# Desktop pipe flow and pipe network demonstrations

In class demonstrations on pipe flow head loss and pipe networks have been a challenge but I think I have found a way using kid’s straw construction kits (e.g. 1, 2, & 3). These kits can be used to build any number of different pipe networks. The T connectors can also be used to add in piezometer tubes to measure the local static pressure in the straw. This, in turn, can be used for measuring head loss along the system.

Equipment needed

1. A desktop constant head tank or other steady water supply.
2. As many straw construction kits as you desire.
3. Tape measure and calipers to measure the straw dimensions.
4. Measuring cylinder and stopwatch to measure flow rate
5. Imagination Photograph of the equipment needed including the desktop constant head tank system, straw ‘pipe fittings’, calipers, tape measure, stop watch, and measuring cylinder. In the experiment the water was collected in a plastic cup and then transferred to the cylinder for measuring.

Example demonstration: Head loss along a pipe and local losses in bends

An easy use of these straws is to measure the head loss in a pipe and around bends. You will need all the equipment listed above.

Demonstration

1. Measure the internal diameter (D) of the straws (they should all be the same in a given set).
2. Build a horizontal pipe with piezometers at the start and immediately before and after each bend (see figure below)
3. Connect the start of the pipe to the upper constant head tank and have the end drain into the overflow tank (see here for details of the constant head tank).
4. Fill the constant head tank and turn on the pump so that water flows along the pipe and also recirculates within the constant head tank system.
5. Have students measure the height of water in each of the piezometer tubes and the length of each pipe section.
6. Have students use the measuring cup to capture a known volume of water over a measured time and calculate the volume flow rate
7. Calculate the average velocity in the pipe (U=Q/A) and Reynolds number (Re=UD/ν).
8. Calculate the head loss hlp along each section of pipe based on the change in piezometer height measurements.
9. Calculate the head loss around the bend (hlB) based on the difference in piezometer heights.
10. Calculate the friction factor for the pipe (f=hlpD2g/U2L) (based on the Darcy-Weisbach equation)
11. Calculate the loss coefficients for the various bends (Kl=hlB2g/U)
12. Compare the pipe friction factor (f) and local loss coefficient (Kl) to standard values.

figure 2. (Left) Photograph of the pipe flow setup. The head loss was measured from the piezometer just downstream from the inlet to the tube just upstream of the bend. The outlet is pointed upward to reduce the total head difference along the pipe and to ensure that the piezometer tubes filled up to a height above the red solid T fittings.  (Right) photograph of a T fitting used to insert a piezometer tube into the pipe system.

Discussion

When I did this test (see photograph above), I got a flow rate of 1.75 ml/s with a straw diameter of 4.4 mm. This led to a mean velocity of 1.15 cm/s and a Reynolds number of 506 (laminar). I measured the head loss over 660 mm length of pipe to be 11 mm leading to a calculated friction factor of f=0.109. This is quite close to the theoretical value of f=64/Re=0.126. The head loss around the 180o bend was 0.6 mm which led to a calculated local loss coefficient of 0.89 which is within the range of values quoted for 180o bends. It is fiddly trying to get the system level with the piezometer tubes vertical. I would suggest using a more stable platform than piles of books. That said, the results were encouraging.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

# A \$19 desktop constant head tank

I have been planning on doing some pipe flow demonstrations in class using straws and rubber connectors. However, to do that I need a constant head tank that will drive the flow. Ideally the entire system would sit on a desktop so that no special mounting would need to be brought into the classroom. I am still working on the pipe flow demonstration but I thought that the budget desktop constant head tank design may be helpful to share.

Equipment

You will need:

1. A small aquarium pump \$8
2. A funnel \$1
3. 2 plastic tubs with straight sides (I used plastic shoe boxes) \$4
4. A small tube of silicone sealant \$3
5. A binder clip \$1
6. A short length of tubing to connect to the pump \$1
7. A hard plastic straw \$1 Figure 1: Materials needed for construction (binder clip missing).

Design

The basic idea is that there is a lower reservoir tank that feeds the upper tank via a pump. The upper tank contains a constant height weir overflow, with return to the reservoir tank, and an outlet below the overflow that will have a constant head. Provided the weir length on the overflow is large and the flow rate through the pump is substantially larger than the flow rate out of the constant head outlet then there will always be water flowing over the weir and the head over the weir will be relatively constant. In this budget design the reservoir and upper tank are plastic shoe boxes and the weir overflow is a funnel. Water is pumped using an aquarium pump from the lower to the upper tank and returns through the funnel to the lower tank. The upper tank rests on the lower so that the entire system can sit on a desk. Construction

1. Drill a hole in the center of the base of one of the shoe boxes with a diameter equal to that of the middle of the funnel neck.
2. Drill a hole in the side of the same shoe box with a diameter a fraction smaller than the straw.
3. Push the straw through the side hole (it should be a tight fit) and then seal around the hole with the silicone sealant on both sides
4. Place the funnel inside the same shoe box with the neck protruding through the hole and seal around the funnel neck on both sides of the hole. The top of the funnel should be below the rim of the box so that water will flow into the funnel before it overflows out of the box.
5. Attach the tubing to the aquarium pump and place it in the second shoe box.
6. Attach the binder clip to the box with the funnel and use it as a mount for the tubing such that the tubing is pointed into the box but not into the funnel
7. Place the box containing the funnel on top of the box containing the pump with the funnel outlet draining into the lower box.

Figure 2: (a) fully assembled constant head tank system. The yellow straw is the constant head outlet. (b) close up of the upper tank showing the inflow tube mounted (from the pump) through the binder clip and the funnel overflow back into the lower reservoir tank. (c) alternate view of the entire system.

