Analytical solution to concentration distribution discharged from a stream of effluent into trapezoidal channel flow
梯形渠道岸边排污浓度分布的理论分析

An analytical solution is presented to determined the distribution of concentration in a trapezoidal channel due to a stream of effluent discharging. Based on the concentration distribution around an instantaneous circle source, the approximate solution to concentration in a region with the trapezoidal boundary is derived with an instantaneous line source. The concentration in the trapezoidal open-channel flow is calculated analytically consequently. The analytical equation indicates that the slope angle has great influence on the concentration distribution and the concentrations will drop off with the slope angle following a hyperbolic law. The approximate solution is verified with the numerical solution to the diffusion equation of concentration, which represents physical mixing processes of the pollutant. The comparison illuminates that the solutions agree with each other very well except the concentrations in the region nearby the source and it can be a reliable tool for the evaluation of the scope of the mixing zone in natural rivers.