Mathematics and Statistics

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Browsing Mathematics and Statistics by Author "Charles Mwaniki Nyaga"

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    Developing a Model for Open Channel Fluid Flow with a Segment Base having Lateral Inflow Channel
    (Journal of Advances in Mathematics and Computer Science, 2024-09-13) Charles Mwaniki Nyaga; Mark Okongo; Jacob Kirimi
    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.
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    Modeling Open Channel Fluid Flow Past a Trapezoidal Cross-section with a Segment Base having Lateral Inflow Channel
    (Journal of Advances in Mathematics and Computer Science, 2024-07-11) Charles Mwaniki Nyaga; Mark Okongo; Jacob Kirimi
    Floods in flood-stricken areas have been a major threat to the survival of lives and livelihoods in various aspects. For instance, increased pot-holes, road disconnection and tearing off as well as bridges being carried away have led to increased cases of accidents leading to loss of lives. This has led to Government over- stretching budgetary allocations to cater for maintenance and repair of 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. The turbulent formation between the lateral inflow channel and the main channel are assumed to be negligible and hence the flow is laminar. The model equations governing the fluid flow are non-dimensionalized and solved using finite-difference method. The numerical values are simulated using Matlab software. It is found that an increase in cross-section area of the lateral channel increases the discharge in the main channel leading to an increase in flow velocity. An increase in surface roughness increases shear stress thereby recording a reduced flow velocity. The findings of this study is highly applicable in the design of drainage systems for road construction, sewer building, street drainage, dams, and airport construction in Kenya and elsewhere. Moreover, the designed efficient channels with optimal dimensions are applicable in draining water to hydro-electric power plants where large volumes of high velocity water are required to turn large turbines for electrical processes.