Calculating volume flow and velcity in open conduits.
The Chezys equation can be used to mean flow velocity in conduits:
v = C (Rh S)1/2 (1)
v = mean velocity (m/s, ft/s)
C = Chezys roughness and conduit coefficient (m1/2/s)
Rh = hydraulic radius of the conduit (m, ft)
S = slope of the conduit (m/m, ft/ft)
In general the Chezy coefficient - C - is a function of the flow Reynolds Number - Re - and the relative roughness - ε/R - of the channel. ε is the characteristic height of the roughness elements on the channel boundary.
The Manning empirical relationship is one way to estimate the roughness coefficient C:
C = (1 / n) Rh1/6
For concrete walls in conduits it's common to use C = 50 (m1/2/s).
Example - Flow in a Concrete Conduit
A rectangular 1 (m) x 1 (m) concrete conduit with slope 1/100 (m/m) is half filled with water.
The cross sectional area of the filled conduit can be calculated as
A = 0.5 * (1 m) * (1 m)
= 0.5 m2
The wetted perimeter of the filled conduit can be calculated as
P = 2 * 0.5 * (1 m) + (1 m)
= 2 m
The hydraulic radius can be calculated as
Rh = A / P
= (0.5 m2) / (2 m)
= 0.25 m
The velocity in the flow can be calculated using eq. (1) as
v = (50 m1/2/s) ((0.25 m) (1/100 m/m))1/2
= 2.5 m/s
The volume flow can be calculated as
q = A v
= (0.5 m2) (2.5 m/s)
= 1.25 m3/s