In this study, a mathematical model have been prepared for al – Kut water supply project depending upon the numerical methods such as Newton - Raphson method and Gaussian elimination method to solve non – linear simultaneous equations with known boundary condition and by using the characteristic method, the partial differential equations are transformed to ordinary differential equations.
In this mathematical model, the values of the generated pressures were calculated when using control devices or without, also, to find the influence of this devices on, the pressure values was found. In addition to, the suitable number of control devices required for each pipeline was found to keep the pressure values within a tolerable limits.
This model was applied on a published case study and the results were quite satisfactory.