Experiment Report: Fluid Friction and Flow Measurement Analysis

This report details an experiment investigating the relationship between fluid friction head loss and the velocity of water flowing through smooth bore pipes. The primary objective was to compare measured head loss values with those calculated using the friction equation of a pipe. The experiment involved measuring head loss at various flow rates through different pipe sizes, revealing three distinct zones: laminar, transition, and turbulent. Data analysis included graphs of h vs. u and log h vs. log u, confirming the expected relationships between head loss and velocity in each flow regime. The results showed a strong correlation between measured and calculated head loss values, validating the use of friction equations for pipe design. The findings emphasize the importance of maintaining optimal fluid velocity to minimize head loss due to friction, whether in laminar or turbulent flow. Engineers can use these findings to design efficient piping systems.

Head Loss and Differential Flow Measurement 1
HEAD LOSS AND DIFFERENTIAL FLOW MEASUREMENT
Name
Course
Professor
University
City/state
Date

Head Loss and Differential Flow Measurement 2
Head Loss and Differential Flow Measurement
Experiment A: Fluid Friction in a Smooth Bore Pipe
Abstract
The main objective of this experiment was to determine the relationship between fluid head loss
and velocity of water flowing through smooth pipes, and to compare the values of measured head
loss and those obtained through calculation using friction equation of a pipe. This was achieved
by obtaining a series of head loss readings at different flow rates of water flowing through varied
smooth test pipes. The findings of the experiment showed that a graph of h vs. u for the different
pipe sizes had three main zones: laminar zone, transition zone and turbulent zone. The graph for
the laminar zone was a straight line (h = u). A graph of log h vs. log u for the different pipe sizes
also had three main zones: laminar zone, transition zone and turbulent zone. The graph for the
turbulent zone was a straight line (h = un) with a gradient of 1.9 and 1.86 (the values of n) for
pipe 8 and pipe 10 respectively. The difference between measured head loss values and
calculated head loss values was relatively small. This confirmed that head loss through a pipe
can be predicted using friction equation of a pipe as long as pipe dimensions and velocity of fluid
flowing through the pipe are known. Engineers can use findings from this experiment to design
pipes so that water flows through them at optimal velocity so as to reduce head loss depending
on whether the flow is laminar or turbulent. Generally, mean velocity has to be kept low so as to
minimize head losses due to friction.
Aim of Experiment

Head Loss and Differential Flow Measurement 3
The aim of this experiment is to determine the relationship between fluid friction head
loss and velocity of water flowing through smooth bore pipes, and to compare measured head
loss values and those obtained through calculation using friction equation of a pipe.
Brief Introduction/Background
Fluid friction head losses occur as a result of an incompressible fluid flow through pipe
flow metering devices, valves, pipes and bends. The values of these losses are different in
smooth and rough pipes, with the latter pipes have higher values than the former pipes (Soumerai
& Soumerai-Bourke, 2014). In smooth pipes, it is possible to determine friction head losses over
Reynold’s numbers ranging between 103 and 105. Within this range, the smooth pipes’ laminar
flow, transitional flow and turbulent flow are covered. In rough pipes, friction head losses are
determined at high Reynold’s numbers. Various pipe components, such as control valves and
pipe fittings, also affects friction head losses.
According to Prof. Osborne Reynolds, the flow of fluid through a pipe can either be
laminar flow or turbulent flow (Launder & Jackson, 2007). Laminar flow occurs when velocity
of the fluid is low (Cerbus, et al., 2018), and the relationship between fluid friction head loss, h,
and fluid velocity, u, is: h ∝u. On the other hand, turbulent flow occurs when velocity of the fluid
is higher (Hanjalic & Launder, 2011); (Jackson & Launder, 2011), and the relationship between
fluid friction head loss and fluid velocity is: h ∝un. There is a phase known as transition phase
that separates the laminar flow and turbulent flow (Launder, 2015); (Wu, et al., 2015). In the
transition flow or phase, h and u do not have any definite relationship (Tribonet, 2018).
The formulae for determining friction head loss and Reynold’s number are provided in equation
1 and 2 below

Head Loss and Differential Flow Measurement 4
h= 4 fLu ²
2 gd ∨ λLu ²
2 gd ………………………………………………. (1)
ℜ= ρud
μ ………………..…….………………………………… (2)
Where L = length of pipe from one tapping to another, u = mean velocity of fluid (or water)
flowing through the pipe (m/s), d = pipe’s internal diameter, f = friction coefficient of pipe, g =
gravitational acceleration (m/s2), ρ = density (999 kg/m3 at 15°C) and μ = molecular viscosity
(1.15 x 10-3 Ns/m2 at 15°C). λ is also equivalent to 4f.
Determining fluid friction head losses helps engineers to estimate the amount of energy lost due
to friction when a fluid is flowing through a pipe (Nuclear Power, 2018).
Description of Apparatus
The apparatus used in this experiment is Armfield C6-MKII-10 Fluid Friction Apparatus
together with Armfield F1-10 Hydraulics Bench. Other devices used are internal vernier caliper
and stop watch. The pipes used in this experiment are assumed to have constant internal
diameters.
Methodology
The pipe network (as shown in Appendix 1) was primed with water. Appropriate valves
were opened and closed so as to obtain the required water flow through the right test pipe.
Readings were taken at different flow rates, with the flow being changed using control valves
fitted on the hydraulics bench. Volumetric tank or measuring cylinder was used to measure flow
rates. Head loss from one tapping to another was also measured using pressurized water

Head Loss and Differential Flow Measurement 5
manometer or portable pressure meter. Readings on all the four smooth test pipes were obtained
and recorded. Internal diameter of the test pipe samples was also measured.
Data, Results and Graphs
Graphs of h vs. u for the different pipes sizes are as follows:
The values of h were measured from the experiment. However, the values of u are calculated
using the equation: u= 4 Q
πd ² (where Q = flow rate through the test pipe (m3/s) and d = internal
diameter of pipe (m).
Graph of h vs. u for pipe 8
In this test, d = 17.2mm = 0.0172m
Sample calculation of u for the first value of Q for pipe 8 is as follows
u= 4 x 0.0008679245
π x 0.0172² = 3.7354 m/s
Calculated values of h are obtained using equation 1 where f = 0.015, L = 1m, g = 10 m/s2 and d
= 0.0172 m
Sample calculation of:
h= 4 x 0.015 x 1 x 3.735²
2 x 10 x 0.0172 =2.4332
Table 1 below shows the Q, u and h data for pipe 8:
Table 1: Experimental data for pipe 8
Flow Rate Q
(m3/sec)
Measured Head loss
(m)
Calculated head loss
(m)
Mean
velocity,

