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EMS420U Experimental Practice & design 2

In your Fluid Mechanics and Thermodynamics module (EMS460U), you will learn how manometers can be used to measure pressures, how Venturi devices can be used to measure flow rates and how Pitot probes are used to measure velocity. Ahead of these theoretical concepts, in this laboratory you will measure flow rates within a tube using a Venturi and compare these results to the flow rate obtained from a velocity profile measured with a Pitot probe.

Objectives

Organisation of the lab sessions

There are about 500 students overall doing this practical, so make sure to follow the rules and procedures for it to run smoothly.

• Two videos have been produced explaining the steps that you must follow during the experiment.

Important Notes:

STUDENTS WHO DO NOT FOLLOW THE SAFETY REQUIREMENTS and INSTRUCTIONS BY THE DEMONSTRATOR WILL BE ASKED TO LEAVE THE LABORATORY AREA AND WILL BE CONSIDERED AS ABSENT.

General:

4- Arrive on time; after 10 minutes you will be considered absent from the experiment and will not be allowed to stay or receive a mark.

1. Apparatus

The apparatus, shown in Figure 2, consists of a circular pipe fed at the inlet (found at the left) with air from a variable speed pump. The outlet of the pipe (at the right) is opened to the atmosphere. The pipe narrows to form a Venturi (red dashed box in Figure 2); the pipe diameters are marked on the apparatus (don't forget to note them down). Pressure tappings at the wide and narrow cross-sections are connected to a water manometer. In addition, there is a Pitot tube (dark blue dashed box in Figure 2) which is placed along the narrow cross-section, the Pitot probe can also be connected to the manometer.

Videos of the experimental setup and procedure are provided on the QM+ module web-page. Do watch them before you plan the activities for the lab.

1.1. Turbulence

In the Fluid Mechanics and Thermodynamics module (EMS460U) you will see examples of laminar flow where different layers of fluids at different velocities slide smoothly past each other. You will also see examples of turbulent flows where this regular movement breaks up into several swirling eddies resulting in (fast) fluctuating pressure and velocities. Even at low speeds, the flow in our duct is turbulent.

These fluctuations are of high frequency and the inertia of the mass in the inclined manometer is too large for the fluid level to show these oscillations: the manometer shows an averaged pressure.

You will also use an electronic pressure transducer (PT) which reacts much faster and is able to resolve some of these pressure fluctuations: you will see the value of measured pressure fluctuate. The PT does not have an averaging mode, but it does have a sample mode that is activated when the 'hold' button is pressed and reports minimum and maximum values in that given interval. You can perform your own averaging by sampling the flow, say, 10 times and computing your own average.

1.2. Post Processing

In fact, the raw experimental data (pressure values or manometer heights) are not that useful on their own. To get interesting results, you will need to work out velocities and flow rates. Some of this post processing, e.g. integrating the velocity profile to obtain the flow rate can start in the lab. If you have any time to spare, be ready to begin with this calculation in the laboratory session so you can get support from the demonstrators.

However, some basic data-processing, e.g. working out the velocity of the Pitot probe, should be done right away. This should be done in the laboratory so you can identify any anomaly within your measurements, review your methods and fix the error.

It is hence essential that you fully understand the theory of Pitot tubes and Venturi devices ahead of the experiment, please watch the videos found in QM+.

• Record temperature and pressure from the barometer.
• Record the values of the diameters or cross-sections of the Venturi as labelled on each device. Estimating the diameter for the tip of the Pitot probe as 1.0 mm is accurate enough.
• Ensure that the blower is turned off. Then set the inclined manometer (IM) and electronic pressure transducer (PT) to zero. Make sure your tubes are connected to the Venturi.
• Calibrate the PT against the IM for the range relevant to the experiment, i.e. 0-100 Pa by comparing IM pressure to PT pressure at various blower speed settings. This data is used to ensure that the values read off the PT are accurate. Note that you need to take several PT samples to deal with the turbulent fluctuations in the pressure. Repeat this process several times to reduce random error.
• Watch the IM, switch on the pump and gradually and carefully increase the speed until you either reach the maximum scale of the IM (don't make it overflow!), or the maximum speed of your motor/transformer. You must run the blower at 80-90% of the maximum setting.
• Take readings of pressure difference across the Venturi with IM and PT.
• Switch the valves to measure the Pitot pressure. Traverse the Pitot tube across the downstream pipe at intervals of at least 2 mm if your apparatus has a 30 mm pipe and 4mm in the case of an apparatus with 50 mm pipe. You may want to use smaller intervals when the probe approaches the wall.
• Read pressure difference for the Pitot tube at each position on the traverse.
• Regularly switch the valves back to the Venturi to make sure your flowrate is constant and the same as the one when you started.
• Repeat your experiment to reduce random error.
• Work out the velocities from the measurements and compare it to the Venturi flow rate. Do the values match? If not, check for sources of error.
• Repeat steps 5 - 10 for up to two further blower speeds with around 2/3 and 1/3 of the initial Venturi pressure.

Note: You must discuss on the experiments you conducted and on the steps you followed on your report. In addition, you need to use the data that you raised with your group. It is a good idea to have one or two group members recording the raw results while other group members conduct the experiment. Change roles appropriately. In any case, you must make sure that all group members have a copy of the data at the end of the session. Do not rely on other group members to copy and email to all group members the data.

For each flow speed setting, calculate the air volumetric flowrate, Q, using the Venturi manometer. Assume inviscid (negligible viscosity) flow. The necessary theory is found in the videos in QM+. Additionally, you will cover these concepts in detail in Fluid Mechanics and Thermodynamics module EMS460U and can also be found in the textbooks from its reading list.

For each flow speed setting, determine the radial profile of the velocity v(r) using the Pitot tube readings. Assume inviscid flow. You will also cover these concepts (later on) in detail in Fluid Mechanics and Thermodynamics module EMS460U and can also be found in the textbooks from its reading list.

3.3. Flow rate computation from velocity profiles

Determine the volumetric flow rate Q from the velocity profile v(r). See the Appendix for instructions as to how to do this.

3.4. Be careful with pressure units and conversion to SI units

Discuss your results in the report. In particular:

Appendix: The Theory of Determining the Flow Rate from the Velocity Profile

Figure 3. Cylindrical stream tube

Consider the pipe cross-section shown in Figure 3. The velocity will fall from a maximum on the pipe centre-line, r = 0, to zero at the pipe boundary (maximum radius) r = R. Since the flow distribution is (very nearly) circumferentially invariant, the velocity will be the same for any fixed distance from the pipe centre where 0 < r < R. If we consider a very, very small thicknesses of the stream-tube r, then the increment of volumetric flow rate Q through an element of area, A, with thickness r at distance r from the centre-line, as shown in Figure 3, is given by:

If we had an analytic equation for v(r) defined over the entire range 0 < r < R, we could integrate (3) to obtain Q. As we have only `discrete' point measurements taken in a limited number (N) of locations, we need to approximate this integral. We can do this by summing up the cylindrical elements that correspond to each of the measurement points from the centre-line to the edge of the pipe:

This can be viewed as integrating the profile of v(r)r for 0 < r < R.The summation of Equation 5 can either be done graphically, by plotting the product v(r)r(but don't expect much credit for such simple solution) or through use of a spreadsheet. You can also use a regression to fit your profile, but this will carry significant errors near the wall. The most appropriate technique is to use the trapezium rule between two measurement points and sum these areas for all intervals between the points. Make sure you have completed and fully understood this exercise.