12 Figure 13: Graph Showing Log of Darcy's Coefficients vs. Log of Reynolds Number Obtained through Haaland's Equation ................................................................................................................................ 13 Figure 14: Moody Diagram .................................................................................................................... 14
The pressure flow of fluid in pipe is not ideal and there is an experience of head loss along its journey. These head losses may include friction loss, exit loss, entry loss, abrupt contraction/expansion loss, bend loss, and elevat ion loss . Consider the formula for pressure:
=ℎ… 1.0 ℎ = …1.1
Δ
Δ
ℎ , , ,ℎ ℎ The loss being studied in this experiment is head loss due to friction. Darcy’s equation is introduced with a method to calculate head loss due to friction:
ℎ = = ∗ 2 …2.0 ℎ = , = ℎ , = =4… 2.1 ℎ ′ Δ
′
Once relative roughness and Reynolds number are acquired, one may be able to read Fanning’s friction factor from the Moody Diagram (see Figure 14 ) or calculated using Haaland’s formula
∝ ( ,)… 3.0 ℎ ℎ = = …3.1 ℎ ℎ ℎ 1 = 3.6log 6.9 +( ).… 3.2 3.71
Fluid flow may be laminar, transitional, or turbulent; where laminar flow has a Reynolds number of 2000 or less and turbulent flow has a Reynolds number of 4000 or greater. Reynolds numbers who don’t match these ranges are considered transitional. In laminar flow, the majority of the friction is caused by the “layers” of fluid sliding past each other. Darcy’s equation which accounts for t he length of the pipe is better suited in calculating friction coefficient in laminar flow. In turbulent flow, a large portion of friction caused co mes from the frequency of collision of fluid particles and the minute mounds on t he pipe’s uneven surface. Haalands formula is more generally used for turbulent flow as the Reynold’s number and relative roughness account for these occurrences of collision. In turbulent flow, the movement is more unpredictable and either method is used.
Objectives This research seeks to complete three objectives: 1) To obtain the Darcy’s coefficient values of fluid friction for two copper pipes and a galvanized pipe from Darcy’s equation and Haa land’s equations for comparison 2) To compare the effects of pipe roughness and cross section on pressure drop along the pipe 3) The coefficient of fluid friction is higher for copper pipes than it is for galvanized pipes. With equal cross section
Apparatus Fluid Friction Loss Measuring System – HM 122 which consists of the following components:
Galvanzied iron and copper pipes of length 1.3 m Cu pipe, 28 x 1mm; d = 26 mm Cu pipe, 18 x 1 mm; d = 16 mm St Pipe, galvanized, ½”, d = 16 mm
Manometeres with graduated scales
Variable area flow meter with two measuring ranges ( 640 l/h, 4 m^3/h)
Figure 1: Diagram Showing Sketch of Apparatus Used for Studying Friction Coefficient in Pipes Procedure
The immersible pump and outlet valve were opened to allow flow of water
The desired flow rate of 4m^3/h was adjusted by using the main flow valve upstream of the copper 26 mm pipe .
The difference in height values on the manometer were read
The procedure was repeated for flow rates of 4 m^3/h, 3m^3/h, 2m^3/h , 500L/h, 200L/h
This process was repeated for the remaining two pipes.
All readings were recorded.
