De-saint venant equation

From Glossary of Meteorology

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, Sf is the friction slope, and S0 is the bottom slope of the channel (positive with decline downstream).