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##### 1.Manning Equation

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**1.Manning Equation**V = R 2/3 S1/2 n Where v = average flow velocity r = hydraulic radius s = channel slope (unitless) n = Manning roughness coefficient R = A/P A = Area P = Wetted Perimeter**1.Manning Equation**For the South River: S = 0.0009 n = 0.04 Q = 1.49*A*R 2/3 S1/2 n Where Q = average flow velocity (ft3/s) R = hydraulic radius (ft) S = channel slope (unitless) n = Manning roughness coefficient R = A/P A = Area (ft2) P = Wetted Perimeter (ft)**A. Sediment Transport 1. Shear Stress**τc = hc ρw g S Shields Equation τc = τ*c (ρs – ρ)gD50 τc = critical boundary shear stress ρs, ρw = grain density (assume 2.65 g/cm3) and water density g = gravitational acceleration (981 cm/s2) D50 = median bed material grain size τ*c = dimensionless critical shear stress (the Shields number) (0.03 for sand; 0.047 for gravel/cobble)**A. Sediment Transport 2. Critical Flow Depth**τc = hc (ρwgS) hc = critical flow depth to mobilize sediment τc = critical boundary shear stress ρw = water density g = gravitational acceleration (981 cm/s2) S = Average bed slope