Evaluation of surge propagation and discharge calculation in a sloping circular pipe

Abstract

The generation and propagation of a positive surge in a sloping circular pipe were studied. Using a lab-scale model, positive surges were generated by rapidly closing a downstream gate, and the resulting flow patterns and surge propagation speeds were observed. The continuity and momentum equations were applied to derive an analytical solution for back-calculating discharge from measured surge speeds and hydraulic conditions. Experimental results showed the surge speed decreased with propagation distance, stabilizing beyond certain distances. The sequent depth ratio for positive surges was investigated, and the results showed that the sequent depth ratio for circular pipes was lower compared to that in a rectangular channel with the same Froude number. An equation was developed to evaluate the sequent depth ratio for positive surges in partially filled flow within a circular pipe. In practical applications, it is necessary to measure the initial water depth, the surge propagation distance, the average speed of the surge corresponding to this distance, and the water depth behind the surge wave front to estimate the discharge in the pipe. The results indicated that a longer observation distance from the disturbance location leads to a smaller error between the calculated and measured discharges, which is generally less than 10 % at measurement locations farther than 3 times the diameter length from the tailgate. Therefore, the proposed discharge calculation equation can be applied in sewer systems as an initial discharge estimation method for quick reference.