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Draining Conical Tank

  1. Jan 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Water drains out of an inverted conical tank at a rate proportional to the depth (y) of water in the tank. Write a diff EQ as a function of time.

    This tank's water level has dropped from 16 feet deep to 9 feet deep in one hour. How long will it take before the tank is empty.


    2. Relevant equations

    V=1/3pir2y

    dV/dt=pi(r0/y0)2y2dy/dt

    3. The attempt at a solution
    The solution to the first question is: dy/dt=-k(y0/r0)2(1/piy)

    I don't really know how to go about finding the time it will take to empty the tank.

    Please help!
     
    Last edited: Jan 23, 2014
  2. jcsd
  3. Jan 23, 2014 #2

    BruceW

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    Homework Helper

    hey, welcome to physicsforums! your solution to the first question is correct. (I'm guessing you're using 'k' as a constant. this is good.) So now, you need to make use of this differential equation to get 'y' as a function of time. You have hopefully done this kind of integral before. It just needs a bit of rearranging to get a nice answer.
     
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