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How do I prove That Toricelli's equation, given here is correct?

  1. Jul 24, 2011 #1
    1. The problem statement, all variables and given/known data

    The problem is shown here, Problem # 48
    Problem-1.jpg



    2. Relevant equations

    I know that V1 = Sqrt of 2*G (h)

    But the A1^2 / A2^2 part is unknown to me, and I've spent hours trying to find an explanation, but now I'm here...

    Can anyone point me in the right direction, please?
     
  2. jcsd
  3. Jul 24, 2011 #2

    gneill

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    Staff: Mentor

    Go back to Bernoulli's Principle. Find a relationship between V2 and V1 in terms of the areas. Substitute for V2 in Bernoulli.
     
  4. Jul 24, 2011 #3
    In Bernoulli's equation I found that

    V1 = V2 * A2 / A1
     
    Last edited: Jul 24, 2011
  5. Jul 24, 2011 #4

    gneill

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    Staff: Mentor

    Solve that for V2 in terms of V1 (since you're looking to replace V2 in Bernoulli's equation.

    Can you write the equation for Bernoulli's principle for this case?
     
  6. Jul 24, 2011 #5
    (Using D for Density)

    If I replace V2 With the equation I get

    1/2 DV1^2 + DGY1 = 1/2D (A1*V1/A2)^2 + DGY2

    By the way, I appreciate your help, I'm lost mostly because I missed this particular day of class, and I'm trying to understand a friend's notes and the book. My test tomorrow is going to kill me =[
     
    Last edited: Jul 24, 2011
  7. Jul 24, 2011 #6

    gneill

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    You're missing the potential energy term (D*g*h) on the left hand side. Remember, there's a height difference between the two locations. P1 and P2 are the ambient air pressure, which can be assumed equal at both locations, so they cancel. Solve for V1.
     
  8. Jul 24, 2011 #7
    1/2 DV1^2 + DGY1 = 1/2D (A1*V1/A2)^2 + DGY2

    1/2 V1^2 (1-A1^2/A2^2) = G (Y2 - Y1)

    V1 = Sqrt 2G(Y2-Y1) / (1-A1^2/A2^2)
     
  9. Jul 24, 2011 #8
    Yeah, I added it up top
     
  10. Jul 24, 2011 #9
    Is it... correct? or closer to being correct? :confused:
     
  11. Jul 24, 2011 #10

    gneill

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    Staff: Mentor

    Can't you compare it with what is given in the problem statement?
     
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