River channel problem using Bernoulli and Continuity

  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. Pyrrhus

    Pyrrhus 2,204
    Homework Helper

    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. 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. Pyrrhus

    Pyrrhus 2,204
    Homework Helper

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