Developing a Model for Open Channel Fluid Flow with a Segment Base having Lateral Inflow Channel

Abstract

An open channel fluid flow is characterized by presence of a free surface. The interface between two homogeneous fluids of different densities is regarded as free surface. It is the surface of the liquid that is in contact with air. Generally, this interface is subject to zero parallel shear stress. The survival of lives and livelihoods has greatly been hampered by occurrence of floods. When there is heavy downpour, accumulation of flooded water has led to bridges being washed away, increased pot holes on the roads and this has led to increased cases of accidents leading to loss of lives. This has posed a huge financial burden to the Government in terms of budgetary allocations to import human capital for maintenance and repair of worn out roads and bridges. This study has developed a model for fluid flow past an open channel with a trapezoidal cross-section with a segment base having lateral inflow channel that has optimal dimensions for maximum discharge. The fluid particles throughout the flow do not crisscross each other and hence the entire flow is assumed to be laminar. The developed model equations are non-dimensionalized, discretized and solved using finite-difference method and numerical values are simulated using Matlab Mathematical software. The findings are discussed, analyzed and presented graphically. It is reported that an increase in length of the lateral channel leads to decrease in flow velocity of the main channel. An angle of inclination of the lateral channel at a range of 300 to 450 exhibit higher values of flow velocity in the main channel compared to other angles. However, maximum velocity at the main channel is attained at an inclination angle of 300. At this angle, there is minimum shear stress hence less resistance to the flow profile. The results of this study is highly applicable in the design of drainage systems for road construction, sewer building, street drainage, airport construction and dams for electric power plants in Kenya and elsewhere.