Calculation of the flow velocity of a siphon

Abstract

Siphons have been known and used since ancient times and are still widely used. We re-examine the siphon process and recognize that the existing classic formula of the flow velocity of a siphon is only applicable to continuous flow; however, the flow of a siphon may be discontinuous flow. This study proposes new formulas, which can cover continuous and discontinuous flow and can consider the influence of the release of air from liquid on the flow velocity. Sixteen experiments were performed to validate our proposed method. The main results show that (a) for some schemes, the calculated values from the existing formula have large errors and the maximum error rate reaches 96%, (b) our method not only calculates the flow velocity of a siphon well but also makes a good prediction of the bubbles observed in the experiments, and (c) Qup/Qw > 1 is an effective way to reduce bubble generation in a siphon pipe, where Qup and Qw are the volumetric flow rates of the liquid phase by analyzing the upward pipe and whole pipe using Bernoulli's equation, respectively. Based on the above understanding, some new siphon systems could be designed to reduce bubble generation in a siphon; for example, a new siphon drainage system with variable diameters can be designed to reduce bubble generation and, hence, to weaken or even avoid cavitation in the process of a siphon.