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River channel problem using Bernoulli and Continuity

  1. Jan 27, 2008 #1
    [SOLVED] River channel problem using Bernoulli and Continuity

    1. The problem statement, all variables and given/known data

    A river (100 m wide) flows through its rectangular channel at a depth of 2.560 m at a velocity of 2.050 m/s. What is the velocity of the discharge if the channel is narrowed to 90 m?

    2. Relevant equations

    Continuity equation: Q1 = 100m x 2.560 m x 2.050 m/s
    Q2 = 90 m x H2 x V2

    Bernoulli equation: V^2/2g + P/pg + z = constant

    3. The attempt at a solution

    I can't seem to set up the equations properly in order to find intercept. I'm sure that P1 (ie. pressure1) is zero, but P2 isn't. I actually tried solving the question with P2=0 but it's wrong.

    A little help?

    (you may have seen this in "Introductory Physics" but I don't know how to move/delete the previous thread, sorry)
     
    Last edited: Jan 27, 2008
  2. jcsd
  3. Jan 28, 2008 #2

    Pyrrhus

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    Hey there, in open channel flow usually the version of Bernoulli equation used is:

    [tex] y + \frac{v^2}{2g} + z = constant [/tex]

    In your case the z value probably can be ignored assuming the river doesn't have any vertical variations in its geometry. You could use this equation which is also known as the specific energy.

    [tex] y + \frac{v^2}{2g} = constant [/tex]
     
  4. Jan 28, 2008 #3
    The height of the water (z) is assumed to change due to the narrowing of the river channel. I think I know how to answer the question now...
     
  5. Jan 28, 2008 #4

    Pyrrhus

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    Great!, good luck, if you have more questions feel free to ask them.
     
  6. Jan 28, 2008 #5
    thanks for your help!
     
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