Computation of Conjugate Depths in Cubic-Shape Open Channels

Abstract

Determining conjugate depths for a given discharge and initial depth requires the solution of a cubic equation for the conjugate depth and there are currently two approaches to avoiding this difficulty in general. One approach is to iteratively try different depths until one is obtained which gives the same value of the Momentum Function as that at the given depth. The other is to construct a Momentum Function versus depth of flow curve for the given discharge, from which the conjugate depth can be read off directly. Either of these procedures is tedious. For rectangular channels, an explicit equation for obtaining the conjugate depth has been derived and is available in any standard hydraulics text. This paper is to develop a procedure for computing the conjugate depth in cubic-shaped open channels, given an initial depth. This procedure involves the use of a table or a chart and avoids any iteration or construction of Momentum Function versus depth of flow curve.