Upstream (cm)
Flow rate , Q
Downstream (cm) Head Loss (cm)
Reading
1
2
Avg
1
2
Avg
3
41.3
41.0
41.2
32.5
32.3
32.4
8.8
3
38.4
38.0
38.2
31.5
31.3
31.4
6.8
3
34.5
34.3
34.4
31.5
31.2
31.4
3.1
34.8
34.5
34.7
32.2
31.9
32.1
2.6
33.6
33.4
33.5
30.5
30.2
30.4
3.2
4m /h 3m /h 2m /h 500L/h 200L/h
Figure 2: Table Showing the Upstream and Downstream Values of Copper 26 mm Pipe
Upstream (cm)
Flow rate, Q Readings
Downstream (cm)
1
2
Avg
1
2
Avg
Head Loss (cm)
3
54.8
55.0
54.9
15.5
15.7
15.6
39.3
3
41.8
41.9
41.9
24.5
24.8
24.7
17.2
41.7
42.0
41.9
25.0
25.3
25.2
16.7
42.0
42.2
42.1
26.3
26.5
26.4
15.7
42.0
42.4
42.2
29.0
29.2
29.1
13.1
2m /h 1m /h 500L/h 400L/h 300L/h
Figure 3: Table Showing the Upstream and Downstream Values for Copper 16 mm Pipe
Flow rate, Q
Upstream (cm)
Readings 3
1
2
Downstream (cm) Avg
1
2
Head Loss (cm) Avg
0.6m /h
63.7
63.5
63.6
6.0
5.8
5.9
57.7
500L/h
48.2
48.0
48.1
21.0
20.8
20.9
27.2
400L/h
44.0
43.9
44.0
29.5
29.3
29.4
14.6
300L/h
39.8
39.6
39.7
32.7
32.5
32.6
7.1
200L/h
37.1
37.0
37.1
34.5
34.3
34.4
2.7
Figure 4: Table Showing The Upstream and Downstream Values of Galvanized Steel 16 mm Pipe
m ∗ 1 = m ⇒ 4∗ 1 =0.0011 h 3600 s 3600 L ∗ 10− = m ⇒ 500∗ 10− =0.00014ms− h 3600 s 3600 1000=1 100=1 Upstream (m)
Flow rate , Q m³ /s
Downstream (m)
Head Loss (m)
Reading
1
2
Avg
1
2
Avg
0.00111
0.413
0.41
0.4115
0.325
0.323
0.324
0.0875
0.00083
0.384
0.38
0.382
0.315
0.313
0.314
0.068
0.00056
0.345
0.343
0.344
0.315
0.312
0.3135
0.0305
0.00014 0.00006
0.348
0.345
0.3465
0.322
0.319
0.3205
0.026
0.336
0.334
0.335
0.305
0.302
0.3035
0.0315
Figure 5: Table Showing Copper 26 mm Converted SI unit Values
Upstream (m)
Flow rate , Q m³ /s
Downstream (m)
Reading
1
2
Avg
1
2
Avg
Head Loss (m)
0.00056
0.548
0.55
0.549
0.155
0.157
0.156
0.393
0.00028
0.418
0.419
0.4185
0.245
0.248
0.2465
0.172
0.00014 0.00011 0.00008
0.417
0.42
0.4185
0.25
0.253
0.2515
0.167
0.42
0.422
0.421
0.263
0.265
0.264
0.157
0.42
0.424
0.422
0.29
0.292
0.291
0.131
Figure 6: Table Showing Copper 16 mm Converted SI Units Values
Upstream (m)
Flow rate , Q m³ /s
Downstream (m)
Reading
1
2
Avg
1
2
Avg
Head Loss (m)
0.00017
0.637
0.635
0.636
0.06
0.058
0.059
0.577
0.00014 0.00011 0.00008 0.00006
0.482
0.48
0.481
0.21
0.208
0.209
0.272
0.44
0.439
0.4395
0.295
0.293
0.294
0.1455
0.398
0.396
0.397
0.3265
0.325
0.32575
0.07125
0.371
0.37
0.3705
0.345
0.343
0.344
0.0265
Figure 7: Table Showing 16 m Galvanized Steel SI Unit Values
= ,ℎ = , = , = − 0. 0 0056 / = 0.026 ≈ 1.05 − 2 − 0. 0 0056 = 0.016 ≈ 2.76 − 2 − 0. 0 0014 = 0.016 ≈ 0.69 − 2
− 0. 0 014 / = 0.026 ≈ 0.26 − 2 − 0. 0 0014 = 0.016 ≈ 0.69 − 2 − 0. 0 0006 = 0.016 ≈ 0.28 − 2
ℎ = 2 ⇒ = 2ℎ − ∗0.026 2∗0. 0 31∗9. 8 1 = 1.3 ∗ 1.046 − ≈0.0109 − ∗0.026 2∗0. 0 26∗9. 8 1 = 1.3 ∗ 0.262 − ≈0.1491
