# Chezy Equation

Mean flow velocity within pipes with turbulent flow

**Contents**

### 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

*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