Stage-Discharge Relationship in Open Channels

Rating curves relating stream discharge to water-surface stage are traditionally established empirically through many measurements of discharge and concurrent stage. However, discharge measurements typically scatter and do not show a unique relation to the stage because the underlying physics are usually not reflected in the rating. Examining the relationship of stage versus discharge in open channels based on the fundamental hydrodynamics of unsteady nonuniform flow identifies terms in the Saint-Venant equations that should considered in rating development. The Hydraulic Performance Graph, which provides a steady-state approximation to the hydrodynamics governing open-channel flow, provides a tool to develop theoretical ratings. Analysis of a hypothetical channel indicates that terms describing the pressure gradient, conveyance, and convective acceleration should be included to develop a rating that applies to the possible range of flow conditions.