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Bernoulli's Equation (Water Outflow Speed of Tank)

  1. Jan 18, 2013 #1
    Problem:

    Suppose the top of a tank is sealed and pressurized to twice atmospheric pressure. What is the speed of the liquid emerging from a small hole at the base of the tank?


    My Solution:

    Using Bernoulli's Equation, and assuming v_top ≈ 0,

    P_top + 1/2*ρ*v_top^2 + ρgh = P_hole + 1/2*ρ*v_hole^2 + ρg*0

    2*P_a + ρgh = P_a + 1/2*ρ*v_hole^2

    Solving for v_hole I get,

    [itex]\sqrt{\frac{2(P_{a}+ρgh)}{ρ}}[/itex]

    While my book has,

    [itex]\sqrt{\frac{2P_{a}}{ρ+gh}}[/itex]

    Anyone know where I went wrong? Or, less likely, if my text is incorrect? Thank you in advance.
     
  2. jcsd
  3. Jan 19, 2013 #2
    The text is incorrect. The sum in the denominator is impossible, the units of the addends do not match.
     
  4. Jan 19, 2013 #3
    Oh wow, I'm foolish for not thinking of that myself. My units come out to be the correct units of velocity.
     
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