Chezy's resistance coefficient in vaulted rectangular conduit

Calculating resistance coefficients for flows in pipes and channels, such as the Darcy–Weisbach coefficient of friction and the Chezy or Manning coefficients, is a complex process aimed at accurately reflecting flow under load or a free surface. Generally, these coefficients are given as constants, although they can be challenging to ascertain due to implicit models expressing these coefficients. Therefore, the design of pipes and channels necessitates an explicit and comprehensible expression of the resistance coefficient, incorporating numerous flow parameters, including aspect ratio, kinematic viscosity, pipe slope, and roughness of internal walls. To achieve this outcome, we suggest employing the rough model method giving the volume flowrate to identify the Chezy's resistance coefficient C in uniform and free surface flow for the vaulted rectangular conduit. This applies in both cases where the diameter of the geometric profile of the conduit is known or unknown.