Head Loss and Differential Flow Measurement 6
(m/s)
Q h h u
8.679E-04 1.10676 2.434E+00
3.735E+0
0
7.667E-04 0.736 1.899E+00
3.300E+0
0
7.041E-04 0.65504 1.602E+00
3.030E+0
0
6.586E-04 0.6118 1.401E+00
2.834E+0
0
6.571E-04 0.51244 1.395E+00
2.828E+0
0
5.247E-04 0.41676 8.895E-01
2.258E+0
0
5.107E-04 0.27232 8.426E-01
2.198E+0
0
4.293E-04 0.28612 5.955E-01
1.848E+0
0
3.987E-04 0.24656 5.135E-01
1.716E+0
0
3.680E-04 0.276 4.375E-01
1.584E+0
0
3.373E-04 0.19044 3.676E-01
1.452E+0
0
3.067E-04 0.15732 3.038E-01
1.320E+0
0
2.760E-04 0.12696 2.461E-01
1.188E+0
0
2.453E-04 0.10028 1.945E-01
1.056E+0
0
2.147E-04 0.07728 1.489E-01 9.239E-01
1.995E-04 0.05336 1.286E-01 8.585E-01
1.840E-04 0.0644 1.094E-01 7.919E-01
1.533E-04 0.04508 7.596E-02 6.599E-01
1.380E-04 0.03864 6.153E-02 5.939E-01
1.227E-04 0.03036 4.861E-02 5.279E-01
1.073E-04 0.02484 3.722E-02 4.619E-01
9.782E-05 0.0184 3.091E-02 4.210E-01
9.200E-05 0.0184 2.734E-02 3.960E-01
7.667E-05 0.01288 1.899E-02 3.300E-01
6.900E-05 0.01104 1.538E-02 2.970E-01
6.133E-05 0.0092 1.215E-02 2.640E-01
5.367E-05 0.00644 9.305E-03 2.310E-01
4.600E-05 0.002576 6.836E-03 1.980E-01
3.833E-05 0.001748 4.747E-03 1.650E-01

Head Loss and Differential Flow Measurement 7
3.462E-05 0.002116 3.872E-03 1.490E-01
3.067E-05 0.00184 3.038E-03 1.320E-01
2.668E-05 0.001656 2.300E-03 1.148E-01
2.300E-05 0.001196 1.709E-03 9.899E-02
1.533E-05 0.00092 7.596E-04 6.599E-02
1.472E-05 0.03772 7.000E-04 6.335E-02
1.454E-05 0.00092 6.831E-04 6.258E-02
1.380E-05 0.00092 6.153E-04 5.939E-02
1.288E-05 0.00828 5.360E-04 5.543E-02
1.233E-05 0.00368 4.910E-04 5.306E-02
1.227E-05 0.00092 4.861E-04 5.279E-02
9.024E-06 0.00552 2.631E-04 3.884E-02
9.091E-05 0.091 2.670E-02 3.913E-01
4.348E-05 0.01 6.107E-03 1.871E-01
4.193E-05 0.024 5.681E-03 1.805E-01
2.827E-05 0.046 2.581E-03 1.217E-01
1.083E-05 0.005 3.792E-04 4.662E-02
The graph of h (measured) vs. u for pipe 8 is as shown in Figure 1 below
0.000E+00 5.000E-01 1.000E+00 1.500E+00 2.000E+00 2.500E+00 3.000E+00 3.500E+00 4.000E+00
0
0.2
0.4
0.6
0.8
1
1.2
Graph of h (measured) vs. u for pipe 8
Mean velocity, u
Measured Head loss, h
Figure 1: Graph of measured h vs. u for pipe 8

Head Loss and Differential Flow Measurement 8
From Figure 1 above, the graph for the laminar flow zone is a straight line. This ascertains the
relationship h ∝u
Graph of calculated head vs. mean velocity for pipe 8 is as shown in Figure 2 below
0.000E+00 5.000E-01 1.000E+00 1.500E+00 2.000E+00 2.500E+00 3.000E+00 3.500E+00 4.000E+00
0.000E+00
5.000E-01
1.000E+00
1.500E+00
2.000E+00
2.500E+00
3.000E+00
Calculated h vs. u
Mean velocity, u (m/s)
Calculated h (m)
Figure 2: Graph of calculated h vs. u for pipe 8
The graphs in Figure 1 and 2 above are similar. This shows that the error in the experiment is
small and that the equation 1 can also be used to predict the values of h.
Graph of h vs. u for pipe 10
In this test, d = 7.7mm = 0.0077m
Sample calculation of u for the first value of Q for pipe 10 is as follows
u= 4 x 0.0000062
π x 0.0077² = 0.13314 m/s
Table 2 below shows the Q, u and h data for pipe 10

Head Loss and Differential Flow Measurement 9
Table 2: Experimental data for pipe 10
Flow Rate Q
(m3/sec)
Measured Head loss
(m)
Calculated head loss
(m)
Q h h
Mean
velocity
an the client give 0 u
6.200E-06 7.943 6.907E-03 1.331E-01
8.400E-06 8.08 1.268E-02 1.804E-01
9.200E-06 0.029 1.521E-02 1.976E-01
1.500E-05 7.987 4.043E-02 3.221E-01
1.540E-05 8.041 4.261E-02 3.307E-01
1.913E-05 0.06 6.578E-02 4.109E-01
2.400E-05 0.67 1.035E-01 5.154E-01
2.476E-05 8.176 1.101E-01 5.316E-01
4.150E-05 0.15 3.094E-01 8.912E-01
4.667E-05 8.257 3.913E-01 1.002E+00
5.807E-05 0.202 6.058E-01 1.247E+00
6.780E-05 0.73 8.259E-01 1.456E+00
8.333E-05 0.873 1.248E+00 1.790E+00
1.073E-04 1.288 2.070E+00 2.305E+00
1.095E-04 1.61 2.154E+00 2.351E+00
1.111E-04 2.317 2.218E+00 2.386E+00
1.230E-04 1.61 2.718E+00 2.641E+00
1.342E-04 2.0125 3.234E+00 2.881E+00
1.346E-04 1.61 3.254E+00 2.890E+00
1.610E-04 2.8175 4.657E+00 3.457E+00
1.610E-04 2.737 4.657E+00 3.457E+00
1.857E-04 3.9445 6.196E+00 3.988E+00
1.878E-04 3.7835 6.339E+00 4.034E+00
1.987E-04 8.363 7.096E+00 4.268E+00
2.000E-04 4.871 7.187E+00 4.295E+00
2.013E-04 3.703 7.277E+00 4.322E+00
2.013E-04 4.508 7.277E+00 4.322E+00
2.143E-04 4.83 8.253E+00 4.603E+00
2.147E-04 4.7495 8.280E+00 4.610E+00
2.292E-04 5.635 9.440E+00 4.922E+00
2.308E-04 5.635 9.570E+00 4.956E+00
2.415E-04 5.957 1.048E+01 5.186E+00
2.632E-04 5.046 1.244E+01 5.651E+00
2.683E-04 7.1645 1.294E+01 5.762E+00
2.683E-04 7.6475 1.294E+01 5.762E+00
2.683E-04 6.8425 1.294E+01 5.762E+00

Head Loss and Differential Flow Measurement 10
2.683E-04 7.728 1.294E+01 5.762E+00
2.683E-04 6.923 1.294E+01 5.762E+00
2.683E-04 7.245 1.294E+01 5.762E+00
2.800E-04 8.05 1.409E+01 6.013E+00
2.952E-04 8.694 1.565E+01 6.339E+00
3.052E-04 10.0625 1.673E+01 6.553E+00
3.067E-04 9.66 1.690E+01 6.586E+00
3.086E-04 8.4525 1.711E+01 6.628E+00
3.212E-04 10.465 1.854E+01 6.898E+00
3.220E-04 10.2235 1.863E+01 6.915E+00
3.220E-04 10.465 1.863E+01 6.915E+00
3.240E-04 4.974 1.887E+01 6.959E+00
3.251E-04 10.465 1.899E+01 6.982E+00
3.389E-04 11.27 2.064E+01 7.279E+00
3.433E-04 11.6725 2.117E+01 7.372E+00
3.488E-04 11.9945 2.186E+01 7.491E+00
3.541E-04 8.42 2.253E+01 7.604E+00
3.757E-04 13.685 2.536E+01 8.067E+00
3.808E-04 5.977 2.606E+01 8.178E+00
4.025E-04 15.8585 2.911E+01 8.644E+00
4.025E-04 15.456 2.911E+01 8.644E+00
4.025E-04 15.295 2.911E+01 8.644E+00
4.049E-04 15.134 2.946E+01 8.696E+00
4.112E-04 7.325 3.038E+01 8.830E+00
4.136E-04 7.87 3.073E+01 8.881E+00
4.136E-04 8.107 3.073E+01 8.881E+00
The graph of h vs. u for pipe 10 is as shown in Figure 3 below

