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Pipe flow and boundary layer analysis CIVE50005
1 Purpose
This coursework will enable you to analyse the development of a boundary layer and the flow profile in a
steady pipe flow based on readily obtained measurements. You will need to read this document carefully,
examine the ‘digital lab’, and then carry out an experimental laboratory in small groups. During the
experimental laboratory you will gather a dataset of measurements from which you can infer the local flow
velocity in order for you to examine the flow profile and boundary layer development within a pipe.
A description of how to gather the required data is provided in section 2 below and the ‘digital lab’ (see
Blackboard) helps you to become more familiar with the experimental equipment — this must be completed
before you enter the experimental laboratory. Section 3 provides guidance for your report and aspects to
include within and section 4 gives helpful hints/reminders to aid you in carrying out your analysis; N.B.
this is just guidance so if you have other sensible ideas or additions then you will receive extra credit.
2 Experimental set-up and procedure for gathering the data
2.1 Experimental principles
Steady air flow is driven by a fan through approximately 6m length of nominal 90mm (actual 89.6mm)
internal diameter clear Perspex pipe. The length of pipe is on the suction side of the fan, and flow enters
through an aluminium bell mouth. The flow velocity is determined from stagnation pressure measurements
at a pressure tapping on a cylindrical steel hypodermic tube that traverses across the diameter. The radial
traverse and the radial location of the stagnation pressure tapping utilise a vernier pointer gauge.
The velocity profile in the pipe can be measured at two locations, an upstream location just beyond the
bell mouth and a downstream location just before the fan. The traversing velocity probes are identical.
2.2 How a manometer provides pressure readings — see also the ‘digital lab’
The active traversing probe is a cylindrical steel hypodermic with a single small pressure tapping (Figure
1). The tapping is not easy to see (you need to locate it) but the hypodermic is bent so that the orien-
tation is correct when the horizontal section of the hypodermic points into the flow. When oriented in
this manner, the tapping is at the forward stagnation point and senses the stagnation pressure pstagnation.
The radial location of this stagnation pressure tapping is traversed across the pipe diameter by means of
a vernier pointer gauge (Figures 2 and 3).
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Pipe flow and boundary layer analysis CIVE50005/HCB Spring Term
The static pressure, pstatic, at the same cross-section along the pipe is simultaneously sensed by a static
pressure tapping in the side of the pipe (Figures 2 and 3).
The stagnation and static pressures are fed to separate sides of a precision tilting reservoir manometer
(Figure 1), such that the manometer measures the difference, the dynamic pressure
pdynamic = pstagnation − pstatic
= ρwaterg(h− h0)
= ρwaterg(l sin θ − l0 sin θ0)
=
1
2
ρairu(y)
2
The manometer fluid is water. Use ρair = 1.23kg/m
3 and ρwater = 1000kg/m
3.
Figure 1: Pressure probe and tilting reservoir manometer
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Pipe flow and boundary layer analysis CIVE50005/HCB Spring Term
2.3 Images of the experimental rig inflow and outflow sections
Figure 2: upstream station
Figure 3: downstream station
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Pipe flow and boundary layer analysis CIVE50005/HCB Spring Term
2.4 Gathering the data, cross reference with the ‘digital lab’
1. Check out the “plumbing”. Identify
inflow bell mouth at upstream end.
long clear Perspex pipe.
fan and motor at downstream end.
motor controls.
traversing velocity probe at upstream end, especially
– stagnation pressure tapping on front face of steel hypodermic.
– static pressure tapping at side of Perspex pipe.
– flexible tubing to tilting reservoir manometer.
– traversing “pointer gauge” with vernier position indicator.
Note: One complete rotation of the vernier screw advances the position by 2mm. The
vernier is marked in 20 sub-divisions, and can be read to 1/10th of a sub-division. It can be
read to the nearest 0.01mm. An unattached vernier gauge will be available for inspection.
You should become familiar with this operation.
tilting reservoir manometer at upstream end, especially
– air-water interface.
– reservoir.
– tilting manometer tube.
traversing velocity probe and manometer at downstream end.
2. Note the distance between the upstream and downstream stations is L = 6m .
3. At the upstream station
Locate the stagnation pressure tapping at the wall of the pipe. This is the y = 0 location for
the velocity profile measurements, so it must be done carefully! Note: the y-direction for the
boundary layer profile is measured radially inwards from the wall. The wall is at y = 0 and the
pipe centreline at y = R.
Record the vertical position Z0 identified by the vernier scale — in your datasets we have set
Z0 = 0 for simplicity.
Move the tilting manometer to the “0.4” slope.
Record the null (no flow) position l0 on the manometer tube.
