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Homework Help: Flow Rate of Merging Streams

  1. Dec 19, 2006 #1
    1. The problem statement, all variables and given/known data

    Figure 14-43 shows the merging of two streams to form a river. One stream has a width of 9.3 m, depth of 4.3 m, and current speed of 2.5 m/s. The other stream is 6.8 m wide and 4.0 m deep, and flows at 2.7 m/s. The width of the river is 10.2 m, and the current speed is 2.7 m/s. What is its depth?

    2. Relevant equations

    [tex]R_v=Av=constant[/tex]

    [tex]A_1v_1=A_2v_2[/tex]

    3. The attempt at a solution

    Sure, the rate flow should be constant for an ideal river of varying cross-sectional area, but I don't understand what to do when more fluid is added. Since two streams are merging, do I say that [tex](A_{stream 1})(v_{stream1})+(A_{stream2})(v_{stream2})=(A_{river})(v_{river})[/tex]?
     

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    Last edited: Dec 19, 2006
  2. jcsd
  3. Dec 19, 2006 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks good to me. That's conservation of mass (the continuity equation) in action.
     
  4. Dec 19, 2006 #3
    Thank you!
     
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