STORMWATER MANAGEMENT Manning’s Equation for gravity flow in pipes & open channels

Previously... Rational Formula: –watershed peak flow rate Continuity Equation: –flow rate for pipes and open channels

Next... Manning’s Equation l used to examine gravity flow of stormwater in pipes and open channels l used to calculate flow rates, capacity, and velocity l used to set slopes and dimensions of pipes and open channels

Basic Form Manning’s Equation –begins with the Continuity Equation: Q = A v

Solving for v... Velocity of water in a pipe or open channel is found using: v = R (2/3) S (1/2) n where: v = velocity (m/s) R = hydraulic radius (m) S = slope (m/m, decimals of %) n = Manning’s roughness coefficient

Manning’s roughness coefficient (n)... The roughness coefficient depends on the material... l n = for concrete l n = for steel corrugated pipe l n = for plastic l n = for natural watercourses

Hydraulic Radius (R)... Hydraulic radius is a ratio between the cross-sectional area and the “wetted perimeter” of the pipe or channel: where: R = hydraulic radius (m) A = cross-sectional area (m 2 ) P = wetted perimeter (m)

Hydraulic Radius (R)... For a shallow channel, there is more drag from contact with the wetted perimeter For a deeper channel, there is less drag for the same cross-sectional area with a smaller wetted perimeter Tarbuck & Lutgens, 2002

Wetted Perimeter (P)... The perimeter of the facility that gets “wet”... is touched by water: hh b P = 2h + b D P=  D s b s P= 2s + b

Manning’s Equation If we multiply the velocity equation by cross-sectional are of flow: Q = A R (2/3) S (1/2) n a la Continuity Equation