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- The Energy of a Fluid: Head Loss through a Pipe

Head Loss through a Pipe Head Loss through a Pipe Introduction Head loss is the loss of the energy of a fluid as it flows through any given pipe. The head loss is divided into minor head losses and major head losses. There are various causes of minor losses which include pipe constrictions, bending in the pipes, joints in the pipe, sudden enlargement of the pipe among others. Major Head losses are caused by friction as the fluid moves through the paper.

This experiment is aimed at determining occurrence of head loss due to friction as a fluid moves through a closed conduit, pipe

Procedure

Apparatus used were pipes, tapered tube flow meters control valves and manometers.

The diameter of the pipe was measured and corresponding Q and h measured together with other pipe dimensions that included the pipe length.

Results, analysis and analysis

No

Q (m³/s)

A

V= Q/A

Hf

Log v

Log hf

Volume

Volume

Time

Q

(m²)

(m/s)

(m)

(ml³)

(m³)

(s)

(m³/s)

1

81

0.000081

30.19

2.68301E-06

82

0.000082

32.4

2.53086E-06

7.07E-06

0.358023

0.065

-0.44609

-1.18709

81

0.000081

30.22

2.68034E-06

2

121

0.000121

30.23

4.00265E-06

122

0.000122

31.44

3.88041E-06

7.07E-06

0.548933

0.085

-0.26048

-1.07058

119

0.000119

30.11

3.95218E-06

3

165

0.000165

30.24

5.45635E-06

165

0.000165

30.35

5.43657E-06

7.07E-06

0.769072

0.152

-0.11403

-0.81816

163

0.000163

30.6

5.3268E-06

4

105

0.000105

15.24

6.88976E-06

106

0.000106

15.44

6.86528E-06

7.07E-06

0.971182

0.294

-0.0127

-0.53165

105

0.000105

15.3

6.86275E-06

Graph of log hf against log V

The equation of the best fit line on the above is hf=1.4747v-0.5946. From the equation, it can be deduced that the values of n and k are like calculated below.

For

For k,

To determine the value of the Darcy’s friction coefficient, the relationship between hf and velocity.

To find the value of K, arbitrary point is taken from the graph and this gives two pints that represents log hf and log V as below

The point is (-0.4, -1.2)

Thus the value of K is

Using the value of K, The Darcy’s Friction factor can be calculated as

Table 2

No

Q (m³/s)

A

V= Q/A

Hf

Log v

Log hf

Volume

Volume

Time

Q

(m²)

(m/s)

(m)

(ml³)

(m³)

(s)

(m³/s)

1

82

0.000082

30.21

2.7143E-06

7.07E-06

0.38397694

0.06

-0.41569485

-1.22184875

80

0.00008

30.3

2.6403E-06

0.37349894

-0.42771062

80

0.00008

30.21

2.6481E-06

0.37461165

-0.42641872

2

150

0.00015

19.65

7.6336E-06

7.07E-06

1.07986813

0.385

0.033370723

-0.41453927

152

0.000152

20.23

7.5136E-06

1.06289343

0.026489724

3

128

0.000128

15.23

8.4045E-06

7.07E-06

1.1889185

0.444

0.075152085

-0.35261703

126

0.000126

15.01

8.3944E-06

1.18749522

0.074631871

4

88

0.000088

10.11

8.7043E-06

7.07E-06

1.23132738

0.47

0.090373535

-0.32790214

88

0.000088

9.92

8.871E-06

1.25491127

0.098613018

From the graph.

is calculated as

Taking an arbitrary point from the trend line, (0,-0.3)

Using the points the value of and v at the given point are;

But This implies that

There are other various methods that can be used to calculate the Darcy’s Friction factor. For a laminar flow, it can be calculated as, for turbulent flow, the Colebrook white equation can be used

Determination of head loss is important since it helps in the determining the net positive suction head in any given flow. Also, Determination of head loss is vital since it facilitates proper determination of fittings along the pipe which include pipe fittings, valves and elbows. Determination of Darcy’s Friction factor helps in the calculation of the Total Dynamic head which is used in the determination of the size of the pump to be used.

Appropriate determination of the required components is vital since it reduces wastage thus eliminating unnecessary costs.

Conclusion

The graph shows that the measured data was not consistent. This can be attributed to the errors that were encountered during the flow. Some of the sources of the errors maybe due to the fluid in the pipe not filling up the pipe and due to parallax errors while making measurements.

Comparing the results of the two graphs, it can be seen that the values of n and k are different in the two results. Thus it can be concluded that the two values varies depending on the pipe properties in any given situation.

From the trend line on the graph, it can be concluded that as velocity increases, hf increases lineally.

References

Spellman, F. R., 2000. The Science of Water: Concepts and Applications, Second Edition. 1st ed. Boca raton: CRC Press.

