Individual home experiment “Super-Siphon Contest”: Bernoulli’s equation
Background
Siphoning, the process of using a tube to carry a liquid over a barrier and to a lower location, can be described well by the mechanical energy equation. In this assignment you will analyse siphoning behaviour theoretically, and then will carry out an experiment using a plastic bottle and length of tubing provided to you.
The plastic bottle has a nominal volume of one litre. However, two marks have been placed on the side of the bottle such that the corresponding volume between the two marks is approximately ∆V = 650 cm3. The plastic tubing given to you has an inside diameter of D = 2 mm and a length of L = 100 cm. In the picture to the right, ∆z is the variable distance between the liquid level in the bottle and the tube outlet level.
The diameter of the tube is small enough that the flow inside will be laminar, an orderly state of flow in which α = 2 in the mechanical energy equation. Furthermore, the friction (wf) term can be expressed as wf = kf Luavg
where kf = 9.5 s−1 is a friction constant for room-temperature laminar flow of water in this particular tubing. L is end-to-end length of tube and uavg is the average velocity in the tube. You may take the water density to be 999 kg/m3.
Pre-experiment
Before beginning the experiment, make sure the following items are available to you:
The plastic bottle and tubing (provided)
A stopwatch
Some sticky tape for attaching the tube to the side of the bottle (provided)
A large dish for collecting water
Clean drinkable water
A ruler or measuring tape
A pair of scissors (optional )
A pipette dropper (provided)
Analysis
For this experiment the analysis will be performed first.
Calculate the volumetric flow rate of the siphon (cm3/s), assuming that L = 100 cm,
∆z = 80 cm, and that there is no friction in the tube (wf = 0). In order to get the volumetric flow rate, you must first calculate uavg. 15 Marks
Predict the volumetric flow rate of the siphon (cm3/s), assuming that L = 100 cm,
∆z = 80 cm, and that there is friction in the tube (wf given by equation above).
15 Marks
Repeat the flow rate calculation from number 2 with the following change: assume a half-length of tubing is used, with L = 50 cm and ∆z = 33 cm. 10 Marks
Discuss the applications and limitation of a siphon (include images and references), 1000 words max. Graphs/Images/Tables and references are not included in the words count. 40 Marks
Experiment and contest
First you will verify the prediction from number 2 above by setting up a working siphon. Second, you will attempt to optimise or improve your siphon system to get the largest flow rate possible, within specified constraints.
Set up and run the siphon
Set aside the cap from the plastic bottle. Fill the bottle nearly full with water. The water line should be above the upper mark on the bottle.
Place one end of the siphon tube into the bottle so that this end is below the lower mark on the bottle. The other end of the tube will dangle from the bottle. Using a piece of tape, secure the tube to the side of the bottle so that it does not slip out. Place the bottle on the edge of a tall surface. Place a collecting dish below the free end of the siphon.
Prime the siphon by sucking gently on the free end using the supplied pipette, so that the tube is entirely filled with water. Upon releasing the free end, water should begin flowing unaided, as long as the free end is below the water level in the bottle. Make sure the water level is still above the upper mark.
As the falling water level (meniscus) reaches the upper mark on the bottle, begin a stopwatch. End it when the level reaches the lower mark. Record the average time here: ± s. 5 Marks
Note: The experiment should be repeated 4 times and each time recorded in the Table below
Experiment N0 Time recorded for each experiment Comments if any
1
2
3
4
Calculate the volumetric average flow rate and standard deviation. Record that here: ˙ ± cm3/s.
10 Marks
How does this result compare to the predicted value in number 2 above?
5 Marks
Super-siphon contest
Modify the siphon system as you see fit in order to get the water out of the bottle (between the two marks) in the shortest time possible. Use your creativity and engineering judgment while observing the following rules and constraints:
The entire siphon system can only be composed of the bottle and tubing provide, and tape to secure the tubing to the bottle or other solid surfaces. The tape cannot come in direct contact with the water.
You must set the bottle on a horizontal surface. You may route the tubing as you see fit, but the water must be delivered from the bottle to a designated collecting dish.
The bottle and tubing should be stationary during each timing attempt.
You may cut or deform the tubing in any way you wish. Cutting is irreversible, so consider any changes carefully.
You may not cut, deform, or otherwise modify the bottle. You may not pressurise the bottle. You do not need to use the bottle cap.
For each attempt, follow step 1(d) above, namely recording the time it takes for the water level to pass from the top mark to the bottom mark. Record your experimental conditions and observations in the space below, and circle your best (lowest) time.
Upload up on Canvas your assignment, including any pictures or video of your setting (date to be provided).
You will bring your siphon system to the University and we will hold a class championship. The three teams reporting the best times will compete by re-running their siphon systems with impartial referees doing the timing. The lecturer will provide water and collecting dishes.