Head Loss and Differential Flow Measurement 11
0.000E+00
1.000E+00
2.000E+00
3.000E+00
4.000E+00
5.000E+00
6.000E+00
7.000E+00
8.000E+00
9.000E+00
1.000E+010
2
4
6
8
10
12
14
16
18
Graph of h vs. u for pipe 10
Fluid velocity, u (m/s)
Head loss, h (m)
Figure 3: Graph of measured h vs. u for pipe 10
From Figure 2 above, the graph for the laminar flow zone is relatively a straight line. This
ascertains the relationship h ∝u
Graph of calculated head vs. mean velocity for pipe 10 is as shown in Figure 4 below

Head Loss and Differential Flow Measurement 12
0.000E+00 2.000E+00 4.000E+00 6.000E+00 8.000E+00 1.000E+01
0.000E+00
5.000E+00
1.000E+01
1.500E+01
2.000E+01
2.500E+01
3.000E+01
3.500E+01
Calculated h vs. u forpipe 10
Man velocity, u (m/s)
Calculated head, h (m)
Figure 4: Graph of calculated h vs. u for pipe 10
The graphs in Figure 3 and 4 above are similar. This shows that equation 1 can be used to predict
the values of h and that errors in the experiment were small thus negligible.
Graph of log h vs. log u for pipe 8
Table 3 below shows log u and log h values for pipe 8
Table 3: Experimental log u and log h (measured and calculated) data for pipe 8
log u
Log h
(measure
d)
Log h
(calculate
d)
0.5723
35 0.044053 0.386263
0.5184
6 -0.13312 0.278512
0.4814
76 -0.18373 0.204545
0.4524 -0.21339 0.146482

Head Loss and Differential Flow Measurement 13
45
0.4515
13 -0.29036 0.144619
0.3537
77 -0.38011 -0.05085
0.3420
07 -0.56492 -0.07439
0.2666
48 -0.54345 -0.22511
0.2344
63 -0.60808 -0.28948
0.1997
01 -0.55909 -0.35901
0.1619
12 -0.72024 -0.43458
0.1205
2 -0.80322 -0.51737
0.0747
62 -0.89633 -0.60888
0.0236
1 -0.99879 -0.71119
-
0.0343
8 -1.11193 -0.82717
-
0.0662
5 -1.27278 -0.8909
-
0.1013
3 -1.19111 -0.96107
-
0.1805
1 -1.34602 -1.11943
-
0.2262
7 -1.41296 -1.21094
-
0.2774
2 -1.5177 -1.31325
-
0.3354
1 -1.60485 -1.42923
-
0.3757
2 -1.73518 -1.50984
-
0.4023
-1.73518 -1.56313

Head Loss and Differential Flow Measurement 14
6
-
0.4815
4 -1.89008 -1.72149
-0.5273 -1.95703 -1.813
-
0.5784
5 -2.03621 -1.91531
-
0.6364
4 -2.19111 -2.03129
-
0.7033
9 -2.58905 -2.16519
-
0.7825
7 -2.75746 -2.32355
-0.8268 -2.67448 -2.41202
-
0.8794
8 -2.73518 -2.51737
-
0.9399
6 -2.78094 -2.63833
-
1.0044
2 -2.92227 -2.76725
-
1.1805
1 -3.03621 -3.11943
-
1.1982
4 -1.42343 -3.15489
-
1.2035
6 -3.03621 -3.16552
-
1.2262
7 -3.03621 -3.21094
-
1.2562
3 -2.08197 -3.27087
-
1.2752
5 -2.43415 -3.30892
-
1.2774
-3.03621 -3.31325

Head Loss and Differential Flow Measurement 15
2
-
1.4107
4 -2.25806 -3.57989
-
0.4075
4 -1.04096 -1.57349
-
0.7278
7 -2 -2.21416
-
0.7435
9 -1.61979 -2.24558
-
0.9148
7 -1.33724 -2.58815
-
1.3313
8 -2.30103 -3.42118
The graph of log h vs. log u for pipe 8 is as shown in Figure 5 below
-2 -1.5 -1 -0.5 0 0.5 1
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
Graph of log h (measured) vs. log u for pipe 8
Log u
Log h
Figure 5: Graph of log h (measured) vs. log u for pipe 8
From Figure 5 above, the graph for the turbulent flow zone is a straight line. This ascertains the
relationshiph ∝u ². The slope of the straight line is determined as follows:

Head Loss and Differential Flow Measurement 16
(0.5723355173, 0.044033455) and (0.023609771, -0.998785675)
Gradient = change in y/change in x =
change∈ y
change∈ x = 0.044033455−−0.998785675
0.5723355173−0.023609771 = 1.04281913
0.5487257463 =1.9
Therefore the value of n = 1.9
The straight line equation for the turbulent flow zone is given by h = un. This can be rewritten as
follows:
Log h = log un
Using the laws of logarithm, the above equation can be written as: log h = n log u. Therefore if a
graph of log h vs. log u is plotted, the gradient of that straight line represents the value of n.
From Figure 5 above, the graph for the turbulent flow zone is a straight line. This ascertains the
relationshiph ∝u ².
-2 -1.5 -1 -0.5 0 0.5 1
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
Log of h (calculated) vs log u
Log u
Log h (calculated)
Figure 6: Graph of log h (calculated) vs. log u for pipe 8

Head Loss and Differential Flow Measurement 17
The graphs in Figure 5 and 6 are similar. This shows that equation 1 can be used to predict the
values of head loss (h).
Graph log h vs. log u for pipe 10
Table 4 below shows log u and log h values for pipe 10
Table 4: Experimental log u and log h data for pipe 10
Log u
Log h
(measure
d)
Log h
(calculate
d)
-
8.757E-
01 9.000E-01 -2.50977
-
7.438E-
01 9.074E-01 -2.24599
-
7.043E-
01
-
1.538E+0
0 -2.16697
-
4.920E-
01 9.024E-01 -1.74237
-
4.806E-
01 9.053E-01 -0.75841
-
3.863E-
01
-
1.222E+0
0 -1.53097
-
2.879E-
01
-1.739E-
01 -1.33413
-
2.744E-
01 9.125E-01 -1.3072
-
5.002E-
02
-8.239E-
01 -0.85845
9.355E-
04 9.168E-01 -0.75654
9.586E-
02
-6.946E-
01 -0.5667

