Critical shear stress approach for self-cleansing design of a rectangular channel

Abstract

The current study aims at the development of an incipient motion equation and a self-cleansing design chart based on the critical shear stress approach for a rectangular channel. Data from previous experimental work on incipient motion for rectangular flumes were subjected to multiple linear regression analysis. Selected regression models were further assessed through cross validation using the remaining data from the previous experimental work and a performance test using another three sets of existing data from the literature. The best regression model from the current study was found to perform much better than two of the existing equations in the literature by Novak and Nalluri and El-Zaemey with respect to having 95% of the predicted value fall within the acceptable discrepancy ratio range of 0.5–2.0. The equations by Novak and Nalluri and El-Zaemey only managed to have 10 and 16%, respectively, of the predicted values fall within the acceptable discrepancy ratio. The developed best regression model has a coefficient of determination $\left(R_p^2\right)$ value of 0.9960, adjusted coefficient of determination $\left(R_{adj}^2\right)$ value of 0.9960, predicted coefficient of determination $\left(R_{pre}^2\right)$ value of 0.9958, mean square error (MSE) value of 0.0004, and Mallow's $C_p$ value of 3.0. The best regression model was further chosen to develop a self-cleansing design chart for rectangular channels. The design chart which relates the minimum sewer slope $S_{min}$ with the minimum critical shear stress, ${\tau }_c$, for the respective standard rectangular channel size of an open channel system could be used to check and determine the suitable minimum slope for self-cleansing design purposes.