# De-saint venant equation

From AMS Glossary

## De-Saint Venant equation

The equation of motion (conservation of momentum) for one-dimensional, unsteady flow in open channels.

The system of equations representing the conservation of momentum and mass is given by where

*Q*is the discharge,*A*is the cross section area,*g*is the acceleration of gravity,*y*is the height of the water surface above the lowest point in the cross section,*x*is the distance along the channel,*t*is time,*q*is the lateral inflow per unit length of the channel,*S*_{f}is the friction slope, and*S*_{0}is the bottom slope of the channel (positive with decline downstream).