STORMWATER STORMWATER MANAGEMENTMANAGEMENT

Manning’s Equationfor gravity flow in pipes

& open channels

Previously...Previously...

Rational Formula: – watershed peak

flow rate

Continuity Equation: – flow rate for pipes

and open channels

360CiA

Q

AvQ

Next... Manning’s EquationNext... Manning’s Equation

used to examine gravity flow of stormwater in pipes and open channels

used to calculate flow rates, capacity, and velocity

used to set slopes and dimensions of pipes and open channels

Basic FormBasic Form

Manning’s Equation – begins with the Continuity Equation:

Q = A v

Solving for 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 Manning’s roughness coefficient (n)...coefficient (n)...

The roughness coefficient depends on the material...

n = 0.013 for concrete n = 0.025 for steel corrugated pipe n = 0.010 for plastic n = 0.040 - 0.10 for natural

watercourses

Hydraulic Radius (R)...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

(m2)P = wetted perimeter

(m)

PA

R

Hydraulic Radius (R)...Hydraulic Radius (R)...For a shallow channel,

there is more drag from contact with the wetted perimeter

units 1.2667.910

PA

R units 30.81210

PA

R

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)...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 EquationManning’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