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Ok so I encountered this question ->

A 10 H.P. motor pumps out water from a well of depth 20m and fills a water tank of volume 22380 litres at a height of 10m from the ground. The running time of the motor to fill the empty water tank is (g = 10ms−2 )

Upon solving this my answer came out to be 15 minutes while the answer in the book is 5min. The book takes the height to be "10m" which is the height from the ground.
My question is do we take the height from the ground or do we take net height because potential energy is relative to height isn't it? If height is relative then shouldn't the total height be 30metres? If the given answer is correct won't it mean that there is ZERO work done in bringing water from the underground no matter how deep it is?

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    $\begingroup$ I think you are right here. The pump needs to do work to lift the water from a depth of 20m to a height of 10m. The net displacement is 30m and this is what you should use. $\endgroup$
    – Yashas
    Commented Jul 27, 2017 at 15:27
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    $\begingroup$ There is some vagueness in the question. For example, what do they mean by a well 20 m deep? Do they mean the surface is 20 m below ground, or that it is 20 m deep with water and the surface is at ground level? What is the capacity of the well? Can we assume it is a large enough resovior to be unaffected in height when we take water from it? Without a schematic or better wording, there are multiple semi-reasonable answers to this problem. $\endgroup$
    – JMac
    Commented Jul 27, 2017 at 15:41

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I agree with JMac's comment that the question is highly ambiguous and cannot be answered definitively. Perhaps the required context or assumptions are provided by the previous sections in the textbook.

If the water level in the well remains 20m below ground level while water is pumped out, and that of the tank at 10m above, then every litre of water is raised through a height of 30m. The same reasoning applies if the water is initially at ground level and the depth of water in the well is 20m. Judging by the answer, perhaps the key insight is that the reservoir of water below ground is so vast that the level of water in the well is not affected by removing 22380 litres. This also assumes that the rate at which water is removed is less that the rate at which it can seep back into the well through its walls and base.

However, if the level of water in the well and/or the storage tank changes, then the calculation is not so straightforward. You can only decide if this is the case from the situation described in the question. If the situation is not described adequately in the question or its context, then there is no way of knowing what the author intended.

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When solving problems in potential energy of the earth mass system, we take an appropriate reference point. We assume the potential energy and height at this reference point to be 0. You can take the reference point anywhere you want. In your specific question, if we take reference point on the ground, the height of water tank is 10m, the height of well is -20m. Total difference in 10-(-20)=30m. If you take the reference point at the bottom of the well, the height of water tank is 30m and that of well is 0m. The difference is 30-0=30m. Therefore the result remains unaffected. And for the answer, I think your solution is correct. Your textbook may be wrong.

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  • $\begingroup$ This assumes that the 20 m depth of the well is 20 m below ground before you reach the water. Although that's a reasonable assumption, the question may not have intended that, instead it may be a 20 m deep well that is filled up to ground level. This question seems ambiguous without a diagram or more specific wording. $\endgroup$
    – JMac
    Commented Jul 27, 2017 at 19:04

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