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Work (Pumping Liquid)

  1. Feb 7, 2013 #1
    1. The problem statement, all variables and given/known data
    A vertical right circular cylindrical tank measures 32 feet high and 8 feet in diameter. It is full of liquid weighing 62.4 lb / ft^3 How much work does it take to pump the liquid to the level of the top of the tank?


    2. Relevant equations
    h=32
    d=8 (radius = 4)
    liquid weight = 62.4 lb / ft^3


    3. The attempt at a solution
    1. integral (0 to 32) (62.4x) dx
    2. (156/5)x^2 | (0 to 32)
    3. answer: 31,948.8

    actual correct answer: 1,605,922 ft-lb
     
  2. jcsd
  3. Feb 7, 2013 #2

    Mark44

    Staff: Mentor

    This (above) is way off.

    Have you drawn a sketch of a typical "layer" of water? Each of the layers has the same volume, and hence the same weight, but a layer at the bottom of the tank has to be lifted all the way to the top, while the layer at the top doesn't have to be lifted at all.

    I don't see any accounting for this in your work.
     
  4. Feb 7, 2013 #3

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi whatlifeforme! :smile:

    ok-ish, but you haven't used the area of the cylinder! :wink:
     
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