Determination of drain pipe diameter using spatially varied flow theorem

Abstract

Flow in a field drain pipe can be simulated as a spatially varied flow with increasing discharge. The drain pipe diameter can be determined by calculating the ‘maximum water depth' along the drain pipe. Based on the current research, when critical section occurs at the downstream end (as usually occurs in agricultural drainage systems), the maximum water depth falls between the upstream end and the downstream end of the drain pipe. To calculate the water surface profile and thus the maximum water depth, a direct solution is presented for critical depth in circular sections. This equation provides a quick and simple way to calculate the control depth as well as the critical slope in drain pipes. Moreover, by means of a finite-difference method, a suitable equation is presented to calculate the water surface profile using Excel Solver. Because the Manning roughness coefficient under the partially full flow condition is greater than that under the full flow condition in circular channels, a variable Manning coefficient is used to calculate the water surface profile in the drain pipes. According to the numerical analysis, the choice of variable Manning coefficient results in reliable selection of drain pipe diameter that matches actual conditions.