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Calculus

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A cylindrical water tank has a radius of 2 feet and a height of 6.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft3.]

  • Calculus - ,

    Height of tank=
    H=6'
    Total volume of water
    V=πr²H
    Total mass
    m=ρV
    Average height raised
    h=H/2 (from centre of gravity to top)
    Total work done
    =mgh
    g=acceleration due to gravity
    =32.2 ft.s-2

    Note:
    If the water is supposed to load a truck below the tank, a pump is necessary to start filling the hose to the top and down, after that, water will flow up the tank, and down to the truck by gravity.

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