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Leaky Tank Differential Eqn Problem

  1. Jun 8, 2015 #1
    1. The problem statement, all variables and given/known data
    http://ocw.mit.edu/courses/electric...s-fall-2011/assignments/MIT6_003F11_sol01.pdf

    http://i.imgur.com/8qj5cWE.png

    #6 Part B



    upload_2015-6-8_4-36-6.png

    2. Relevant equations
    None



    3. The attempt at a solution
    Don't understand why we care about when r1=r0

    The tank will overflow when the height of the tank is greater than 1. Why care about r1=r0? What is our motivation for think about the r1=r0 case? That's steady state sure. But they are asking about overflow which I thought just depends on water level

    upload_2015-6-8_4-36-6.png
     

    Attached Files:

  2. jcsd
  3. Jun 8, 2015 #2

    NascentOxygen

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    Staff: Mentor

    Once r1=r0 the water level in the top tank will cease to rise farther. If that tank has not overflowed by the stage r1 attains r0, then that tank is never going to overflow.

    Each tank has two outlets: the normal outlet at its base, and the overflow being its top rim.
     
  4. Jun 10, 2015 #3

    rude man

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    Homework Helper
    Gold Member

    Max. outflow rate of tank 1 without spilling is r1(h1max). This obviously must be >= r0.
    If r0 > r1(h1max) then tank 1 will spill since more water has to flow out of tank 1 than its hole can accommodate.

    NOTE: "r1(h1max)" means "r1 of h1max, not r1 times h1max.
     
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