The Initial Phase of the Rising Hydrograph of Turbulent Free Surface Flow with Unsteady Lateral Inflow

An exact solution is obtained for the de Saint Venant equations describing flow over a plane or in a very wide channel with a general turbulent friction law and with a uniform lateral inflow as a power function of time valid for the space‐time domain bounded by 0 ≤ x ≤ L , t = 0, by the forward characteristic originating at x = 0, t = 0, and by the backward characteristic originating at x = L , t = 0. The quantity L denotes the length of the flow region, x the direction of flow, and t the time. We found that, for very small values of time, the uniform flow velocity is everywhere directly proportional to t regardless of the nature of the lateral inflow. For a very large slope or a large roughness of the plane, or for a very small constant lateral inflow, the present solution reduces to the result obtainable with the kinematic wave approximation. (Key words: Hydraulics; overland flows; runoff)