Flow to a collector pipe laid under a stream bed

Abstract

With the increase in population growth, there is tremendous pressure on the decision-makers to look for sustainable sources of safe and adequate water supply for different purposes. Therefore, during recent times, engineers are looking toward cost-effective process of water treatment. Collector wells constructed on the banks of a river are cost-effective means of supplying adequate and safe water supply to people living on the banks of a river. Collector pipes act as a carrier of water to the collector well. Collector pipes placed under a riverbed are the most effective in terms of quantity of water. Previously researchers have derived an analytical solution for potential and flow to the collector pipe under steady-state flow condition. In this study, an analytical method using conformal mapping has been suggested to estimate the potential at different locations in the flow domain. Further, expressions have been derived for estimating the quantity of flow to the collector pipe, entrance velocity, and the travel time of a parcel of water from the stream bed to the collector pipe along the shortest path. Using the travel time, the log cycle reduction in bacteria concentration has been found using logistic function.