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Water flow duration

  1. Oct 27, 2011 #1

    Pzi

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    Hello.

    1. The problem statement, all variables and given/known data
    There is a vertical cylinder-shaped reservoir full of water:
    Height h = 18 meters
    Radius R = 2 meters
    If suddenly a hole appeared on the bottom (radius r = 0.25 meters) how long would it take to empty the reservoir?


    2. Relevant equations
    Probably related to Bernoulli's principle somehow someway.


    3. The attempt at a solution
    To be honest with you I just reposted this problem from elsewhere. Some girl tried to solve it and since I am a pure mathematician I pretty much do not have a clue about those things. Tried to google it, but without proper knowledge did not succeed.
    Some kind of powerful formula and basic steps would be appreciated.

    Thanks.
     
  2. jcsd
  3. Oct 27, 2011 #2

    gneill

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    Staff: Mentor

    Bernoulli is the key. His principle gives you the speed of the water exiting the orifice, hence the flow rate and rate of change of velocity in the tank. [EDIT: I meant change of VOLUME, not change of velocity!].

    Essentially, for a depth of water h above the opening, the velocity of the water will be given by [itex]\sqrt{2 g h}[/itex] .

    With the flow rate and opening size you can construct the differential equation for the volume of water in the tank.
     
    Last edited: Oct 28, 2011
  4. Oct 28, 2011 #3

    Pzi

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    So it seems that I am supposed to solve this
    [PLAIN]http://img708.imageshack.us/img708/6712/eqn9284.png [Broken]

    Can you confirm?
     
    Last edited by a moderator: May 5, 2017
  5. Oct 28, 2011 #4

    gneill

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    Staff: Mentor

    Yes, that is one differential equation that fits the bill!
     
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