Friction Coefficient in Pipes

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

Reynolds Number ......................................................................................................................... 10

Haalands Equation ........................................................................................................................ 11

Calculated Results .......................................................................................................................... 11

Discussion ............................................................................................................................................ 13

Limitations: ........................................................................................................................................... 15

Source of Error ...................................................................................................................................... 15

Conclusions ........................................................................................................................................... 16

References............................................................................................................................................ 16

Table of Figures

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 Downstream 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


Copper 16 mm Pipe ............................................................................................................................... 11


Galvanized Steel 16 mm Pipe ................................................................................................................. 12

Figure 11: Graph Comparing Darcy's Coefficient 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

Theory

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 elevation loss . Consider the formula for pressure:

= (1.0)

=

(1.1)

, , ,

The loss being studied in this experiment is head loss due to friction. Darcys equation is

introduced with a method to calculate head loss due to friction:

=

=

2

2 (2.0)

= , = , =

= 4 (2.1)

Once relative roughness and Reynolds number are acquired, one may be able to read Fannings

friction factor from the Moody Diagram (see Figure 14) or calculated using Haalands formula

(

, ) (3.0)

=

=

(3.1)

1

= 3.6 log10 (

6.9

+ (

3.71)

1.1

) (3.2)

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 dont 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. Darcys equation which accounts for the length of the pipe is better suited in calculating

friction coefficient in laminar flow.

In turbulent flow, a large portion of friction caused comes from the frequency of collision of

fluid particles and the minute mounds on the pipes uneven surface. Haalands formula is more

generally used for turbulent flow as the Reynolds 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 Darcys coefficient values of fluid friction for two copper pipes and a

galvanized pipe from Darcys equation and Haalands 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, , 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.

Results

Experimental Results

Copper 26mm

Figure 2: Table Showing the Upstream and Downstream Values of Copper 26 mm Pipe

Copper 16mm

Figure 3: Table Showing the Upstream and Downstream Values for Copper 16 mm Pipe

Galvanized Steel, 16 mm

Figure 4: Table Showing The Upstream and Downstream Values of Galvanized Steel 16 mm Pipe

Flow rate , Q

Reading 1 2 Avg 1 2 Avg

4m3/h 41.3 41.0 41.2 32.5 32.3 32.4 8.8

3m3/h 38.4 38.0 38.2 31.5 31.3 31.4 6.8

2m3/h 34.5 34.3 34.4 31.5 31.2 31.4 3.1

500L/h 34.8 34.5 34.7 32.2 31.9 32.1 2.6

200L/h 33.6 33.4 33.5 30.5 30.2 30.4 3.2

Upstream (cm) Downstream (cm)

Head Loss (cm)

Flow rate, Q

Readings 1 2 Avg 1 2 Avg

2m3/h 54.8 55.0 54.9 15.5 15.7 15.6 39.3

1m3/h 41.8 41.9 41.9 24.5 24.8 24.7 17.2

500L/h 41.7 42.0 41.9 25.0 25.3 25.2 16.7

400L/h 42.0 42.2 42.1 26.3 26.5 26.4 15.7

300L/h 42.0 42.4 42.2 29.0 29.2 29.1 13.1

Downstream (cm)Upstream (cm)Head Loss (cm)

Flow rate, Q

Readings 1 2 Avg 1 2 Avg

0.6m 3 /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

Downstream (cm)Upstream (cm) Head Loss (cm)

Conversions

Flow Rates

m3

h

1

3600=

m3

s 4

1

3600= 0.00113

L

h

103

3600=

m3

s 500

103

3600= 0.00014m3s1

Diameters

1000 = 1

Height Readings

100 = 1

Figure 5: Table Showing Copper 26 mm Converted SI unit Values

Figure 6: Table Showing Copper 16 mm Converted SI Units Values

Flow rate , Q m /s


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 0.348 0.345 0.3465 0.322 0.319 0.3205 0.026

0.00006 0.336 0.334 0.335 0.305 0.302 0.3035 0.0315

Head Loss

(m)

Downstream (m)Upstream (m)

Flow rate , Q m /s


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 0.417 0.42 0.4185 0.25 0.253 0.2515 0.167

0.00011 0.42 0.422 0.421 0.263 0.265 0.264 0.157

0.00008 0.42 0.424 0.422 0.29 0.292 0.291 0.131

Upstream (m) Downstream (m) Head Loss

(m)

Figure 7: Table Showing 16 m Galvanized Steel SI Unit Values

Calculations

Velocity

=

, = , = , =

Copper 26 mm

2 3/ =0.0005631

(0.026

2)

2 1.05 1 500/ =

0.001431

(0.026

2)

2 0.26 1

Copper 16 mm

2

3

=0.0005631

(0.016

2 )2 2.76

1 500

=0.00014 31

(0.016

2 )2 0.69

1

Galvanized Steel 16 mm

500

=0.00014 31

(0.016

2 )2 0.69

1 200

=0.00006 31

(0.016

2 )2 0.28

1

Formula for head loss:

