Fluid Mechanics 2 (SCEE08003) laboratory briefing note
F4: Real flow in pipes: determination of friction coefficients for laminar and
turbulent flows
1. Safety
A copy of the completed Risk Assessment “RA1” form for this experiment is kept with each
set of the apparatus.
The experiment carries very little safety risk, but we require that you wear safety glasses,
safety (steel toe-capped) boots/shoes, and a lab coat while in the laboratory. The apparatus
is set up in the main, open area of the lab in which there can be a variety of other activities
happening at the same time as your work on this experiment. Because there are no physical
partitions within this large space, we must adopt the level of PPE which aligns with the
highest level required anywhere in the lab. You will not be allowed to enter the work area
unless you are wearing your safety glasses, your safety boots, and your lab coat.
The apparatus is located away from the immediate proximity of mains electricity outlets.
Nevertheless, you should check that there are no mains extension cables nearby, which
could be reached by any splash from the apparatus. If you are in any doubt, you should
consult a member of staff.
2. Background
In Chapter 5 of the course, we are becoming familiar with methods to correct Bernoulli to
account for viscous energy losses (or “head losses”, or “pressure losses”) in pipe flows. For
simple, straight lengths of pipe, the unrecovered head loss due to friction, Hf, is given by
Darcy’s equation: ∆! = 2!"
The key to making this equation work for us is to be able to know the friction coefficient, cf.
The usual way to find cf is from the Moody chart (Figure F3.1) and/or from an equation
fitted to the lines on the chart. We can identify four distinct physical regimes on the chart:
1. Laminar flow, in which cf depends only upon Re.
2. Transitional conditions between laminar and turbulent flow; cf undefined unless flow
condition known.
3. Turbulent flow, in which cf depends upon Re AND the relative roughness of the pipe.
4. Complete turbulence, where cf depends only upon the relative roughness, and no longer
changes with changes in Re.
In this experiment, we will explore the regions identified in Figure F4.1, and be able to plot
cf vs. Re over a range of Re spanning laminar and turbulent flows.
Figure F4.1: The Moody chart, with regions explored by this experiment highlighted.
3. Objectives
Objective 1. For laminar flow, predict the variation of cf with Re over the range 300 < Re <
4000, and compare with cf derived from experimental measurements.
Objective 2. For turbulent flow, predict the variation of cf with Re over the range 3000 < Re
< 12000, and compare with cf derived from experimental measurements.
Objective 3. Draw clear, concise conclusions relating to Objectives 1 to 3. These should be
quantitative where possible, and supported by the evidence of your measurements.
4. Preparation
Introductory note: Now that you have successfully worked through experiments F1, F2 and F3
plus the ‘homework’, you will need much less detailed guidance on how to proceed with this
experiment. Progress!
Objective 1: losses in laminar flow
The first part of the experiment will explore the friction coefficient’s variation with Re in
laminar flow.
Preparation task 1: Prepare a chart that will become your Moody chart. Plot the predicted
line for cf as a function of Re for laminar flow.
0.025
0.02
0.018
0.016
0.014
0.012
0.010
0.008
0.006
0.005
0.004
0.003
0.0025
0.002
103 104 105 107106 108
Friction2Coefficient
Reynolds2Number2
Roughness2Ratio
(k/d)
0.01
0.001
0.0001
0.00001
0.00004
0.0002
0.0006
0.002
0.004
0.006
0.02
0.04
0.06
We will be using a range of flow rates to give us a range of Re values over approximately
300 < Re < 4000. At each flow rate, we will measure a pressure drop over a 0.4 m length of 3
mm diameter pipe.
Preparation task 2: Extend your spreadsheet so that it is ready to accept your measured
values of flow rate (Q) and manometer height difference (Dz), change these to a pressure
drop (Dp) and then determine the cf value from the measurements.
Objective 2: losses in turbulent flow
This second part of the experiment will explore how the friction coefficient varies with Re in
turbulent flow. We will be using a range of flow rates to give us a range of Re values
extending upwards from c.3000 to c.13000. As before, for each flow rate, we will measure a
pressure drop over the same 0.4 m length of 3 mm diameter pipe. Hopefully, you will have
spotted that for turbulent flow, we also need to know the relative roughness, k/D. The pipe
is a brass pipe.
Preparation task 3: Plot, over an appropriate range, the predicted line for cf as a function of
Re for turbulent flow conditions. Aide memoire: the Moody chart uses logarithmic axes.
