Chezys Conduit Flow Equation

The Chezys equation can be used to mean flow velocity in conduits:

v = C (R_h S)^1/2                           (1)

where

v = mean velocity (m/s, ft/s)

C = Chezys roughness and conduit coefficient (m^1/2/s)

R_h = 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) R_h^1/6

where

n = Manning coefficient of roughness

For concrete walls in conduits it's common to use C = 50 (m^1/2/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 (0.5) 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

R_h = A / P

    = (0.5 m²) / (2 m)

    = 0.25 m

The velocity in the flow can be calculated using eq. (1) as

v = (50 m^1/2/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