Chezy’s resistance coefficient in a horseshoe-shaped tunnel

Abstract

The calculation of Chezy’s resistance coefficient (CRC) is typically not provided a priori in a design problem, and its value is often selected subjectively from the literature in most open channels and conduits for the uniform flow. The evaluation of this coefficient is crucial to channel design and for computing its normal depth. The primary purpose of this research study is to revisit the mathematical formulation for the resistance coefficient. A general explicit relation of the resistance coefficient in turbulent flow is set with different geometric profiles of conduits and channels, mainly the horseshoe-shaped tunnel using the rough model method (RMM). CRC is firmly based on the internal walls' absolute roughness of the channel, the liquid kinematic viscosity, the longitudinal slope, the discharge and the filling rate. Additionally, a simplified method is proposed to determine CRC with a restricted number of variables such as the kinematic viscosity, the absolute roughness, the slope of the conduit, and the discharge. Based on studying the variation of CRC as a function of the filling rate, another explicit expression is provided to compute this coefficient efficiently when its maximum value is reached. To demonstrate how Chezy’s resistance coefficient can be calculated in a horseshoe-shaped tunnel, some examples of calculations are proposed.