=2

2 =

2

2

Copper 26mm

2

3

=2 0.031 9.81 1 0.026

1.3 (1.046 1)2 0.0109

500

=2 0.026 9.81 1 0.026

1.3 (0.262 1)2 0.1491

Flow rate , Q m /s


0.00017 0.637 0.635 0.636 0.06 0.058 0.059 0.577

0.00014 0.482 0.48 0.481 0.21 0.208 0.209 0.272

0.00011 0.44 0.439 0.4395 0.295 0.293 0.294 0.1455

0.00008 0.398 0.396 0.397 0.3265 0.325 0.32575 0.07125

0.00006 0.371 0.37 0.3705 0.345 0.343 0.344 0.0265

Upstream (m) Downstream (m) Head Loss

(m)

Copper 16mm

2

3

=2 0.393 9.81 1 0.016

1.3 (2.763 1)2 0.0124

500

=2 0.167 9.81 1 0.016

1.3 (0.691 1)2 0.845


500

=2 0.272 9.81 1 0.016

1.3 (0.6911)2 0.1376

200

=2 0.027 9.81 1 0.016

1.3 (0.276 1)2 0.838

Reynolds Number

=

Copper 26 mm

2

3

=1.05 1 0.026

8.94 107 21 30432

500

=0.26 1 0.026

8.94 107 21 7608

Copper 16 mm

2

3

=2.76 1 0.016

8.94 107 21 49452

500

=0.69 1 0.016

8.94 107 21 12363


500

=0.69 1 0.016

8.94 107 21 12363

200

=0.28 1 0.016

8.94 107 21 4945

Haalands Equation

1

= 1.8 log [

6.9

+ (

3.71)

1.11

] = {1.8 log [6.9

+ (

3.71)

1.11

]}

2

Copper 26 mm

500

= {1.8 log [6.9

12363+ (

0.000001

3.71 0.026 )

1.11

]}

2

0.0333

Copper 16 mm

500

= {1.8 log [6.9

12363+ (

0.000001

3.71 0.016 )

1.11

]}

2

0.0292


500

= {1.8 log [6.9

12363+ (

0.0001

3.71 0.016 )

1.11

]}

2

0.0292

Calculated Results

Copper 26 mm

Figure 8: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Copper 26 mm Pipe

Copper 16 mm

Figure 9: Table Showing Reynold's Numbers and Darcy's Coefficients Obtained for Various Flow Rates in Copper 16 mm Pipe

Readings

Darcy Haaland Re

2m3/h 0.0078 0.019827 60863

1m3/h 0.0108 0.021145 45648

500L/h 0.0109 0.023237 30432

400L/h 0.1491 0.033344 7608

300L/h 1.1289 0.044134 3043

Readings Darcy Haaland Re

2m3/h 0.0124 0.020765 49452

1m3/h 0.0218 0.024431 24726

500L/h 0.0845 0.029162 12363

400L/h 0.1241 0.03098 9890

300L/h 0.1841 0.033586 7418


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

Readings Darcy Haaland Re

2m3/h 0.2028 0.027794 14835

1m3/h 0.1376 0.029163 12363

500L/h 0.1150 0.030981 9890

400L/h 0.1002 0.033587 7418

300L/h 0.0838 0.037857 4945

Figure 13: Graph Showing Log of Darcy's Coefficients vs. Log of Reynolds Number Obtained through Haaland's Equation

Discussion

According to the theory, Darcys 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 Darcys equation (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 Darcys

coefficient of friction.

Darcys equation considers the variables head loss & diameter (directly proportional) and pipe

length & fluid velocity (inversely proportional) to Darcys coefficient.

Haalands equation considers the relative roughness of the pipe (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 from moodys diagram.

Figure 14: Moody Diagram

The Reynolds number decrease as volume flow rate decrease, verifying the formula for

Reynolds number. The range of all the Reynolds numbers were above 4000, except for a flow

rate of 200L/h, where the Reynolds number placed the fluid in transition flow.

When comparing Darcys equation and Haalands equation with a controlled variable (500L/h) for

the three pipes, it was found that Darcys equation yields higher and less stabilized values. Haaland

equations 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 roughness) 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 Darcys equation but a higher

friction factor using Haalands equation (2)for 500L/h the friction factor values where higher

when there is a higher diameter when using both equations. Categorizing Darcys equation

calculations for 2m^3/h as an error, it can be shown that 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 Haalands equation, the galvanized

steel has a higher friction factor, than the copper 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.

Limitations:

Students are only able to observe 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

Source of Error

Vibration of the apparatus may affect fluid flow

Parallax Error: Meniscus may not have been read at 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 of heat around the pipe.

Faulty equipment: equipment kept leaking, altering the fluid flow

Conclusions

Not including the errors or discrepancies

1) Haalands equations results for Darcys coefficients were more precise, consistent and

lower in value for all diameters, roughness and flow rates when compared to those obtained

from Darcys 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 8th 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, Darcys 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/

http://www.slideshare.net/oscarpiopatino/darcys-lawhttp://neutrium.net/fluid_flow/pressure-loss-in-pipe/

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Friction Coefficient in Pipes