Study on the concentration distribution in a trapezoidal open-channel flow with a side discharge

The number and distribution of pollutant concentration in a trapezoidal open channel flow with a side discharge is calculated and effects of the bank gradient are investigated in this paper. A sigma-coordinate water quality numerical model is used to simulate the process of both water and pollutant transportation in the trapezoidal channel open flow. The diffusion coefficient used in the prediction is determined by two methods including constant coefficient and the depth-averaged k-epsilon turbulence closure model. The change of the concentration with the bank gradient is acquired based on the simulation of cases with different bank gradients. An analytical formula is derived by using the mirror image method and related diffusion theories, ignoring the discharge momentum and the influence of the opposite bank. The formula can predict the number and distribution of pollutant concentration with some acceptable errors. The results demonstrate that the bank gradient has great influence on the concentration distribution which will decrease with the increase of the bank gradient approximately following a hyperbolic law.