Friction models in open-channel flow

Friction models in open-channel flow

1. Manning formula

1
V = ^____ R^2/3 S^1/2
n

(1)

2. Chezy formula

V = C R^1/2 S^1/2

(2)

3. Dimensionless Chezy

V = (C/g^1/2) g^1/2 R^1/2 S^1/2

(3)

4. Quadratic velocity equation

V = (C/g^1/2) g^1/2 R^1/2 S^1/2

(4)

V ² = (C ²/g) g R S

(5)

ρ V ² = (C ²/g) ρ g R S

(6)

ρ V ² = (C ²/g) γ R S

(7)

ρ V ² = (1/f ) γ R S

(8)

ρ V ² = (1/f ) τ

(9)

τ = f ρ V ²

(10)

5. Prof. Ponce's friction formula

τ = f ρ V ²

(10)

γ D S = f ρ V ²

(11)

S = f V / (gD) ²

(12)

S = f F²

(13)

6. Darcy-Weisbach formula

h_f = f_D (L / D) [V ² / (2g)]

(14)

S = f_D [V ² / (2g D)]

(15)

S = f_D [V ² / (8 g R]

(16)

S = (f_D / 8) (V ² / g R)

(17)

g R S = (f_D / 8) V ²

(18)

τ = (f_D / 8) ρ V ²

(19)

τ = f ρ V ²

(20)

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