Jomba Jason2026-06-112026-06-112024Jomba, J. (2024). Modelling fluid flow in an open horseshoe channel with lateral inflow channels (Doctoral thesis, Chuka University).https://repository.chuka.ac.ke/handle/123456789/22979A Thesis Submitted to the Graduate school in Partial Fulfilment of the Award of the Degree of Doctor of Philosophy in Applied Mathematics of Chuka University Supervisors: Dr. Mark Onyango Okong’o , Dr. Jacob Kirimi,Flooding has been an issue for many years, particularly during periods of heavy rainfall. Channels have been constructed to reduce flooding by directing water to rivers, lakes and oceans. Engineers have faced a challenge of designing a hydraulically efficient chan- nel for conveying maximum amount of water for generating electric power, drainage ditches, floodways, navigation channels and irrigation canals. Horseshoe-shaped chan- nels with lateral inputs have received less attention in open channel flow studies than rectangular, parabolic, trapezoidal, and circular channels. This study aims at modeling a uniform flow with horseshoe cross-section with lateral inflows. The choice of a lat- eral horseshoe shape is due to its distinctive combination of geometric and functional advantages. In fluid dynamics, this shape is particularly valuable for promoting stream- lined flow. Its curved form allows fluids to move around it with reduced turbulence and drag, making it ideal for minimizing flow resistance. This study investigates the effects of increasing lateral inflows, varying lateral inflow channel angles, increasing lateral inflows’ cross-sectional areas, and increasing lateral inflows’ lengths on the velocity of the primary channel’s flow. To obtain particular governing equations, the physical conditions of the flow problem were applied to conservation equations. The finite dif- ference technique is utilized to resolve the differential equations governing the flow due to its accuracy, consistency and convergence. The equations are first represented in dimensionless form. Numerical values are simulated using the Python program, and the results obtained from this study are represented graphically. The findings showed that when lateral inflows increased, the main channel’s velocity reduced. Furthermore, it was noted that the velocity decreased as the lateral inflows’ angles increased. Simi- larly, the velocity in the primary channel decreased as the cross-sectional area of the lat- eral inflows increases. Conversely, the results showed that when the length of the lat- eral inflows increased, it also increased the main channel’s velocity. This research will help engineers construct open horseshoe channels with lateral inflows that are hydrauli- cally efficient and can transfer the most water possible for a variety of uses. One of the main applications is irrigation, because efficient water flow is necessary for productive farming. The findings of the study will also be helpful in the production of hydroelectric power since they offer information on how to optimize water flow to improve energy output. The research also intends to improve channel designs that can manage high water volumes in an effort to aid in flood reduction efforts.enOpen channel flowHorseshoe channelLateral inflowFluid flow modellingFinite difference methodHydraulic efficiencyComputational fluid dynamics.Thesis