Explicit equations for uniform flow depth

Conventional approach in uniform open channel flow is to express the resistance coefficient in the Manning, Darcy-Weisbach or Chezy form. However, for practical cross-sections, including rectangular and trapezoidal ones, the governing equation is implicit in the uniform water depth. For these sections the water depth, corresponding to known values of the flow discharge, slope channel and resistance coefficient, is presently obtained by trial and error procedure. In this paper exact analytical solutions of uniform flow depth for rectangular and trapezoidal section have been obtained in the form of fast converging power series.