How are the Saint-Venant equations used for unsteady flow modeling?

Saint-Venant equations (shallow water equations) describe unsteady open channel flow: Continuity: dA/dt + dQ/dx = ql (lateral inflow), Momentum: dQ/dt + d(Q^2/A)/dx + gA*dh/dx + gA*Sf = 0. Terms: local acceleration, convective acceleration, pressure gradient, friction slope. Solution methods: finite difference (implicit schemes stable for larger timesteps), finite volume, or characteristics. Applications: flood wave propagation, dam break, tidal hydraulics, storm surge. Models: HEC-RAS unsteady, MIKE 11, ISIS. 2D equations add lateral dimension for floodplain modeling.