# 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 with water.

The cross sectional area of the filled conduit can be calculated as

*A = 0.5 * (1 m) * (1 m) *

* = 0.5 m ^{2}*

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 m ^{2}) / (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 m ^{2}) (2.5 m/s)*

* = 1.25 m ^{3}/s*

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