The computation of gradually varied flow (GVF) profiles involve at least in all the major hydraulic engineering activities of free surface flow. Generally the GVF occurs at the upstream of Dam or a Barrage, and the depth at control section of such profile would determine the exact height of training works to be provided to prevent the surrounding area from inundation. The first and foremost objective of computation of gradually varied flow profiles is to determine the variation of depth of flow with reference to the distance of the channel. The computation of gradually varied flow profiles is a very complex and tedious problem, as it involves basically the solution of dynamic equation of gradually varied flow. Unfortunately exact mathematical solution of the differential equation does not exist due to the non linearity of the equation.


The main objective of the thesis was to determine the most efficient numerical method(s), among the numerical methods under consideration, for solving the nonlinear GVF equation. For this purpose, the equation of steady gradually varied flow is solved using four different numerical techniques. The numerical techniques considered in this study were: Modified Eulerís method, Trapezoidal Integration method, Taylorís Series method and Milneís method. A computer model in PASCAL language was developed using the numerical methods under consideration. The developed model can be applied for any type of prismatic channel such as circular, rectangular, trapezoidal as well as triangular channel section. The developed model calculates the depth of GVF profiles at different section as well as the normal and critical depth of the channel. The solution of the developed model was compared with the laboratory data, generated for rectangular channel shape, in order to determine the most efficient channel section. The comparison the results of the numerical methods with the experimental data show that Modified Eulerís method, Trapezoidal Integration method, and Milneís method does not show any distinct difference in the solutions and can predict the GVF profile. However, the Taylorís Series method shows little bit deviation from the experimental Solution. This may be due to the truncation of higher order derivatives of Taylorís Series.