Manning's Equation | Santa Fe College - Edubirdie

University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

237

Pages:

5
Author:

Jabin F.

Manning's Equation Q = A/n R^(2/3) S_o^(1/2) Q = A * 1/n (A/P)^(2/3) S_o^(1/2) Q = A^(5/3) / P^(2/3) * 1/n * S_o^(1/2) By Manning, Q is proportional to (A^5 / P^2)^(1/3) Q_max when A^5 / P^2 is Max. => d/dθ (A^5 / P^2) = 0 3θ - 50 cosθ - 2 sinθ = 0 By solve. θ ≈ 302° 20' y = r - r cos(θ/2) y = 0.938 D R ≈ 0.29 D Same for Both case. (ii) Condition of Max. mean Velocity For Both Mannings and chezy formula, V max. when A/P is max. 0 = d(A/P) / dθ = [P(r^2/2 (1-cosθ)) - A(r)] / P^2 rθ(r^2/2 (1-cosθ)) = (r^2/2 (θ-sinθ)) r θ(1-cosθ) = θ-sinθ θ - θcosθ = θ - sinθ sinθ - θcosθ = 0

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