Head Loss and Differential Flow Measurement 18
1.632E-
01
-1.367E-
01 -0.43209
2.527E-
01
-5.899E-
02 -0.25291
3.627E-
01 1.099E-01 -0.03308
3.713E-
01 2.068E-01 -0.01588
3.777E-
01 3.649E-01 -0.00303
4.218E-
01 2.068E-01 0.085223
4.596E-
01 3.037E-01 0.16074
4.609E-
01 2.068E-01 0.163349
5.388E-
01 4.499E-01 0.319102
5.388E-
01 4.373E-01 0.319102
6.007E-
01 5.960E-01 0.443064
6.057E-
01 5.779E-01 0.452996
6.302E-
01 9.224E-01 0.501969
6.330E-
01 6.876E-01 0.50751
6.357E-
01 5.686E-01 0.512922
6.357E-
01 6.540E-01 0.512922
6.630E-
01 6.839E-01 0.567591
6.637E-
01 6.766E-01 0.568979
6.922E-
01 7.509E-01 0.625933
6.951E-
01 7.509E-01 0.631889
7.148E-
01 7.750E-01 0.671285
7.521E-
01 7.029E-01 0.745883
7.606E-
01 8.552E-01 0.7628
7.606E- 8.835E-01 0.7628

Head Loss and Differential Flow Measurement 19
01
7.606E-
01 8.352E-01 0.7628
7.606E-
01 8.881E-01 0.7628
7.606E-
01 8.403E-01 0.7628
7.606E-
01 8.600E-01 0.7628
7.791E-
01 9.058E-01 0.799766
8.020E-
01 9.392E-01 0.845585
8.164E-
01
1.003E+0
0 0.874492
8.186E-
01 9.850E-01 0.878783
8.214E-
01 9.270E-01 0.884316
8.387E-
01
1.020E+0
0 0.91908
8.398E-
01
1.010E+0
0 0.921162
8.398E-
01
1.020E+0
0 0.921162
8.425E-
01 6.967E-01 0.926658
8.440E-
01
1.020E+0
0 0.929541
8.621E-
01
1.052E+0
0 0.965715
8.676E-
01
1.067E+0
0 0.976756
8.745E-
01
1.079E+0
0 0.990686
8.811E-
01 9.253E-01 1.003721
9.067E-
01
1.136E+0
0 1.055056
9.126E-
01 7.765E-01 1.066861
9.367E-
01
1.200E+0
0 1.114982
9.367E-
01
1.189E+0
0 1.114982
9.367E-
01
1.185E+0
0 1.114982

Head Loss and Differential Flow Measurement 20
9.393E-
01
1.180E+0
0 1.120209
9.460E-
01 8.648E-01 1.133523
9.485E-
01 8.960E-01 1.138538
9.485E-
01 9.089E-01 1.138538
The graph of log h vs. log u for pipe 10 is as shown in Figure 7 below
-1.000E+00 -5.000E-01 0.000E+00 5.000E-01 1.000E+00 1.500E+00
-2.000E+00
-1.500E+00
-1.000E+00
-5.000E-01
0.000E+00
5.000E-01
1.000E+00
1.500E+00
Graph of log h vs. log u for pipe 10
Log u
Log h
Figure 7: Graph of log h (measured) vs. log u for pipe 10
From Figure 7 above, the graph for the turbulent flow zone is a straight line. This ascertains the
relationshiph ∝u ². The slope of the straight line is determined as follows:
(0.9367, 1.189) and (0.5388, 0.4499)
Gradient = change in y/change in x = change∈ y
change∈ x = 1.189−0.4499
0.9367−0.5388 = 0.7391
0.3979 =1.86
Therefore the value of n = 1.86

Head Loss and Differential Flow Measurement 21
Graph of log h (calculated vs. log u for pipe 10
-1.000E+00 -5.000E-01 0.000E+00 5.000E-01 1.000E+00 1.500E+00
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
Log h (calculated) vs. log u for pipe 10
Log u
Log h (calculated)
Figure 8: Graph of log h (calculated) vs. log u for pipe 10
The graphs in Figure 7 and 8 are similar. This shows that equation 1 can be used to predict the
values of head loss (h).
Estimation of Reynolds number (Re) at the start and finish of transition phase
Re is calculated using equation 2
For pipe 8:
Re at the start of transition phase
At the start of transition phase, ρ = 999 kg/m3, d = 0.0172m, μ = 1.15 x 10-4 kgs/m2 and u = 1.452
m/s
Using equation 2, Re is calculated as follows:

Head Loss and Differential Flow Measurement 22
ℜ= ρud
μ = 999 x 1.452 x 0.0172
1.15 x 10−3 = 21,695.2
Re at the start of transition phase
At the end of transition phase, ρ = 999 kg/m3, d = 0.0172m, μ = 1.15 x 10-4 kgs/m2 and u = 2.834
m/s.
Using equation 2, Re is calculated as follows:
ℜ= ρud
μ = 999 x 2.834 x 0.0172
1.15 x 10−3 = 42,344.4
For pipe 10:
Re at the start of transition phase
At the start of transition phase, ρ = 999 kg/m3, d = 0.0077m, μ = 1.15 x 10-4 kgs/m2 and u = 4.034
m/s
Using equation 2, Re is calculated as follows:
ℜ= ρud
μ = 999 x 4.034 x 0.0077
1.15 x 10−3 = 26,983.3
Re at the start of transition phase
At the end of transition phase, ρ = 999 kg/m3, d = 0.0172m, μ = 1.15 x 10-4 kgs/m2 and u = 5.762
m/s.
Using equation 2, Re is calculated as follows:
ℜ= ρud
μ = 999 x 6.915 x 0.0077
1.15 x 10−3 = 46,254.1

Head Loss and Differential Flow Measurement 23
Comparison between calculated and measured head losses
For pipe 8:
Calculated head loss, he= λLu ²
2 gd (where L = 1m, g = 10 m/s2, d = 0.0172 m, λ = obtained from
Moody’s diagram, and u = calculated values
u Re f λ Calculated head
loss, he
Measured head loss, h
3.735 55806 0.00
5
0.02 1.39502 1.10676
0.0466
2
697 0.02
4
0.096 0.00607 0.005
For pipe 10:
u Re f λ Calculated head
loss, he
Measured head loss, h
0.133 890 0.018 0.072 8.317 7.943
8.881 59404 0.0048 0.019
2
9.833 8.107
Interpretation & Discussion of Results
From Figure 1 and 2 above, the laminar flow zone, transition flow zone and turbulent
flow zone are identified by the vertical dotted lines. The first zone is the laminar flow zone
where the graph of h vs. u is a straight line. This means that head loss in laminar flow is
proportional to the mean velocity of water flowing through the pipe. The second zone is the
transition flow zone where there is no definite relationship between h and u. The third zone is the
turbulent flow zone where the graph of h vs. u is not perfectly linear.

