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Homework Help: Height of fluid and Bernoullis equation

  1. May 27, 2013 #1
    1. The problem statement, all variables and given/known data

    An ideal liquid flows horizontally through a pipe of cross sectional area 3cm2 with a velocity 1ms-1. The pipe narrows to a cross sectional area 1cm2. 2 vertical pipes are connected to the pipe, one in either region.
    Calculate the height difference of the liquid between the 2 vertical pipes.

    2. Relevant equations

    p1 + 0.5ρv12 + ρgh1 = p2 + 0.5ρv22 + ρgh2

    A1v1 = A2v2

    3. The attempt at a solution

    I think i'm a bit confused on what my variables represent in bernoullis equation:
    Using the continuity equation gives v2 = 3ms-1.
    Then I said that for the pipes p1 = p2 (because they're both open to the atmosphere), putting everything into bernoullis equation and rearranging gives
    h1 - h2 = 0.4 m
    The book says the answer is 4x10-3 m.

    Am I not allowed to consider the heights of the fluid in the vertical pipe because I calculated the speeds of the fluid in the horizontal pipe? I can't think of any other way to do the problem.
  2. jcsd
  3. May 27, 2013 #2
    Oh sorry nevermind, I got it.
    Turns out the velocity is initially 0.1 ms-1, then doing what I said gives the answer.

  4. May 27, 2013 #3


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    Staff Emeritus
    Science Advisor
    Homework Helper

    IMO, the book's answer is wrong.

    I see that the OP had missed a decimal in the initial velocity. Book answer is OK.
    Last edited: May 27, 2013
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