− ∗0.016 2∗0. 3 93∗9. 8 1 = 1.3 ∗ 2.763 − ≈0.0124 − ∗0.016 2∗0. 1 67 ∗9. 8 1 = 1.3 ∗ 0.691 − ≈0.845 − ∗0.016 2∗0. 2 72 ∗9. 8 1 = 1.3 ∗ 0.691− ≈0.1376 − ∗0.016 2∗0. 0 27 ∗9. 8 1 = 1.3 ∗ 0.276 − ≈0.838
= − ∗0.026 1. 0 5 = 8.94∗10− − ≈30432
− ∗0.026 0. 2 6 = 8.94∗10− − ≈7608
− ∗0.016 2. 7 6 = 8.94∗10− − ≈49452 − ∗0.016 0. 6 9 = 8.94∗10− − ≈12363 − ∗0.016 0. 6 9 = 8.94∗10− − ≈12363 − ∗0.016 0. 2 8 = 8.94∗10− − ≈4945
1 = 1.8log[6.9 + ( ). ] ⇒={1.8log[6.9 +( ). ]}− 3.71 3.71 √ . − 6. 9 0. 0 00001 ={1.8log[12363 +(3.71∗0.026 ) ]} ≈0.0333 . − 6. 9 0. 0 00001 ={1.8log[12363 +(3.71∗0.016 ) ]} ≈0.0292 . − 6. 9 0. 0 001 ={1.8log[12363 +(3.71∗0.016 ) ]} ≈0.0292
Readings Darcy 3
2m /h
Haaland
Re
0.00 78
0.0 19 82 7
60 86 3
1m /h 500L/h
0.01 08
0.0 21 14 5
45 64 8
0.01 09
0.0 23 23 7
30 43 2
400L/h 300L/h
0.1491
0.033344
7608
1.1289
0.044134
3043
3
Figure 8: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Copper 26 mm Pipe
Readings Darcy 3
2m /h 3
1m /h 500L/h 400L/h 300L/h
Haaland
Re
0.0124
0.020765
49452
0.0218
0.024431
24726
0.0845
0.029162
12363
0.1241
0.03098
9890
0.1841
0.033586
7418
Figure 9: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Copper 16 mm Pipe
Readings Darcy 3
2m /h 3
1m /h 500L/h 400L/h 300L/h
Haaland
Re
0.20 28
0.0 27 79 4
14 83 5
0.13 76
0.0 29 16 3
12 36 3
0.1150
0.030981
9890
0.1002
0.033587
7418
0.0838
0.037857
4945
Figure 10: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Galvanized Steel 16 mm Pipe
Figure 11: Graph Comparing Darcy's Coefficient vs. Reynold's number for Varying Flows in Three Different Pipes
Figure 12: Graph Comparing Darcy's Coefficient Obtained from Darcy's Equation and Haaland's Equation for a Flow Rate of 500L/h for Three Different Pipes
Figure 13: Graph Showing Log of Darcy's Coefficients vs. Log of Reynolds Number Obtained through Haaland's Equation
Discussion According to the theory, Darcy’s equation is affected by several variables. The results are analyzed in terms of: equation used, flow rate, cross sectional area of pipe, roughness of the pipe. When the coefficient of friction was used using Darcy’s equat ion (See equation 2.0, Figure 11) and the Haalands Equation (see equation 3.2, Figure 13) , it was found that for both equations, the coefficient values increased as the flow rate increased, with the exception of experimental galvanized steel pipe. With galvanized steel, the coefficient of friction tends to increase as the flow rate increases. The latter may due to an error in the experiment as the majority of the results verify the theory that flow rate (and thus velocity) is inversely proportional with Darc y’s coefficient of friction.
