# 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.

# Video of “A \$19 desktop constant head tank”

Here is a link to a video from the “A \$19 desktop constant head tank” post. The video shows the water being pumped from the lower tank up into the constant head tank, overflowing into the funnel and draining back into the lower tank. The outflow is bent upward to prevent water flowing out, but can be connected to tubing to provide constant flow rate over prolonged periods of time.

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.

# Video Update for “Pump performance curves”

In the initial “Pump performance curves ” post I had forgotten who I had learned it from. It turns out to have been John Cimbala and Laura Pauley from Penn State. They have kindly passed on the videos they showed at the 2007  APS-DFD meeting in Salt Lake City. The full videos are linked here, here, and here. GIFS are below. It is so simple but there is so much in it. This is one of my favorite labs we do now.

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.

# Video of Pipe networks and head loss

Here is a video of the “Pipe networks and head loss” demonstration. The full video is here. Sorry that it is sideways. 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.