Spellman, F. R., 2008. Handbook of Water and Wastewater Treatment Plant Operations, Second Edition. 2nd ed. Boca Raton: CRC Press.

This experiment is aimed at determining occurrence of head loss due to friction as a fluid moves through a closed conduit, pipe

Procedure

Apparatus used were pipes, tapered tube flow meters control valves and manometers.

The diameter of the pipe was measured and corresponding Q and h measured together with other pipe dimensions that included the pipe length.

Results, analysis and analysis

No

Q (m³/s)

A

V= Q/A

Hf

Log v

Log hf

Volume

Volume

Time

Q

(m²)

(m/s)

(m)

(ml³)

(m³)

(s)

(m³/s)

1

81

0.000081

30.19

2.68301E-06

82

0.000082

32.4

2.53086E-06

7.07E-06

0.358023

0.065

-0.44609

-1.18709

81

0.000081

30.22

2.68034E-06

2

121

0.000121

30.23

4.00265E-06

122

0.000122

31.44

3.88041E-06

7.07E-06

0.548933

0.085

-0.26048

-1.07058

119

0.000119

30.11

3.95218E-06

3

165

0.000165

30.24

5.45635E-06

165

0.000165

30.35

5.43657E-06

7.07E-06

0.769072

0.152

-0.11403

-0.81816

163

0.000163

30.6

5.3268E-06

4

105

0.000105

15.24

6.88976E-06

106

0.000106

15.44

6.86528E-06

7.07E-06

0.971182

0.294

-0.0127

-0.53165

105

0.000105

15.3

6.86275E-06

Graph of log hf against log V

The equation of the best fit line on the above is hf=1.4747v-0.5946. From the equation, it can be deduced that the values of n and k are like calculated below.

For

For k,

To determine the value of the Darcy’s friction coefficient, the relationship between hf and velocity.

To find the value of K, arbitrary point is taken from the graph and this gives two pints that represents log hf and log V as below

The point is (-0.4, -1.2)

Thus the value of K is

Using the value of K, The Darcy’s Friction factor can be calculated as

Table 2

No

Q (m³/s)

A

V= Q/A

Hf

Log v

Log hf

Volume

Volume

Time

Q

(m²)

(m/s)

(m)

(ml³)

(m³)

(s)

(m³/s)

1

82

0.000082

30.21

2.7143E-06

7.07E-06

0.38397694

0.06

-0.41569485

-1.22184875

80

0.00008

30.3

2.6403E-06

0.37349894

-0.42771062

80

0.00008

30.21

2.6481E-06

0.37461165

-0.42641872

2

150

0.00015

19.65

7.6336E-06

7.07E-06

1.07986813

0.385

0.033370723

-0.41453927

152

0.000152

20.23

7.5136E-06

1.06289343

0.026489724

3

128

0.000128

15.23

8.4045E-06

7.07E-06

1.1889185

0.444

0.075152085

-0.35261703

126

0.000126

15.01

8.3944E-06

1.18749522

0.074631871

4

88

0.000088

10.11

8.7043E-06

7.07E-06

1.23132738

0.47

0.090373535

-0.32790214

88

0.000088

9.92

8.871E-06

1.25491127

0.098613018

From the graph.

is calculated as

Taking an arbitrary point from the trend line, (0,-0.3)

Using the points the value of and v at the given point are;

But This implies that

There are other various methods that can be used to calculate the Darcy’s Friction factor. For a laminar flow, it can be calculated as, for turbulent flow, the Colebrook white equation can be used

Determination of head loss is important since it helps in the determining the net positive suction head in any given flow. Also, Determination of head loss is vital since it facilitates proper determination of fittings along the pipe which include pipe fittings, valves and elbows. Determination of Darcy’s Friction factor helps in the calculation of the Total Dynamic head which is used in the determination of the size of the pump to be used.

Appropriate determination of the required components is vital since it reduces wastage thus eliminating unnecessary costs.

Conclusion

The graph shows that the measured data was not consistent. This can be attributed to the errors that were encountered during the flow. Some of the sources of the errors maybe due to the fluid in the pipe not filling up the pipe and due to parallax errors while making measurements.

Comparing the results of the two graphs, it can be seen that the values of n and k are different in the two results. Thus it can be concluded that the two values varies depending on the pipe properties in any given situation.

From the trend line on the graph, it can be concluded that as velocity increases, hf increases lineally.

References

Spellman, F. R., 2000. The Science of Water: Concepts and Applications, Second Edition. 1st ed. Boca raton: CRC Press.

Spellman, F. R., 2008. Handbook of Water and Wastewater Treatment Plant Operations, Second Edition. 2nd ed. Boca Raton: CRC Press.