Nonlinear Kinematic-Wave Model for Predicting Open-Channel Flow Rate

An approximate model for predicting open-channel flow rate is developed. The Saint-Venant equations are approximated by a nonlinear kinematic equation for flow depth. The flow velocity is formulated as a function of flow depth to satisfy the continuity of flow. The model has two constants expressed in terms of the Froude number of initial uniform flow to partially satisfy the dynamic equation for small perturbations of flow depth about an initial constant value. Under subcritical flow conditions the model gives results close to those of the Saint-Venant equations. For a given upstream flow depth the approximate magnitude of flow rate at a downstream section is readily obtained in analytical form. The model is simple, and may be useful for rapid calculations during channel routing.