# The Chezy Equation

In 1775, french hydraulic engineer Antoine de Chezy developed a formula for determining the flow velocity of water in an open channel:

$V = c\sqrt{RS}$

where:

c = coefficent of roughness (m3/s or ft3/s)
R = hydraulic radius (m or ft) = Flow Area / Wetter Perimeter
S = channel slope (m/m or ft/ft)

In 1890, Manning published the value of c in the Chezy formula as:

$c = \frac{R^{\frac{1}{6}}}{n}$

where:

n = manning’s coefficient of roughness

The Chezy equation is thus a precursor to the manning equation which is in widespread use today in the practice of hydrology, as it applies to culvert design.  The full Manning equation is:

$V = \frac{R^{\frac{2}{3}}S^{\frac{1}{2}}} {n}$