Operation

1. Block the end of the outlet straw or connect it to the test rig to be used.
2. Fill the lower box until it is almost overflowing and the upper box until it is about to overflow into the funnel.. This is most easily done by pouring water into the upper tank and allowing it to overflow through the funnel into the lower tank.
3. Turn on the pump. The water will be pumped into the upper box and drain through the funnel back into the lower box. The head in the upper box will remain essentially constant provided there is water overflowing into the funnel.

The \$19 budget is approximate. You will use only a fraction of the \$3 tube of sealant and may need to buy a box of binder clips to get the one you want. The whole thing takes about 15 minutes to assemble provided you have an electric drill with the appropriate drill bits for cutting the holes.

# Video of the “Pendulums and deriving the work energy equation” demonstration

Here is a video of the “Pendulums and deriving the work energy equation” demonstration The full video is here. The video clearly shows that the amplitude of oscillation decreases due to losses in the first minute. The spring is almost not moving after 3 minutes (not shown).

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

# Pendulums and deriving the work energy equation

Obviously deriving the work energy equation is not a demonstration (other than a demonstration of one’s memory and math ability). This demonstration was used by Ben Sill to illustrate the terms in the work energy equation that can then form the basis for the derivation.

Equipment

You will need either a string pendulum with a weight on the end or a spring with some mass on the end. I use the spring mass system that I also use for dimensional analysis. Demonstration

Start the pendulum or spring moving with some initial deflection. Talk to the students about what they observe. Perhaps ask them to predict what will eventually happen (maybe a clicker question). Maybe get them to reflect on why the amplitude of the oscillation decreases over time. Once there is a substantial, noticeable reduction in the amplitude stop the demonstration.

Analysis

Write down a generic work energy equation

Total energy at time (2) = Total energy at time (1) + work done on the system – losses (i.e. work done by the system)

I keep the losses separate even though they are work done by the system and hence work done with a minus sign. This just keeps things a little more physically accessible as students seem to be able to think in terms of losses rather than in terms of the pendulum or spring doing work on the surroundings. The work done is the energy spent initially raising the pendulum or pulling down the spring. The total energy at time (1) is zero if you take this time to be before you touch it. The losses are due to drag on the object and internal damping. There is no need to get into details of how to model these terms, it is the bulk equation that you want to demonstrate.

From this point it is possible to derive the work energy equation with the caveat that the energy terms are energy fluxes and the work and loss terms are rates of work and loss.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.

# Pump performance curves

I sometimes use this as an in class demonstration and sometimes as a lab test toward the end of the semester. It is good for illustrating experimental method and measurement uncertainty while demonstrating pump performance characteristics. I first saw a version of this demonstration at an APS DFD meeting about 8 years ago though I am having trouble recalling who presented it.

Equipment

1. Bucket
2. Stopwatch
3. Tape measure
4. Measuring cup
5. Aquarium pump
6. Extension cord
7. Tube connected to the outlet of the aquarium pump Demonstration

1. Fill the bucket with enough water to fully cover the pump, attach the tube to the pump outlet and place the pump in the bucket.
2. Hold the tube vertically above the pump and turn it on (typically there is no on – off switch so plugging it in turns it on). The water should rise up the tube and then stop. Measure the head difference between the top of the water in the tube and the top of the water in the bucket. This is the shut off head.
3. Lower the tube outlet until water starts to flow. Holding the outlet steady measure the distance from the bucket water surface to the outlet and the time taken to fill the measuring cup. Calculate the flow rate.
4. Repeat step 3 until you have 6 to 8 different head – flow rate data pairs ranging from the shut off head to negligible elevation difference.
5. Write up the head flow rate pairs on the board and plot the data by hand with elevation on the vertical axis and flow rate on the horizontal axis.

Analysis The data plotted should show an increase in flow rate with decreasing elevation like a typical pump performance curve. However, the data needs to be corrected to account for head loss in the tubing.

Draw a sketch of the pump – bucket – tube system with a control volume around the whole system. Write down the work energy equation from the water surface and the tube outlet.

Z1 + u12/2g + p1/g + EP= Z2 + u22/2g + p2/ g +  hl

All the terms on the left hand side are zero except the pump head EP while the pressure at the outlet is p2=0. Using the Darcy–Weisbach equation for the head loss then Eis given by

EP= h+ (u22/2g)(1+ fL/D)

where f is the friction factor, L is the tube length, and D is the tube diameter. The exit velocity can be calculated based on the flow rate u2=Q/A=4Q/πD2. The main problem here is that the friction factor f varies with the Reynolds number and, therefore, the flow rate. Therefore, you need to calculate the friction factor and exit velocity for each data point. This can be given to the class as an in class exercise. Once the actual EP values have been calculated they can be plotted on the same graph. Some aquariums pumps actually come with a pump performance curve that can be compared to the measured data. In that case you can print the manufacturer curve on an overhead transparency. My experience with this is that cheap pumps rarely behave exactly as given in the manufacturer curve.

The demonstration presents a great opportunity to discuss experimental error. The first major source of error is the head measurement because it is hard to hold the tube steady, the water level in the bucket drops while you are filling the measuring cup, and you need to keep the tape measure vertical (though small angles away from the vertical will not make much difference). The second major error is in the measurement of the time taken to fill the measuring cup. Even if you use a 4 cup measure, it still fills in a few seconds for the larger flow rates. Therefore, a small error in timing of say half a second can lead to 10-20% error in the flow rate calculation. Both of these errors can be reduced by making multiple measurements at each height. It is also possible to estimate the individual errors and use them to place error bars on the pump performance curve data.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.