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Work problem -- lifting water out of tanks

  1. Jan 28, 2017 #1
    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >

    I've encountered 2 problems in a row that involve lifting water out of tanks and finding the work needed. I am getting the incorrect answer.
    w = ⌠ab pgA(y)D(y)dy

    here is one of the problems:
    A water tank is shaped like an inverted cone with a height 6m and a base radius of 1.5m...
    a) if the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank?

    *Attempt*:
    I drew a graph and a line from (0,0) to (1.5, 6) and found that the equation of that line is y = 4x or x = (1/4)y
    cross-sectional volume of a slice: πr²h
    r = y/4
    V = π(y/4)²dy = A(y)
    D(y) i think = 6m
    g = 9.8 m/s²
    p = 1000kg/m3
    061000(9.8m/s²)(πy²/16)(6m)dy

    I am getting the incorrect answer....
     
    Last edited by a moderator: Feb 16, 2017
  2. jcsd
  3. Jan 28, 2017 #2

    Orodruin

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    Your D(y) must be a function of y ...
     
  4. Feb 16, 2017 #3
    Here's something interesting about this problem.

    Does it take more work to pump water from bottom of tank or from top of tank as you slowly lower the hose?
     
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