Interesting physics question - has my class in controversy?

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Blocks2hell

New member
There is a water tank which is 2m high, it is full and contains 20,000L of water. There is an output in the side of the tank which leads to a tap 20m vertically below the bottom output of the water tank. What is the potential energy of the water relative to the output.

My class has came up with three different answers:

1)You measure the height from the bottom of the water tank and so the potential energy is
PE = 20000*9.8*20 = 3920000J

2)You measure the height from the top of the water tank so the potential energy is
PE = 20000*9.8*22 = 4312000J

3)You measure the height from the middle of the water tank so the potential energy is
PE = 20000*9.8*21 = 4116000J
I think the answer is 1. I think you should disregard everything but the water and therefore have the water suspended 20m high and just calculate the PE.
What do you think, justify your answer?
 
The water in the tank and the water in the line leading to the tap is one continuous structure holding the water, regardless of the shape of the container. If that is true, the bottom level is the height of the tap. tap-height =0, then there is no height for the water at all. That means the water has the same PE whether the tank is high or a large low pool. The height of the water in the tank would be irrelevant. That is not correct. Answer #1 is wrong.

Answer #2 is also wrong. The height of the water in the tank gets lower as you drain it out. Imagine you turn the tap on and off several times to drain the tank. Each time you draw a little water from the tank you spend some of the PE and you lower the level of water in the tank. If the PE is measured from the top, the top gets lower each time you use it. The honest method is to measure the average height of the water in the tank. That would be the middle of the tank's height. Correct answer is #3.
 
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