5. Experiment
Please be certain to bring your PPE (lab coat and safety glasses) with you. These will NOT be
loaned to you in the lab. Upon arrival, please don your PPE.
DO NOT COMMENCE any work with the apparatus until your safety and technical briefing
has been completed by the demonstrator.
During the experiment, if you have any concerns about your safe or correct operation of the
equipment, or if you feel unsafe, STOP THE WORK immediately and seek advice.
For the laminar flow tests (objective 1), we need a very low flow rate. Thus, we are not
going to use the pump directly but instead, use the pump to raise the level in a reservoir,
whose static head will drive the flow through the pipe. The combination of the pump
keeping the reservoir topped up and an overflow fixing its surface level means that we
should have a steady flow in the pipe. For the low flow, we expect small pressure drops, so
we will use the two water standpipe manometers.
For the tests in turbulent flow, the pump will be used to drive the flow directly. For the
larger Qs, the pressure drops will be larger and will be measured instead using the pressure
meter.
Take a minute or two to look at and understand how the apparatus will be configured for
the laminar flow tests. The flow in from the pump can either be directed into the reservoir,
or bypass the reservoir and be pumped directly into the pipe. Locate the valves that control
whether the flow goes into the reservoir, or through the bypass. The flow rate will be
controlled by the setting of the outlet valve, which you should also locate, and set open to
begin with.
Readying the apparatus for both phases of F3 is much easier than for F2!
For laminar flow tests:
1. (Very gently) connect the pipe pressure taps to the standpipe manometers.
2. Open the outlet valve.
3. Close the valves for the bypass.
4. Open the valve to supply the reservoir.
5. Switch on the pump.
6. Allow the reservoir to fill to the depth of the overflow.
7. Gently close the outlet valve until you have a very low flow rate.
8. Record the pressure drop over the 0.4 m section of pipe.
9. Measure the flow rate in the usual way.
10. Repeat for at least four more flow rates, exploring the full range that can be achieved.
The flow rate is adjusted upwards by opening the outlet valve gently, while watching the
response of the standpipes.
For turbulent flow tests:
11. (Very gently) connect the pipe pressure taps to the pressure meter.
12. Open the outlet valve.
13. Open the valves for the bypass.
14. Close the reservoir entry valve.
15. Switch on the pump. (There should now be no flow entering the reservoir.)
16. Gently close the outlet valve until you have a low flow rate which gives a pressure drop
reading near the bottom end of the measurable scale.
17. Record the pressure drop over the 0.4 m section of pipe.
18. Measure the flow rate in the usual way.
19. Repeat for at least five more flow rates, exploring the full range that can be achieved.
The flow rate is adjusted upwards by opening the outlet valve gently, while watching the
response of the pressure meter.
The experimental measurements are now complete.
Switch off the pump and open all valves allowing the system to drain and return to its
starting state.
6. Analysis (after lab visit)
If you have done your preparation tasks 1 – 3 well, and carried out the experiment with
care, then the analysis should be quite straightforward.
Analysis task 1: For all tests, add your measured flow rates and pressure drops to your
spreadsheet, and check through the calculation of the friction coefficient cf derived from
these measurements. Get these measured (cf, Re) points plotted on your graph, ensuring
that the data for laminar and turbulent conditions are easily distinguished (e.g. by using
different markers and/or colours).
Analysis task 2: Work through your “uncertainty treatment” for all measured and derived
quantities. As before, this is probably most easily and elegantly done by adding additional
columns in the spreadsheet for the measurement uncertainties, and the for the consequent
(fed-though) uncertainties in the derived quantities.
Analysis task 3: Add the uncertainty estimates for the experimentally derived cf and Re
values onto your graphs as “error bars”.
Analysis task 4: Just as for F2 - meriting a separate task number… take a little time to ensure
that your graph is looking really good = fully professional according to the conventions set
out in the graphs document.
Finally, 33% of the mark rests with the “quality of conclusions” drawn from the experiment.
You will need to re-read, carefully, the guidance notes on Writing Conclusions.
Analysis task 5: Following that guidance, and looking carefully back at the experiment’s
objectives for further inspiration, draft 3 to 5 conclusions as text in a new worksheet (called
“conclusions”) in the same Excel file as all of your analysis. Check these conclusions against
the guidance and redraft as necessary.
You should now check the work, and then submit the Excel file (only) to the “Experiment F4”
drop box on Learn. The deadline for submission is 1600 on Thursday 17th November. You
can submit sooner, of course!
This lab is weighted at 10% of the Fluid Mechanics 2 mark.