This study investigates the suitability of trapezoidal cross-section with segment base in drainage system design. The study has considered steady uniform open channel fluid 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. The effects of the channel radius, area of the cross section, the flow depth and the manning coefficient on the flow of velocity investigated. 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 established that increase in cross section area of flow led to a decrease in flow velocity. Further, increase in channel radius and cross section area of flow led to a decrease in flow velocity and increase in roughness coefficient which causes the flow velocity to decrease. Additionally, increase in flow depth increases the flow velocity. The physical conditions of the flow channel were applied to conservation equations to arrive at specific governing equations. The results of the study have been presented graphically.The study recommends further research on the effect of energy on flow velocity and turbulent flow on the same cross section.The plate 1.1 below shows drainage channel in use on the road in Meru town.The rectangular channel shown below has a lot of alluvial deposits and due to this fact, the channel is not able to carry water efficiently. Such channel systems are not able to discharge run off properly due channel blockages and this will cause overflows which will result in hydroplaning on road and subsequently cause traffic jams, accident or destruction of the drainage system. Furthermore, it will require regular maintenance.