Errors of kinematic-wave and diffusion-wave approximations for time-independent flows in infiltrating channels

Time-independent (or steady-state) cases of channel flow were treated and errors of the kinematic-wave and diffusion-wave approximations derived for finite flow at the upstream end. The diffusion-wave approximation was found to be in excellent agreement with the dynamic wave representation, with error magnitudes of 0.2% for values of KF₀²7.5, where K is the kinematic-wave number and f₀ is the Froude number. Even for small values of KF₀²(e.g., KF₀²=0.75), the errors were typically in the range of 1.3 to 3.7%. The approximate analytical diffusion-wave solution performed poorly with error magnitudes greater than 30% even for large values of KF₀². The kinematic-wave approximation was also found to be in good agreement with the dynamic-wave representation with errors of about 1.2% for KF₀²=7.5 and varying from 15 to 44% for KF₀²=0.75.