Limit Slope in Uniform Flow Computations

Abstract

A method to prepare design charts for uniform flow in open channels is presented by introducing the concept of limit slope which is the smallest critical slope for a given channel shape and roughness. Equations are obtained for limit slope in rectangular, parabolic, and circular channels. The condition for limit slope in trapezoidal channels is given and it is shown that no limit slope exists for z ≥ 0.5. The design chart correlating the Froude number, discharge, depth of flow and bed slope is presented for rectangular, parabolic, and trapezoidal channels. It is shown that for a given bed slope, width and roughness, the maximum Froude number in rectangular channels always occurs at a depth equal to 1/6 the width and a simple expression is given for its value.