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D.E. problem

  1. May 25, 2008 #1

    ehrenfest

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    [SOLVED] D.E. problem

    1. The problem statement, all variables and given/known data
    See the attachment.


    2. Relevant equations



    3. The attempt at a solution
    dh/dt = 1/100 - 1/4h

    Why is the limit not h = 1/25 or 4 cubic feet?
     

    Attached Files:

    ehrenfest, May 25, 2008
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  3. May 25, 2008 #2

    HallsofIvy

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    Staff Emeritus
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    Please be careful about parentheses! I had first interpreted "1/4h" as "1/(4h)" and got a silly answer!

    However, your equation is wrong. Since water comes in at 1 cubic foot per second and the "water tower" has a uniform cross section area of 100 square feet, yes, that causes the water level to rise at 1/100 feet per second which are the correct units for dh/dt.

    But the water is also going out at (1/4)t cubic feet per second which is NOT the correct units. If water is going out at (1/4)t cubic feet per second, how fast is the water level dropping in feet per second?
     
    HallsofIvy, May 25, 2008
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