Darcy’s equation considers the variables head loss & diameter (directly proportional) and pipe length & fluid velocity (inversely proportional) to Darcy’s coefficient.
Haaland’s equation considers the relative roughness of the p ipe (equation 3.0) and Reynolds number (equation 3.1) to be directly proportional to the coefficient of friction. With these values it is also possible to read the friction factor fro m moody’s diagram.
Figure 14: Moody Diagram
The Reynolds number decrease as vo lume flow rate decrease, verifying the formula for Reynold’s number. The range of all the Reynold’s numbers were above 4000, except for a flow rate of 200L/h, where the Reynold’s number placed the fluid in transition flow. When comparing Darcy’s equation and Haaland’s equat ion with a controlled variable (500L/h) for the three pipes, it was found that Darcy’s equation yields higher and less stabilized values. Haaland equation’s more consist results emphasizes its practicability in turbulent flow calculations. The only drawback seems to be lack of repeated tests to ensure quality of results to verify what caused the discrepancy in galvanized steel pipes.
Different cross section of pipes (with a controlled variable of equal ro ughness) were analyzed for two flow rates which both pipes had in common: 2m^3/h and 500 L/h. The results showed (1) for 2m^3/h, the greater diameter has a lower friction factor using Darcy’s equation but a higher friction factor using Haaland’s equation (2)for 500L/h the friction factor values where higher when there is a higher diameter when using both equations. Categorizing Darcy’s equation calculations for 2m^3/h as an error, it can be shown t hat the greater cross sectional area does
yield a higher friction factor because there is a more area (greater circumference of the pipe for roughness to occur: increasing fluid particle collision)
In terms of roughness, galvanized steel has a higher value of friction factor than compared to copper of the equal diameter and flow rate. However, with Haaland’s equation, the galvanized steel has a higher friction factor, than the co pper pipes of equal diameter and flow rate. It was already analyzed before that galvanized steel values may have been affected by lab errors and experimentally do not agree with fluid flow friction theories.
Students are only able to o bserve the experiments of one pipe and will have little or no access to errors that occurred in other teams.
There is a lack of iteration and results cannot be verified through several attempts
The negligible head losses do contribute, albeit slightly, to the head loss
Imperfect design to equipment, no smooth bell shape curve to inlets, unnecessary roughness, imprecise flow meters
Vibration of the apparatus may affect fluid flow
Parallax Error: Meniscus may not have been read a t eye level
Human Error: The inconsistent meniscus level was left to the subjectivity of the experimenter
Heat Loss: some energy was lost in the form o f heat around the pipe.
Faulty equipment: equipment kept leaking, altering the fluid flow
Not including the errors or discrepancies
1) Haalands equations results for Darcy’s coefficients were more precise, consistent and lower in value for all diameters, roughness and flow rates when compared to t hose obtained from Darcy’s equation. 2) It was found that a higher cross sectional area and relative roughness values, increased the friction factor, therefore giving a greater head loss. 3) The coefficient of fluid friction for galvanized pipe is greater than the coefficient of fluid
friction for copper due to its increased roughness.
References Bernard Massey, “Mechanics of Fluids 8 th Edition”, Reader Emeritus in Mechanical Engineering, University College London, Published by Taylor and Francis Group, London and New York , 2006 Class Notes, “Turbulent Flow in Pipes”, Mechanics of Fluids, the University of the West Indies, St. Augustine, Trinidad and Tobago Philip B. Bedient, “Darcy’s Law and Flow”, Civil and Environmental Engineering, Rice University, [online], last updated: July 20, 2010, [Site accessed March 12, 2014], http://www.slideshare.net/oscarpiopatino/darcys-law Native Dynamics, “Pressure Loss in Pipe” Neutrium, [online], (Last Updated: April 29, 2012), [ site accessed March 12, 2014], http://neutrium.net/fluid_flow/pressure-loss-in-pipe/
