A Mathematical model of Fluid Flow in an Open Trapezoidal Channel with Lateral Inflow Channel

  • Samuel Macharia Karimi Faculty of ICT and Engineering, Zetech University, P. O. Box 2768-00200, Nairobi, Kenya
Keywords: open channel, lateral inflow channel, finite difference, wetted perimeter


In this paper, an incompressible fluid flow in an open trapezoidal channel with one lateral inflow channel is investigated.  The flow parameters that are investigated include the cross-sectional area, angle, length and velocity of the lateral inflow channel. The flow variables in the main trapezoidal channel include the depth and velocity of the fluid. These flow parameters in the lateral inflow trapezoidal channel are investigated on how varying each parameter independently affects the flow velocity in the main trapezoidal channel. The continuity and momentum equations are equations that govern this flow. Since these two equations are highly nonlinear, the finite difference method is used to approximate the solutions.  The results are then presented by velocity profiles graphs and discussed. It is noted that a decrease in the cross-sectional area leads to an increase in the flow velocity and an increase in the length of the lateral inflow channel leads to a decrease in the flow velocity. It is also noted that an increase in the velocity of the lateral inflow channel leads to an increase in the flow velocity and an angle of between thirty and fifty degrees increased the flow velocity compared to other angles in the lateral inflow channel.


. V.T. Chow. Open Channel hydraulics: McGraw Hill Book Company, New York, 1959; pp.1-40.

. F.M. Henderson. Open Channel Flow: Macmillan Publishing Company, New York, 1966.

. A. Chadwick and J. Morfet. Hydraulics in Civial Engineering and Environmental Engineering: Chapman & Hall 1993, pp.187-200.

. P. Fan and J.C. Li. “Diffusive wave solutions for open channel flows with uniform and concentrated lateral inflow.” Advances in Water Resources, pp.1000–1019, 2005.

. A. Masjedi and A. Taeedi. “Experimental Investigations of Effect Intake Angle on Discharge in Lateral Intakes in 180 Degree Bend.” World Applied Sciences Journal, 15 (10), pp.1442-1444. 2011,

. F. Yang, H. Chen and J. Guo. “Study on “Diversion Angle Effect of Lateral Intake Flow.” In 33th IAHR Congress, Vancouver, Canada, pp. 4509-4516, 2009.

. J.K. Kwanza, M. Kinyanjui and J.M. Nkoroi. “Modelling fluid flow in rectangular and trapezoidal open channels.” Advances and Applications in Fluid Mechanics, vol. 2, pp. 149-158. 2007.

. M. Karimi, D. Theuri and M. Kinyanjui. “Modelling Fluid Flow in an Open Rectangular Channel with Lateral Inflow Channel.” International Journal of Sciences: Basic and Applied Research (IJSBAR), vol. (17), pp. 186-193, 2014.

. P.K. Marangu, E. Mwenda and D.M. Theuri. “Modeling Open Channel Fluid Flow with Trapezoidal Cross Section and a Segment Base.” Journal of Applied & Computational Mathematics, pp. 1-5, 5: 292, 2016.

. D.P. Tsombe, M.N. Kinyanjui, J.K Kwanza and K. Giterere. “Modeling fluid flow in open channel with circular cross-section. Jagst, pp. 80-91, 13, 2011.

. J. H. Pu. “Turbulent rectangular compound open channel flow study using multi-zonal approach.” Environ Fluid Mech, vol. 19, pp. 785–800 (2019).

. A. Triki and E. Hadj-Taïeb. “Numerical Solution for One-Dimensional Open-Channel Transient Flow.” International Journal of Modelling and Simulation, vol. 30:2, pp. 211-217, (2010).

. J.C. Amanda. Accurate and efficient numerical solutions to saint venant, equations. University of Nottingham, UK 12-38, 2009.