Analytical solution, Gaussian hyper-geometric function, Gradually varied flow, Numerical solution, Water surface profile

The presence of the in-flow hydraulic structures create gradually varied flow (GVF) profiles which the computation of the hydraulic parameters based on the dynamic equation of flow with high accuracy has significant aspect among researchers. In this study, while doing dimensionless process of flow dynamic equation using yn and yc, Gaussian Hyper-Geometric Function (GHF) has been implemented to solve the equation analytically for five main channel slopes namely Mild (M), Steep (S), Critical (C), Horizontal (H) and Adverse (A). also, a comparison has been done using laboratory data between the accuracy of numerical Rung-Kutta 4th order method and GHF analytical solver based on root mean square error (RMSE), determination coefficient (R2) and mean percent error € for M1, S2 and C3 profiles. While The values of RMSE and R2 indices for M1, S2 and C3 profiles for GHF solver obtained (0.0173,0.9986), (0.0167,0.9984) and (0.0204,0.9988) respectively, corresponds values for Rong-Kutta method were (0.0458,0.9864), (0.0259,0.991) and (0.0327,0.9869). The results showed that using GHF analytical solver to solve the differential equation of GVF is more accurate.