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Homework Help: Fluid Dynamics

  1. May 20, 2015 #1
    1. The problem statement, all variables and given/known data

    A water storage tank is open to air on the top and has a height of 1 m. If the tank is completely full and a hole is made at the center of the wall of the tank, how fast will water exit the tank?

    2. Relevant equations

    Pressure is the same as atmospheric pressure because the tank is open to the air. Also, linear flow speed at the surface is essentially zero, so...
    Bernoulli's equation can be simplified to:

    rho * g * h1 = 1/2 * rho * v2^2 + rho * g * h2

    3. The attempt at a solution

    rho= density
    g= 10 m/ s^2
    height 1 (or height initial)= 1 m
    Here is where I don't understand the solution...
    height 2 is apparently = 0.5 m, but this is not in the question stem....

    rho * g * h1 = 1/2 * rho * v2^2 + rho * g * h2

    My attempt at solving for v2 ultimately comes out to be:
    v2= sq rt 2g (h1-h2)= sq rt 2* 10 m/s * (1 m - 0) = sq rt 20 meters

    But the correct way to solve was:
    v2= sq rt 2g (h1-h2)= sq rt 2* 10 m/s * (1 m - 0.5 m) = sq rt 10 meters

    So, I guess my question is why would the final height (height 2) be 0.5 m?
    Or, is there any other way to get the correct answer of sq rt 10 meters?
    Last edited: May 20, 2015
  2. jcsd
  3. May 20, 2015 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper

    Your post is hard to follow, since you don't define the variables used in your equations nor do you list their values. How do you expect anyone to help? :oops: :rolleyes: o_O

    In any event, have you heard of Torricelli's Law?

  4. May 20, 2015 #3
    They asked for the case where the hole is half way down the wall of the tank, not at the bottom of the tank.

  5. May 20, 2015 #4
    ahhh, the case where i make a problem much more difficult by not understanding the question... the word "center" should have tipped me off to the fact that the final height would be 0.5!

    Thank you for your help i appreciate it!
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