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Math Help - help on work problem

  1. #1
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    help on work problem

    a cylinder tank lies on the ground, all filled with water. the radius of the circled top is 2m the total length is 10m, what is the work required to pump all the water out?

    - i got integral of 4(pi) from [0,10] which equals 40pi but im pretty sure this is wrong because density of water isnt included, how would i fit that in the integral?
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  2. #2
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    Quote Originally Posted by jinsda View Post
    a cylinder tank lies on the ground, all filled with water. the radius of the circled top is 2m the total length is 10m, what is the work required to pump all the water out?

    - i got integral of 4(pi) from [0,10] which equals 40pi but im pretty sure this is wrong because density of water isnt included, how would i fit that in the integral?


    I think you mean that your cylindrical tank is lying on its side on the ground. If this is the case then the work done to let the water run out on the ground will be negative and will be numerically equal to the gravitational potential energy of the water in the tank.

    First imagine that the tank is half burried. In this state it has (on average) nil gravitational potential and a mass of \pi*r^2*L*Density=pi*1^2*10*1000=10000pi kg

    Now imagine lifting the tank until it sits fully on the ground. This is a 1 m lift.

    GPE added=mgh=10000pi*9.81*1

    In SI units the density of water is 1 kg per litre or 1000 kg per m^3.
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