Browsing by Author "Jacob Kirimi"

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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.
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.
Modelling Fluid Flow in Zone 1 of an Open Horseshoe Channel with Lateral Inflow Channels
(Journal of Advances in Mathematics and Computer Science, 2024-05-24) Jomba Jason; Mark Okongo; Jacob Kirimi; Jimrise Onyango
For many years, flooding has been a significant issue, especially after heavy rainfall. Engineers have constructed channels to direct water into rivers, lakes, and oceans, aiming to mitigate flooding. The challenge lies in designing drainage ditches, irrigation canals, and navigation channels that maximize hydraulic efficiency for water transport and electricity generation. Most studies have focused on rectangular, parabolic, trapezoidal, and circular open channels, leaving a knowledge gap in the study of horseshoe-shaped channels with lateral inflows. This research aims to model a uniform flow in Zone 1 with a horseshoe-shaped cross- section and lateral inflows. The study aimed to determine how variations in the angle of lateral inflowchannels and the increase in lateral inflows in Zone 1 affect the main channel flow velocity. Governing equations were derived by applying conservation equations to the physical conditions of the flow. These equations were solved using the finite difference approximation method due to its precision, stability, and convergence. The results, presented graphically, revealed that the main channel velocity decreases as the number of lateral inflow channels increases. Ultimately, the main channel velocity decreases as the angles of the lateral inflows increase. Mitigating floods and collecting water for irrigation drive scientific, technological, and engineering progress by demanding creative remedies and infrastructure that enhance crop production and tolerance to climate changes. By enhancing food security and enabling sustainable farming practices, these developments promote economic growth and raise living standards in communities while also generating job possibilities. Water management that incorporates scientific and technological advancements allows society to more effectively utilize natural resources, which in turn promotes greater socioeconomic empowerment.