Head Loss and Differential Flow Measurement 24
The graphs in Figure 3 and 4 shows the relationship between log h and log u for pipe 8
and pipe 10. From these graphs, the turbulent flow zones show linear relationship between log h
and log u. The straight lines of the graphs in the turbulent flow zone are represented by the
equation log h = n log u (h = un). Therefore the gradients of these straight lines represent the
values of n.
Therefore the graph for the turbulent flow zone in Figure 3 above is a straight line. This
ascertains the relationship h ∝u ². Also, the graph for the turbulent flow zone in Figure 4 above is
a straight line. This ascertains the relationshiph ∝u ². This means that head loss in turbulent flow
is proportional to the square of mean velocity of water flowing through the pipe.
There was some small differences between the measured head loss values and calculated
head loss values. These differences were probably due to possible sources of errors. One of the
possible sources of errors was defective apparatus and devices. If any of the apparatus or devices
used was defective then it generated a systematic error throughout the experiment. Another
possible source of error is incorrect reading and recording of measurements. The errors may also
have been due to unsteady temperature. The temperature of water used in this experiment was
assumed to be 15°C. It is likely that this temperature was not maintained throughout the
experiment resulting to errors. Last but not least, the errors may have been due to incorrect
calculations (arithmetic errors). In the future, the experiment can be improved by ensuring that
apparatus and devices used are not defective, all measurements are read and recorded correctly,
temperature of the water used is maintained at the recommended value or the variations are
considered in the calculations, and all arithmetic or calculations are done correctly.
Conclusion

Head Loss and Differential Flow Measurement 25
This experiment demonstrated that was flowing through a rough pipe exhibits laminar
flow, transition flow and turbulent flow. Each of these flows have unique head loss and mean
velocity. Velocity of laminar flow is less than that of transition flow while that of turbulent flow
is the greatest. The relationship between h and u for laminar flow is linear, and the relationship
between h and un for turbulent flow is also linear. However, the relationship between h and u or h
and un for transition flow was not definite. For pipe 8, the gradient (value of n) of the straight line
of log h vs. log u graph was 1.9, while for pipe 10, the gradient (value of n) of the straight line of
log h vs. log u graph was 1.86. The results obtained also showed small differences between
measured and calculated values of head loss. Therefore head losses through a pipe can be
obtained either by taking measurements or calculating using pipe friction equation, depending on
which method is easier or the resources provided. From this experiment, it is evident that
velocity of water flowing through a pipe has a direct impact on head loss. Low velocity results to
a smaller head loss and vice versa. Therefore findings from this experiment can be used to design
pipes so that water flows at optimal velocity depending on whether the flow is laminar or
turbulent. To minimize head losses due to friction, mean velocity of water through pipes has to
be kept low.
Experiment B: Head Loss in Pipe Fittings
Abstract
The objective of this experiment was to determine head loss of water flowing through typical
fittings used in plumbing installations. This was achieved by measuring differential head from
one tapping to another on test valves and fittings. From the experiment, it was found that head

Head Loss and Differential Flow Measurement 26
loss is proportional to the fluid’s mean velocity. A graph of fitting factor against flow rate
showed that the fitting factor was constant for the 45° elbow and 90° elbow fittings. However,
this was not the case for the isolating valve fitting. Therefore pipe fittings cause head loss
making it important to select and use appropriate type of fittings for plumbing works so as to
reduce head loss.
Aim of Experiment
The aim of this experiment is to determine head loss of water flowing through typical
fittings that are used in plumbing installations.
Brief Introduction/Background
Pipe fittings experience head loss when water is flowing through them. The pipe fitting’s
head loss is proportional to the fluid velocity head. This relationship is represented by equation 3
below
h= Ku ²
2 g …………………………………………………………………………. (3)
Where K = loss factor of the pipe fitting, u = water/fluid’s mean velocity (m/s) and g =
gravitational acceleration (m/s2). It is important to note that control valves of flow are pipe
fittings that have adjustable K factor.
Description of Apparatus
The apparatus used in this experiment is Armfield C6-MKII-10 Fluid Friction Apparatus
together with Armfield F1-10 Hydraulics Bench. Other devices used are internal vernier caliper
and stop watch. The pipes used in this experiment are assumed to have constant internal
diameters. The following valves and fittings were also provided for the experiment: sudden

Head Loss and Differential Flow Measurement 27
enlargement, sudden contraction, 45° Y junction, 45° mitre, 45° elbow, ball valve, in line
strainer, globe valve, gate valve, 90° T junction, 90° long radius bend, 90° short radius band and
90° elbow.
Methodology
The pipe network was connected in accordance with the diagram provided in the lab
manual. After setting up the equipment, the pipe network was primed with water. Appropriate
valves were opened and closed so as to obtain the required water flow through the desired fitting.
Readings of volume and time were taken and recorded at different flow rates, with the control
valve fixed on the hydraulics bench being used to adjust flow of the water. Volumetric tank was
used to measure flow rates of the water. Pressurized water manometer, sensors or hand held
pressure meter was used to measure differential head from one tapping to another on various
fittings.
Data, Results and Graphs
The internal diameter of pipe 8, d = 17.2 mm = 0.0172 m, and g = 10 m/s2
The values of u are calculated using the equation: u= 4 Q
πd ² (Q is the measured flow rate from the
experiment).
The values of hv are calculated using the equation: hv= u ²
2 g
The values of K are calculated using the equation: K ¿ h
hv
Table 5 below shows the experimental data for pipe 8

Head Loss and Differential Flow Measurement 28
Table 5: Experimental data for pipe 8
Flow
Q
(m3/s
)
Head loss
elbow 45
(m)
Head loss
isolating
valve (m)
Head
loss 90°
(m) u hv
K
(elb
ow)
K
(isolatin
g valve)
K
(90
)
7.590E-
06 0.0161 0.00805 0.0069
3.26
7E-
02
5.335
31E-
05
301.7
629
150.88146
84
129.
327
1.128E-
05 0.03105 0.0046 0.0069
4.85
5E-
02
0.000
1178
44
263.4
833
39.034557
62
58.5
518
4
1.541E-
05 0.0138 0.023 0.00805
6.63
2E-
02
0.000
2199
29
62.74
764
104.57939
67
36.6
027
9
1.610E-
05 0.01035 0.0184 0.01725
6.92
9E-
02
0.000
2400
65
43.11
339
76.646026
4
71.8
556
5
1.818E-
05 0.0023 0.01265 0.00115
7.82
3E-
02
0.000
3059
7
7.517
081
41.343944
41
3.75
854
1.840E-
05 0.0391 0.00345 0.0092
7.91
9E-
02
0.000
3135
54
124.6
995
11.002896
37
29.3
410
6
3.335E-
05 0.02645 0.03565 0.01265
1.43
5E-
01
0.001
0300
73
25.67
779
34.609189
68
12.2
806
8
3.752E-
05 0.228 0.544 0.52
1.61
5E-
01
0.001
3039
54
174.8
528
417.19253
97
398.
787
6.499E-
05 0.878 0.521 0.538
2.79
7E-
01
0.003
9112
18
224.4
825
133.20657
2
137.
553
7.494E-
05 0.38 0.019 0.093
3.22
5E-
01
0.005
2012
1
73.05
993
3.6529963
73
17.8
804
6
9.518E-
05 0.818 0.634 0.543
4.09
7E-
01
0.008
3907
66
97.48
811
75.559247
53
64.7
139
9
1.223E-
04 0.0046 0.00805 0.00345
5.26
3E-
01
0.013
8469
62
0.332
203
0.5813549
48
0.24
915
2
1.421E-
04 0.0256 0.506 0.568
6.11
5E-
01
0.018
6972
57
1.369
185
27.062792
98
30.3
787
9

