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# Chezy Equation

Mean flow velocity within pipes with turbulent flow
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### Key Facts

Gyroscopic Couple: The rate of change of angular momentum () = (In the limit).
• = Moment of Inertia.
• = Angular velocity
• = Angular velocity of precession.

## Overview

The Chezy equation applied to pipes with turbulent flow is

where
• i is or head loss due to fiction over the pipe length,
• m is or wetted area divided by the wetted perimeter,
• and C is where f is the coefficient of friction.

## Theory

For the flow of a fluid within a pipe with velocity (v), there will be a reduction in mean pressure with distance, which is usually referred to as "head loss".

Frictional resistance is proportional and the wetted area around the circumference of the pipe. Therefore,
where
• P is the perimeter of the pipe ,
• L is the length of the pipe section
• and f is the coefficient of friction

Rearranging

where:

where m is the hydraulic mean depth

where h is the slope of the hydraulic gradient.

Note: C is not a constant since f is a function of Reynolds number