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Bernoulli's equation book problem

  1. Mar 20, 2012 #1
    1. The problem statement, all variables and given/known data

    This book is skipping over too many steps

    Screenshot2012-03-20at23208PM.png

    where A1 = 1m2
    A2 = .5 m2

    y1 - y2 = 5m

    3. The attempt at a solution

    I'm having trouble getting from one step to another.

    By my reckoning this equation

    Screenshot2012-03-20at23208PM-1.png

    can be simplified by removing P0 and ρ since they are the same on both sides of the equation. Then we can multiply each term by 2.

    That makes

    v12 + 2gy1 = ((A1/A2)v2)2 + 2gy2

    Now I subtract 2gy1 from both sides. That makes:

    v12 = ((A1/A2)v2)2 + 2gy2 - 2gy1

    The book is showing that that is a mistake. I can't figure out why.

    Also if I subtract ((A1/A2)v2)2 from both sides that would make (ignoring 2gy)

    v12 - ((A1/A2)v2)2

    But the book has it as

    v12 multiplied by (1- ((A1/A2)v2)2

    Why?
     
    Last edited: Mar 20, 2012
  2. jcsd
  3. Mar 20, 2012 #2

    Doc Al

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    Staff: Mentor

    OK.

    Shouldn't that be v1 on the right hand side, not v2?
     
  4. Mar 20, 2012 #3
    Yea, I guess it should but I'm still stuck with my two questions.
     
  5. Mar 20, 2012 #4

    Doc Al

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    Staff: Mentor

    First change that v2 to a v1 and your questions may go away.
     
  6. Mar 20, 2012 #5
    Ok, I understand the part about v1 and v2, but would about

    2gy2 - 2gy1
     
  7. Mar 20, 2012 #6
    y2-y1 is the height difference between the two points under consideration.
     
  8. Mar 20, 2012 #7

    Doc Al

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    Staff: Mentor

    What about it? Realize that your book is calling Δy = h.
     
  9. Mar 20, 2012 #8
    In the final step it should be

    √h

    not

    √(2gh)

    Because the 2g - 2g = 0
     
  10. Mar 20, 2012 #9

    Doc Al

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    Staff: Mentor

    The '2g' factor doesn't cancel!

    Example: 5a - 3a = 2a, not 2.
     
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