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
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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