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Math Help - Question about using integrals to find work

  1. #1
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    Question about using integrals to find work

    My problem says that I need to figure out how much work has to be done to pump all of the water out over the side of a 5 foot tall circular pool, but the water is only 4 feet deep. I was wondering, would my integral be from 0 to 4 or 1 to 5?

    Here is what I've set up:

    Given: Weight of water = 62.4 lbs per cubic foot, diameter of pool = 24 ft

    W = 62.4(144pi/25) integral (5y^3 - y^4)dy

    Is that right? And would the integral be from 1 to 5 or 0 to 4?
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  2. #2
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    Quote Originally Posted by WahooMan View Post
    My problem says that I need to figure out how much work has to be done to pump all of the water out over the side of a 5 foot tall circular pool, but the water is only 4 feet deep. I was wondering, would my integral be from 0 to 4 or 1 to 5?

    Here is what I've set up:

    Given: Weight of water = 62.4 lbs per cubic foot, diameter of pool = 24 ft

    W = 62.4(144pi/25) integral (5y^3 - y^4)dy

    Is that right? And would the integral be from 1 to 5 or 0 to 4?
    Take h=0 as the bottom of the pool with h measured positive upward, to the rim of the pool is at h=5, and the top of the water is initially at h=4. Let r be the radius of the pool. Let \rho be the density of water and g the acceleration due to gravity.

    Consider a layer of thickness \delta h, at a height h<4 above the bottom of the pool. The work needed to pump this out is the change in potential energy when the layer is lifted form h to 5 which is:

    \delta W=(\pi r^2 \delta h)\times \rho \times g\times(5-h)

    So the total work is the sum of the work for all the layers of thickness \delta h and proceeding to the limit we get:

     <br />
W=\int_{h=0}^4 (\pi r^2 )\times \rho \times g\times(5-h)\ dh<br />

    CB
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    Thank you.
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    Slightly disappointed this thread isn't about using integrals to find employment.
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  5. #5
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    Quote Originally Posted by undefined View Post
    Slightly disappointed this thread isn't about using integrals to find employment.
    Yep, employers just never give calculus skills sufficient credit!
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