Positive surge in trapezoidal and circular channels

Abstract

A series of algorithms is proposed for calculating the flow depth ratio and surge wave velocity for positive surge waves in open channels of rectangular and trapezoidal sections and for circular sections running part full. These algorithms make use of the standard formulations for the solution of problems of this kind and propose some iterative protocols (Newton–Raphson, numerical interpolation) for finding the desired result. The algorithms may be incorporated into a spreadsheet or a similar software package for use by hydraulic design engineers. Some results for a few selected cases are presented and show a dependence of depth ratio and surge wave velocity on flow ratio and on Froude number prior to the arrival of the surge wave. There is also a dependence on flow and channel scale in all cases, except that for rectangular flows; the depth ratio is independent of scale for the conditions investigated. There is also evidence of a minimum surge wave velocity for surge waves moving downstream at a specific Froude number for rectangular and circular sections, although not for trapezoidal sections. The algorithms generally give good agreement with the literature, although it is noted that in real situations an undular wave front is generally observed, and that most of the experiments cited have hitherto only been carried out in rectangular channels. Given the effect of friction on moderating the passage of the surge wave, the idealised assumption of a frictionless channel is clearly of importance.