Head Loss and Differential Flow Measurement 29
1.827E-
04 0.024 0.495 0.608
7.86
2E-
01
0.030
9077
11
0.776
505
16.015420
96
19.6
714
7
1.827E-
04 0.026 0.024 0.069
7.86
2E-
01
0.030
9077
11
0.841
214
0.7765052
59
2.23
245
3
2.493E-
04 0.0414 0.0621 0.13455
1.07
3E+0
0
0.057
5828
97
0.718
963
1.0784452
21
2.33
663
1
3.187E-
04 0.119 0.099 0.22
1.37
2E+0
0
0.094
0525
44
1.265
25
1.0526031
04
2.33
911
8
3.501E-
04 0.311 0.045 0.279
1.50
7E+0
0
0.113
5429
1
2.739
053
0.3963259
36
2.45
722
1
4.040E-
04 0.223 0.179 0.36
1.73
9E+0
0
0.151
1421
7
1.475
432
1.1843154
03
2.38
186
3
4.472E-
04 0.153 0.207 0.442
1.92
5E+0
0
0.185
2391
71
0.825
959
1.1174742
32
2.38
610
4
4.980E-
04 0.4 0.82 0.54
2.14
3E+0
0
0.229
6936
61
1.741
45
3.5699722
71
2.35
095
7
6.384E-
04 0.23 0.3289 0.77395
2.74
7E+0
0
0.377
4014
59
0.609
431
0.8714857
68
2.05
073
4
6.559E-
04 0.3036 0.4301 0.9568
2.82
3E+0
0
0.398
4218
32
0.762
006
1.0795091
16
2.40
147
5
8.214E-
04 0.253 0.08625 0.12075
3.53
5E+0
0
0.624
9079
3
0.404
86
0.1380203
32
0.19
322
8
8.232E-
04 0.4025 0.5589 1.3225
3.54
3E+0
0
0.627
5947
4
0.641
337
0.8905428
37
2.10
725
2
8.801E-
04 0.44275 0.59225 1.4421
3.78
8E+0
0
0.717
3687
97
0.617
186
0.8255865
08
2.01
026
3
9.583E-
04 1.357 0.414 0.5865
4.12
4E+0
0
0.850
5691
27
1.595
402
0.4867329
26
0.68
953
8
A graph of fitting factor (K) against flow rate (Q) for 45° elbow is as shown in Figure 5 below

Head Loss and Differential Flow Measurement 30
0.000E+00 2.000E-04 4.000E-04 6.000E-04 8.000E-04 1.000E-03 1.200E-03
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
K against Q for 45° elbow
Flow rate, Q
Fitting factor, K
Figure 5: Graph of K against Q for 45° elbow
A graph of fitting factor (K) against flow rate (Q) for isolating valve is as shown in Figure 6
below
0.000E+00 2.000E-04 4.000E-04 6.000E-04 8.000E-04 1.000E-03 1.200E-03
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
K against Q for isolating valve
Flow rate, Q
Fitting factor, K
Figure 6: Graph of K against Q for isolating valve

Head Loss and Differential Flow Measurement 31
A graph of fitting factor (K) against flow rate (Q) for 90° elbow is as shown in Figure 7 below
0.000E+00 2.000E-04 4.000E-04 6.000E-04 8.000E-04 1.000E-03 1.200E-03
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
K against Q for 90°elbow
Flow rate, Q
Fitting factor, K
Figure 7: Graph of K against Q for 90° elbow
Interpretation & Discussion of Results
The graphs of fitting factor (K) versus flow rate (Q) in Figure 5 and 7 above shows that K
is a constant for 45° elbow and 90° elbow past a certain value of flow rate. At the start (low flow
rate), fitting factor decreased gradually with increasing flow rate. This is probably because when
flow rate was starting to increase, the flow through the pipe was relatively stable hence the
interaction between the water and internal surface of the pipe was regulated. As the flow rate
continued to increase, the interaction between water and internal pipe surface became normalized
and that is why the fitting factor became constant (Burger, et al., 2010). However, this was not
the case for isolating valve (as shown by the graph in Figure 6 above) where K is not constant.
This shows that for 45° elbow and 90 °elbow pipe fittings, head loss remains constant regardless
of the flow rate of water through the pipe fitting.

Head Loss and Differential Flow Measurement 32
Conclusion
This experiment confirmed that head loss is proportional to the fluid’s mean velocity. A
graph of fitting factor against flow rate showed that fitting factor was constant for the 45° elbow
and 90° elbow fittings even as flow rate increased. However, the trend was different for the
isolating valve fitting because fitting factor was not constant. This experiment showed that pipe
fittings cause head loss making it important to select and use appropriate type of fittings for
plumbing works so as to reduce head loss.
Experiment C: Fluid friction in a Rough Bore Pipe
Abstract
The objective of this experiment was to determine the relationship between coefficient of friction
and Reynolds’ number of water flowing through a rough bore pipe. This was achieved by
obtaining a series of head loss readings at different flow rates of water flowing through the rough
test pipes. A graph of friction coefficient against Reynolds’ number showed that friction
coefficient or factor was constant beyond a particular value of Reynolds’ number (about 103).
Therefore once the Reynolds’ number of a rough pipe is known, it is possible to predict the
friction factor of that particular pipe and the expected head loss due to water flow through the
pipe.
Aim of Experiment
The main objective of this experiment is to determine the relationship between coefficient
of friction of the fluid and Reynold’s number for water flowing through a rough pipe. This is

Head Loss and Differential Flow Measurement 33
attained by taking and recording head loss readings at different flow rates of water flowing
through the rough test pipes.
Brief Introduction/Background
Frictional head loss in a pipe is calculated using equation 4 below
h= 4 fLu ²
2 gd ∨ λLu ²
2 gd ……………………………………………………….. (4)
Where = frictional head loss (m), f = friction coefficient of the pipe, L = length of the pipe from
one tapping to another (m), u = mean velocity of water flowing through the pipe (m/s), g =
acceleration due to gravity (m/s2), and d = internal diameter of the pipe (m). In most cases, λ can
be expressed in form of f as λ = 4f.
Reynolds’ number can be calculated using equation 5 below
ℜ= ρud
μ ………………………………………………………………………. (5)
Where Re = Reynolds’ number, ρ = density (999 kg/m3 at a temperature of 15°), u = mean
velocity of water flowing through the pipe (m/s), d = internal diameter of the pipe (m), and μ =
molecular velocity (1.15 x 10-3 Ns/m2 at a temperature of 15°C).
Description of Apparatus
The apparatus used in this experiment is Armfield C6-MKII-10 Fluid Friction Apparatus
together with Armfield F1-10 Hydraulics Bench. Other devices used are internal vernier caliper
and stop watch. The pipes used in this experiment are assumed to have constant internal
diameters.
Methodology

Head Loss and Differential Flow Measurement 34
The pipe network was primed with water. Appropriate valves were opened and closed so
as to obtain the required water flow through the only roughened test pipe. Readings were taken at
different flow rates, with the flow being changed using control valves fitted on the hydraulics
bench. Volumetric tank or measuring cylinder was used to measure flow rates. Head loss from
one tapping to another was also measured using manometer, sensors or handheld meter. A
vernier caliper was used to estimate the test pipe’s nominal internal diameter. The values
obtained were then used to estimate the pipe’s roughness factor k/d.
Data, Results and Graphs
The internal diameter of pipe 7, d, is assumed to be 15.2 mm = 0.0152 m and length of the pipe,
p = 1 m.
Table 6 below shows data for pipe 7
Table 6: experimental data for pipe 7
Flow Rate Q
(m3/sec)
Measured
Head loss (m) u Re f
3.433E-04 0.849505 1.892E+00
2.498E+0
4
1.803E-
02
4.656E-04 1.397388 2.566E+00
3.388E+0
4
1.613E-
02
3.236E-04 0.946864 1.783E+00
2.354E+0
4
2.263E-
02
2.977E-04 0.656696 1.641E+00
2.166E+0
4
1.854E-
02
1.909E-04 0.313076 1.052E+00
1.389E+0
4
2.150E-
02
1.591E-04 0.1899455 8.767E-01
1.158E+0
4
1.878E-
02
1.258E-04 0.0964045 6.930E-01
9.151E+0
3
1.525E-
02
8.055E-05 0.0467705 4.439E-01
5.861E+0
3
1.804E-
02
1.495E-05 0.0047725 8.241E-02 1.088E+0 5.341E-

