Computation of steady-state, gradually varied flows in parallel channels

Abstract

To compute the water-surface profiles in steady-state, gradually varied flows in open channels, an algorithm is presented that allows calculation of the flow depths and discharges at all sections of a parallel-channels system simultaneously instead of by the presently used trial-and-error computations. This algorithm is accurate, efficient, and suitable for computer solution. As compared to other methods, it may be used directly for computing flows in parallel channels without necessitating graphical plots or other trial-and-error manual computations. A procedure is outlined so that the resulting matrix for a parallel-channels system may be banded in order to increase accuracy and to reduce computer time and storage. A parallel-channels system is solved for illustration purposes and the results are compared with those obtained by the fourth-order Runge–Kutta method. Key words: backwater profiles, computer algorithms, gradually varied flows, mathematical models, Newton–Raphson method, open-channel flows, parallel channels, water surface profiles.