# The Energy of a Fluid: Head Loss through a Pipe – Lab Report Example

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.