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Power_Forumula_Derivations

Power_Forumula_Derivations - 4 1 f 3 1 143 1 4 1 ⎟ ⎠...

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Hydraulic 4202 Derivation of Power Formulas The derivation of all 6 power formulas for predicting the mean velocity m V in a pipe or channel start with Chezy’s formula: 2 1 2 1 ' 4 1 2 4 S R f g V m = (1) For Range I Laminar flow combine equation (1) with the following definition of ' f : m RV f 1 4 ' ν = (2) to obtain: S R g V m 2 4 2 ν = (3) For Range II Smooth Turbulent Blasius flow combine equation (1) with the following definition of ' 4 1 f : 8 1 ' 060 . 1 ' 4 1 e R f = (4) to obtain: 7 4 7 5 7 1 7 4 72 . 7 S R g V m ν = (5) For Range II Smooth Turbulent Hazen & Williams flow combine equation (1) with the following definition of ' 4 1 f : 12 1 ' 627 . 1 ' 4 1 e R f = (6) to obtain: 11 6 11 7 11 1 11 6 25 . 11 S R g V m ν = (7)
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