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yrivers36

Please explain how to set up and find answer. Thank you To protect cities from flooding during heavy rains, open channels are sometimes constructed to handle runoff. The rate R at which water flows through the channel is modeled by R=k sqrt m, where m= slope of the channel and k is a constant determined by the shape of the channel. a) suppose that a channel has a slope of m = 0.01 and a runoff rate of R=340 cubic feet per second. Find K. b) If the slope of the channel increases to m=0.04 what happens to R?

  • 2 years ago
  • 2 years ago

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  1. raspberryjam
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    Ok so to sum it up you have the equation: \[R=k\sqrt{m}\] where R = rate at which water flows through the channel m = slope of the channel k = a constant a). In this part you are given m and R, so just plug them into the equation and solve for k. b). You can use the same k you found in part a to answer part b, but this time use .04 for m and solve for R. Compare this answer to the one in part a, what happened? Did R increase or decrease?

    • 2 years ago
  2. yrivers36
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    I think that I just figured out a. 340=[\sqrt{0.01}\]

    • 2 years ago
  3. yrivers36
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    divide the sqrt on both side and I got 3400

    • 2 years ago
  4. raspberryjam
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    Yep so that gives you k.

    • 2 years ago
  5. yrivers36
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    for b I got R= 680 cubic feet per second

    • 2 years ago
  6. raspberryjam
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    Okay so what does this tell you about the relationship between R and m?

    • 2 years ago
  7. yrivers36
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    the slope rised double

    • 2 years ago
  8. raspberryjam
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    Yep so as m increases so does R right? This makes them proportional.

    • 2 years ago
  9. yrivers36
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    yes

    • 2 years ago
  10. yrivers36
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    Thank u

    • 2 years ago
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