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Math Help - Manning Formula Solution for Angle to edges of Water

  1. #1
    Newbie SgtDan's Avatar
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    Manning Formula Solution for Angle to edges of Water

    1-2R/r=(Sin G)/G
    Where G is the angle to the edges of the water and is less then Pi radians, from the centre of the pipe. R is a known from the Manning Formula as we solve for it from V and a known Slope. r is the radius of the pipe in Feet and is chosen based on the community size. How do we solve for the Angle G?
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  2. #2
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    Since that involves G both as the argument of a transcendental function (sine) and outside of it, there will not be any simple algebraic solution. You will have to use a numerical solution.
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  3. #3
    Newbie SgtDan's Avatar
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    Explanation

    I am looking for a numerical value. We have other formulae that supply the person with a value for R and r. We currently have them guessing at values for G until the get one where the (Sin G)/G is approx equal to the Left Side (LS) of the equation.
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  4. #4
    Newbie SgtDan's Avatar
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    added Information

    would it help if I told you that

    G=2ArcCose((r-d)/r)

    Where r is the same as previous formula and d is the depth of water in the pipe. Could you then rearrange formulae to solve for d?
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