This study investigates the suitability of trapezoidal cross-section with segment base in drainage system design. The study has considered steady uniform open channel flow. The saint-Venant partial differential equations of continuity and momentum governing free surface flow in open channels have been solved using finite difference approximation method. We investigate the effects of the channel radius, area of the cross section, the flow depth and the manning coefficient on the flow velocity. The flow variables are velocity and the flow depth while the flow parameters are cross section area of flow, channel radius, slope of the channel and manning coefficient. The study has established that increase in cross section area of flow leads to a decrease in flow velocity. Further, increase in channel radius and cross section area of flow leads to a decrease in flow velocity and increase in roughness coefficient cause flow velocity to decrease. Additionally, increase in flow depth increases velocity. The physical conditions of the flow channel have been applied to conservation equations to arrive at specific governing equations. The results of the study have been presented graphically.