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Controlling the flow from a draining tank

  1. Nov 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Torricelli’s law says that if you drain a tank like the one in the figure shown, the rate y
    at which water runs out is a constant times the square root of the
    water’s depth x. The constant depends on the size and shape of the
    exit valve.


    Suppose that for a certain tank. You are trying to
    maintain a fairly constant exit rate by adding water to the tank
    with a hose from time to time. How deep must you keep the water
    if you want to maintain the exit rate

    a. within 5.7 L/min of the rate y0=28.3L/min
    b. within 2.8 L/min of the rate y0=28.3L/min

    2. Relevant equations

    3. The attempt at a solution

    I could not understand neither the question nor the method i should use. Should it be done via epsilon-delta method? Or simply by differentiating ?
    Last edited: Nov 17, 2011
  2. jcsd
  3. Nov 17, 2011 #2


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    Homework Helper

    Figure not attached.
  4. Nov 17, 2011 #3


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    Homework Helper

    I'm guessing you have an initial rate, q0, at the initial height, y0:

    Now see if you can write the rate in terms of the height, based on the information it is proportional to the square root of the height
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