Mass Conservation: 1‐D Open Channel Flow Equations

Abstract

Unsteady flow simulation in natural rivers is often complicated by meandering channels of compound section. Hydraulic properties and the length of the wetted channel may vary significantly as a meandering river inundates its adjacent floodplain. The one-dimensional, unsteady, open-channel flow equations can be extended to simulate floods in channels of compound section if it is assumed that the lateral velocities are negligible, the water surface is level across the section, and the effects of turbulence and friction may be adequately described by resistance laws used for uniform flow. It is shown that the equations derived from the addition of differential equations individually describing flow in main and overbank channels do not conserve mass when overbank and main channels are of different lengths. Equations derived through the use of appropriate integral relations, however, do conserve mass and momentum in the general case and are not limited to the specification of one main and two overbank channels.