Head Loss and Differential Flow Measurement 35
3 02
3.866E-05 0.0047725 2.130E-01
2.813E+0
3
7.992E-
03
3.514E-05 0.0047725 1.937E-01
2.557E+0
3
9.670E-
03
3.182E-04 0.8065525 1.753E+00
2.315E+0
4
1.994E-
02
1.591E-04 0.1479475 8.767E-01
1.158E+0
4
1.463E-
02
1.193E-04 0.089723 6.575E-01
8.682E+0
3
1.577E-
02
7.342E-05 0.043907 4.046E-01
5.343E+0
3
2.038E-
02
6.818E-05 0.032453 3.757E-01
4.961E+0
3
1.747E-
02
2.450E-05 0.007636 1.350E-01
1.783E+0
3
3.184E-
02
2.580E-05 0.0066815 1.422E-01
1.877E+0
3
2.512E-
02
1.145E-05 0.005727 6.312E-02
8.335E+0
2
1.092E-
01
8.447E-06 0.0047725 4.655E-02
6.147E+0
2
1.674E-
01
4.454E-04 1.765825 2.455E+00
3.241E+0
4
2.227E-
02
4.136E-04 1.536745 2.279E+00
3.010E+0
4
2.248E-
02
3.818E-04 1.326755 2.104E+00
2.778E+0
4
2.278E-
02
3.500E-04 1.116765 1.929E+00
2.547E+0
4
2.282E-
02
3.182E-04 0.925865 1.753E+00
2.315E+0
4
2.289E-
02
2.864E-04 0.754055 1.578E+00
2.084E+0
4
2.301E-
02
2.545E-04 0.5965625 1.403E+00
1.852E+0
4
2.304E-
02
2.227E-04 0.45816 1.227E+00
1.621E+0
4
2.311E-
02
1.909E-04 0.3388475 1.052E+00
1.389E+0
4
2.327E-
02
1.591E-04 0.1384025 8.767E-01
1.158E+0
4
1.369E-
02
1.432E-04 0.1909 7.890E-01
1.042E+0
4
2.330E-
02
1.273E-04 0.15272 7.014E-01
9.261E+0
3
2.360E-
02

Head Loss and Differential Flow Measurement 36
1.114E-04 0.1193125 6.137E-01
8.103E+0
3
2.408E-
02
9.545E-05 0.0906775 5.260E-01
6.946E+0
3
2.491E-
02
7.954E-05 0.066815 4.383E-01
5.788E+0
3
2.643E-
02
7.159E-05 0.05727 3.945E-01
5.209E+0
3
2.797E-
02
6.363E-05 0.047725 3.507E-01
4.630E+0
3
2.949E-
02
5.568E-05 0.0429525 3.068E-01
4.052E+0
3
3.467E-
02
4.773E-05 0.028635 2.630E-01
3.473E+0
3
3.146E-
02
2.273E-05 0.002 1.252E-01
1.654E+0
3
9.690E-
03
1.267E-05 0.001 6.980E-02
9.217E+0
2
1.560E-
02
1.933E-06 0.004 1.065E-02
1.407E+0
2
2.678E+0
0
3.977E-05 0.01909 2.192E-01
2.894E+0
3
3.020E-
02
3.182E-05 0.01909 1.753E-01
2.315E+0
3
4.719E-
02
2.386E-05 0.01909 1.315E-01
1.736E+0
3
8.390E-
02
1.591E-05 0.0162265 8.767E-02
1.158E+0
3
1.605E-
01
1.432E-05 0.009545 7.890E-02
1.042E+0
3
1.165E-
01
1.273E-05 0.0085905 7.014E-02
9.261E+0
2
1.327E-
01
3.595E-06 0.0047725 1.981E-02
2.616E+0
2
9.239E-
01
3.754E-06 0.0047725 2.069E-02
2.732E+0
2
8.473E-
01
1.273E-04 0.122176 7.014E-01
9.261E+0
3
1.888E-
02
1.909E-04 0.313076 1.052E+00
1.389E+0
4
2.150E-
02
3.471E-04 0.937319 1.913E+00
2.526E+0
4
1.947E-
02
4.088E-04 1.3028925 2.253E+00
2.975E+0
4
1.951E-
02
3.433E-04 0.7550095 1.892E+00
2.498E+0
4
1.603E-
02
3.471E-04 1.032769 1.913E+00 2.526E+0 2.145E-

Head Loss and Differential Flow Measurement 37
4 02
5.663E-06 0.005727 3.121E-02
4.121E+0
2
4.468E-
01
3.182E-04 0.8065525 1.753E+00
2.315E+0
4
1.994E-
02
4.136E-04 1.231305 2.279E+00
3.010E+0
4
1.801E-
02
3.341E-06 0.0047725 1.841E-02
2.431E+0
2
1.070E+0
0
1.074E-05 0.0047725 5.918E-02
7.814E+0
2
1.036E-
01
1.551E-05 0.0104995 8.548E-02
1.129E+0
3
1.092E-
01
2.335E-05 0.0181355 1.287E-01
1.699E+0
3
8.325E-
02
2.991E-05 0.013363 1.648E-01
2.176E+0
3
3.739E-
02
3.818E-05 0.0047725 2.104E-01
2.778E+0
3
8.193E-
03
5.785E-05 0.047725 3.188E-01
4.209E+0
3
3.569E-
02
7.954E-05 0.03818 4.383E-01
5.788E+0
3
1.510E-
02
1.061E-04 0.07636 5.845E-01
7.717E+0
3
1.699E-
02
6.937E-04 3.312115 3.823E+00
5.048E+0
4
1.722E-
02
3.579E-06 0.0047725 1.973E-02
2.605E+0
2
9.322E-
01
6.395E-06 0.005727 3.524E-02
4.654E+0
2
3.504E-
01
6.250E-04 2.586 3.444E+00
4.548E+0
4
1.657E-
02
4.545E-04 2.139 2.505E+00
3.308E+0
4
2.591E-
02
3.333E-04 1.432 1.837E+00
2.426E+0
4
3.225E-
02
2.778E-04 0.909 1.531E+00
2.021E+0
4
2.948E-
02
2.500E-04 0.589 1.378E+00
1.819E+0
4
2.358E-
02
1.623E-05 0.0181355 8.942E-02
1.181E+0
3
1.724E-
01
1.909E-05 0.0181355 1.052E-01
1.389E+0
3
1.245E-
01
4.009E-05 0.020999 2.209E-01
2.917E+0
3
3.270E-
02

