The US oil reserves are stored in enormous underground tanks. When oil is needed

Question

The US oil reserves are stored in enormous underground tanks. When oil is needed it must be pumped up 30 feet from the storage tanks to a cylindrical holding tank that is 20 feet tall and has a radius of 10 feet. There are two ways to fill the holding tank: 1) pump it in from the bottom of the holding tank or 2) pump it to the top of the holding tank. Does one way involve less work than the other or are they equal? It is your job to determine the answer to the previous question, supporting your answer with appropriate mathematics.

Explanation / Answer

Filling from the bottom will require less effort. If we have to fill from top, then "all" of the water need to be raised to 30+20 = 50 feet. If we have to fill from bottom, then first few particles of water will have to be raised to 30 feet. Next few particles would have to be raised to 30 feet + the height accumulated by the particles sent in the earlier packet. Towards the end, almost full tank will be full. This process continues until the last few particles of fluid in underground tank are left which have to be pumped to 30+20 = 50 feet. Hence, work required will gradually increase in this case and would be about half of the previous case.

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