This is a really simple demonstration that I typically use twice a semester. I do it first when we are discussing Bernoulli’s equation and cavitation. I then repeat it when we are covering head loss in pipes. The basic activity of the demonstration is to measure the time taken to siphon water out of a tank.
- Two fish tanks (mine are about 25 x 50 cm and 30 cm deep),
- a table,
- a length of tubing that will comfortably reach from the bottom of the tank on the table to the top of the tank on the floor below (the lower tank is only to collect the water so it can be a bucket as long as it is big enough),
- a tape measure,
- a stopwatch, and
- a couple of student helpers.
Put a vertical strip of tape on one edge of the top tank and draw two horizontal lines separated vertically by 10cm so that you can measure depth change.
Set up one fish tank on the table and one on the floor below.
- Fill the upper tank to the upper line on the vertical scale.
- Measure the dimensions of the upper fish tank including the depth of water, the distance from the bottom of the upper tank to the top of the lower tank (bucket), the tube length, and the tube diameter.
- Flood the tube with water in the upper tank.
- Hold one end of the tube near the base of the upper tank and, with your thumb over the other end of the tube, place it on the lip of the lower tank. This can be tricky and you may want to enlist another student to hold the upper end of the tube in the tank.
- Take your thumb off the tube allowing the water to flow into the lower tank. Have a student measure the time taken for the water level to drop from the upper line on the scale to the lower line on the scale.
There is only limited opportunity for discussion as the demonstration does not result in any unexpected behavior. The water level drops as the water drains. You can discuss how siphons work and some applications, it is also an opportunity to talk about cavitation which limits the height you can siphon over. Incidentally, the plot of the world war two movie ‘the battle of the bulge’ turns on someone realizing the Germans are running out of fuel because the German prisoners are all carrying hoses to siphon fuel into their tanks.
The payoff in the demonstration is in the analysis and the analysis all hangs on drawing the correct diagram (see figure below).
The main points are that the reference height for Bernoulli’s equation (or the energy equation if including head loss) is at the tube outlet and that there is a control volume around the whole upper tank and the tube. The analysis is as follows:
- Write down Bernoulli’s equation and show that the velocity out of the tube is given by (2gz1)1/2 and that the flow rate out of the tube is Atube(2gz1)1/2.
- Write down conservation of volume dV/dt+Qout-Qin=0 and note that the volume of fluid in the upper tank is V=Atankh= Atank(z1-H). Therefore, conservation of volume can be written as
This is a separable first order ODE that can be solved for the variation of depth with time. Separating and integrating from the initial to the final depth gives the time taken for the depth change.
You will find that the calculated time is a lot less than the measured time due to the head loss in the pipe.
If you want to do a follow up on the head loss then the work energy equation leads to
The main problem is that you do not know the friction factor, f, and f will vary during the flow as the flow rate, and hence Reynolds number, decreases with z1. As a first approximation assume that f is fixed and estimate the Reynolds number based on the average flow rate from the experiment. The final result is that the time is increased by a factor of
This gives a much better estimate of the draining 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 (email@example.com). I also welcome comments (through the comments section or via email) on improving the demonstrations.