Head Loss and Differential Flow Measurement 38
4.104E-05 0.022908 2.262E-01
2.987E+0
3
3.403E-
02
5.154E-05 0.0391345 2.840E-01
3.751E+0
3
3.686E-
02
5.918E-05 0.047725 3.261E-01
4.306E+0
3
3.410E-
02
1.050E-04 0.066815 5.786E-01
7.640E+0
3
1.517E-
02
1.260E-04 0.104995 6.943E-01
9.168E+0
3
1.655E-
02
3.355E-04 0.715875 1.849E+00
2.441E+0
4
1.592E-
02
3.391E-04 0.734965 1.869E+00
2.467E+0
4
1.600E-
02
4.977E-04 1.60356 2.743E+00
3.621E+0
4
1.620E-
02
5.966E-04 2.300345 3.288E+00
4.341E+0
4
1.618E-
02
6.263E-04 3.03531 3.452E+00
4.557E+0
4
1.936E-
02
6.877E-04 3.0544 3.790E+00
5.004E+0
4
1.616E-
02
7.286E-04 3.426655 4.015E+00
5.302E+0
4
1.615E-
02
7.522E-04 4.132985 4.145E+00
5.473E+0
4
1.828E-
02
3.985E-04 1.154945 2.196E+00
2.900E+0
4
1.820E-
02
8.829E-06 0.005727 4.866E-02
6.425E+0
2
1.838E-
01
1.814E-05 0.0181355 9.994E-02
1.320E+0
3
1.380E-
01
2.864E-05 0.013363 1.578E-01
2.084E+0
3
4.078E-
02
3.245E-05 0.011454 1.788E-01
2.362E+0
3
2.722E-
02
3.484E-05 0.011454 1.920E-01
2.535E+0
3
2.361E-
02
7.018E-05 0.028635 3.868E-01
5.107E+0
3
1.455E-
02
9.312E-05 0.05727 5.132E-01
6.776E+0
3
1.653E-
02
2.357E-04 0.353165 1.299E+00
1.715E+0
4
1.591E-
02
3.767E-04 0.906775 2.076E+00
2.741E+0
4
1.599E-
02
5.492E-04 2.08081 3.027E+00 3.996E+0 1.726E-

Head Loss and Differential Flow Measurement 39
4 02
4.167E-05 0.033 2.296E-01
3.032E+0
3
4.757E-
02
A graph of friction coefficient of the pipe against Reynolds’ number is as shown in Figure 8
below
0.000E+00 1.000E+04 2.000E+04 3.000E+04 4.000E+04 5.000E+04 6.000E+04
0.000E+00
5.000E-01
1.000E+00
1.500E+00
2.000E+00
2.500E+00
3.000E+00
Pipe friction coefficient vs. Reynolds' number
Reynolds' number, Re
Pipe friction coefficient, f
Figure 8: Pipe friction coefficient against Reynolds’ number
Interpretation & Discussion of Results
Generally, head loss increases with increase in flow rate through a roughened pipe. This
is simply because when flow rate increases, it means that volume of water through the pipe and
the mean velocity of the water have also increased (Furuichi, et al., 2015). This increase in
velocity and volume of water through the pipe causes an increase in contact area between water
and internal surface of the pipe thus increasing frictional coefficient (Nazemi, et al., 2011).
Figure 8 above shows a graph of pipe friction coefficient against Reynolds’ number. The graph

Head Loss and Differential Flow Measurement 40
shows that pipe friction coefficient starts by decreasing with increasing Reynolds’ number before
becoming constant even with increasing Reynold’s number past a particular value of Reynolds’
number (a higher Reynolds’ number) (Masuyama & Hatakeyama, 2009). This basically means
that at high Reynolds’ number, friction coefficient of the pipe becomes constant (Furuichi, et al.,
2009). At higher Reynolds’ number, the flow becomes more stable thus reducing the
bombardment of water on internal pipe surface (Ahsan, 2014).
Conclusion
Once Reynolds’ number of water flowing through a pipe is known, friction coefficient of
the fluid can be obtained from Moody’s diagram. A graph of friction coefficient against
Reynolds’ number obtained in this experiment showed that friction coefficient or factor remains
constant beyond a particular value of Reynolds’ number (about 103 in this experiment).
Therefore once the Reynolds’ number of a rough pipe is known, it is possible to predict the
friction factor of that particular pipe and the expected head loss due to water flow through the
pipe.
References
Ahsan, M., 2014. Numerical analysis of friction factor for a fully developed turbulent flow using
k–ε turbulence model with enhanced wall treatment. Beni-Suef University Journal of Basic and
Applied Sciences, 3(4), pp. 269-277.
Burger, J., Haldenwang, R. & Alderman, N., 2010. Friction factor-Reynolds number relationship
for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes.
Chemical Engineering Science, 65(11), pp. 3549-3556.

Head Loss and Differential Flow Measurement 41
Cerbus, R., Liu, C., Gioia, G. & Chakraborty, P., 2018. Laws of Resistance in Transition Pipe
Flows. Physical Review Letters, 120(5-2).
Furuichi, N., Sato, H., Terao, Y. & Takamoto, M., 2009. A new calibration facility of flowrate
for high Reynolds number. Flow Measurement and Instrumentation, 20(1), pp. 38-47.
Furuichi, N., Terao, Y., Wada, Y. & Tsuji, Y., 2015. Friction factor and mean velocity profile for
pipe flow at high Reynolds numbers. Physics of Fluids, 27(9).
Hanjalic, K. & Launder, B., 2011. Modelling Turbulence in Engineering and the Environment:
Second-Moment Routes to Closure. Cambridge, UK: Cambridge University Press.
Jackson, J. & Launder, B., 2011. Osborne Reynolds: A Turbulent Life. In: P. Davidson, Y.
Kaneda, K. Moffatt & K. Sreenivasan, eds. A Voyage Through Turbulence. Cambridge, UK:
Cambridge University Press, pp. 1-39.
Launder, B. E., 2015. First steps in modelling turbulence and its origins: a commentary on
Reynolds (1895) ‘On the dynamical theory of incompressible viscous fluids and the
determination of the criterion’. Philosophical Transaction of the Royal Society A, 373(2039).
Launder, B. & Jackson, D., 2007. Osborne Reynolds and the Publication of His Papers on
Turbulent Flow. Annual Review of Fluid MEchanics, Volume 39, pp. 19-35.
Masuyama, T. & Hatakeyama, N., 2009. On Relation between Friction Factor and Reynolds
Number for Pseudo-Plastic Fluid Flow in Concentric Annular Tubes with Roughness. Shigen-to-
Sozai, 122(9), pp. 451-455.
Nazemi, A., Shui, L. & Davoudi, M., 2011. Friction Coefficient (F)-Reynolds Number (Re)
Relationship in Non-cohesive Suspended Sediment Laden Flow thorough Pervious Rockfill

Head Loss and Differential Flow Measurement 42
Dams. Research Journal of Environmental Sciences, Volume 5, pp. 674-681.
Nuclear Power, 2018. Head Loss - Pressure Loss. [Online]
Available at: https://www.nuclear-power.net/nuclear-engineering/fluid-dynamics/bernoullis-
equation-bernoullis-principle/head-loss/
[Accessed 14 March 2018].
Soumerai, H. & Soumerai-Bourke, B., 2014. Analytical method of predicting turbulence
transition in pipe flow. Scientific Reports, 2(214).
Tribonet, 2018. Studying Transitional Flow With Reynolds Friction Laws. [Online]
Available at: https://www.tribonet.org/studying-transitional-flow-with-reynolds-friction-laws/
[Accessed 13 March 2018].
Wu, X., Moin, P., Adrian, R. & Baltzer, J., 2015. Osborne Reynolds pipe flow: Direct simulation
from laminar through gradual transition to fully developed turbulence. Proceedings of the
National Academy of Sciences of the United States, 112(26), pp. 7920-7924.
Appendix
Appendix 1: Pipe Network of Armfield C6-MKII-10 Fluid Friction Apparatus

Head Loss and Differential Flow Measurement 43