4. Repeat 3. at the downstream station.
5. Start the fan motor.
6. Traverse the velocity probe at the upstream station:
Be careful not to obstruct the flow into the bell mouth! This will change the flow
through the experiment, invalidate the results, and require that you repeat the experiment.
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Pipe flow and boundary layer analysis CIVE50005/HCB Spring Term
Record Z and l at the initial y = 0 location.
Repeat the measurements for Z in intervals of order
– 0.2mm for 0 < y < 4mm,
– 1mm for 4 < y < 10mm, and
– 5mm for y > 10mm
7. Repeat the traverse for the downstream station.
8. Stop the fan motor.
9. Leaving at least a minute for the flow to return to zero, confirm your measurements of the null (no
flow) position l0 on the manometer tube for both the upstream and downstream stations.
10. Repeat the entire test series, and obtain a second set of measurements. This includes
both the downstream and the upstream locations.
11. Complete the analysis and report.
3 Aspects to analyse and present in your report
Guidance: Good lab reports tend to be around 10–15 pages in length. You should feel free to attach
Matlab code but only as an additional appendix and only when you really feel it adds to your report.
Below is a list of points that you should include but try to extend the analysis where possible.
1. Compute and list the velocity profiles, u(y), for 0 < y < R at the upstream and downstream
stations. Plot the velocity profiles, u(y), together on the same diagram.
Note: The flow pattern immediately adjacent to the wall follows a horseshoe vortex pattern (Figure
4). This results in a spurious velocity prediction in this region. However, at y = 0, the no slip
condition imposes u = 0, which can be used as a secure result, over-riding the measurement.
2. Determine the mass flux in the pipe at the upstream and downstream stations and consider your
results with the knowledge that mass must be conserved.
3. Characterise the type of the flow and identify the extent of the boundary layer on each profile
(upstream and downstream). List the thickness of the boundary layer and discuss the differences
between the profiles in the two sections.
4. Compare the velocity profiles of the upstream and downstream stations to the Hagen-Poiseuille
solution and discuss the differences.
Note: Make sure that the computed Hagen-Poiseuille solution is comparable to your experimental
data. The adopted mass flow should be as close as possible to the experimentally observed mass flow.
5. Based on the momentum conservation law determine the wall shear force acting between the up-
stream and downstream cross sections. Given this estimate, determine the average wall shear
stress across the pipe-wall, τ0.
6. Is there another way to compute the wall shear stress? If yes, compare and discuss the results of the
estimate of the previous question.
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Pipe flow and boundary layer analysis CIVE50005/HCB Spring Term
7. From your estimates of wall shear stress compute and list the pipe-averaged Darcy-Weisbach friction
factor, f , for this pipe flow.
8. Given your estimates of wall shear stress, calculate an estimate the characteristic roughness for the
pipe and comment on the validity of your answer. What sources of uncertainties are included in your
answer?
9. Given your measurements can you estimate the shear stress profiles at the two stations?
10. Assume that in your initial measurements of l0 you introduced an error of +1mm in both upstream
and downstream stations. How would this error affect your answers in the questions above? Give
a qualitative description.
11. Discuss any differences between the two sets of measurements (test series 1 and 2).
4 Hints to help your analysis
1. The cross-section-integrated mass flux is given by
ρQ = ρ
∫ R
0
2πru(r)dr = ρ
∫ R
0
2π(R− y)u(y)dy (1)
which can be evaluated using the trapezium rule. Note especially that the volume flux is NOT simply
the area under the velocity profile for a circular cross section. Make sure to apply the no slip over-ride
at y = 0.
2. The cross-section-integrated momentum flux is given by
J = ρ
∫ R
0
2πru2(r)dr = ρ
∫ R
0
2π(R− y)u2(y)dy (2)
which can be evaluated using the trapezium rule. Again, please make sure to apply the no slip
over-ride at y = 0.
3. Identifying a control volume that extends from the downstream to the upstream section, the
integral momentum equation for this horizontal steady flow becomes
Rate of change of momentum = (Jdownstream − Jupstream) = Applied Force
4. The wall shear force is the integral of the pipe-averaged wall shear stress over the wall surface:
T = τ02πRL, (3)
where τ0 is the pipe-averaged boundary shear stress and L is the distance between the downstream
and the upstream stations.
5. To apply the velocity defect law in your data:
Plot u(y) against Y = log yR for a fully developed turbulent velocity profile. Draw the best-fit straight
line approximation to these data points, ignoring the small y data which are contaminated by the
horseshoe vortex. This best-fit line is the velocity defect law approximation to the fully-developed
turbulent boundary layer. Estimate Umax from the Y = 0 axis intercept and u⋆/κ from the slope of
the velocity defect law approximation.
