Optimizing a trapezoidal open-channel for least velocity fluctuation during overflow using mathematical efficiency criterion (original) (raw)

Abstract

In open channels, fluid velocity increases with depth of flow. Sewers are particularly susceptible to overwhelming storm water velocities during rains. When flow velocities exceed a certain threshold, damage of channel by scouring may result, or, conversely, siltation of suspended matter. Channel design must optimize dimensions and shapes which both minimize cost, maximizing discharge in normal seasons and regulate the discharge to minimize velocity fluctuations during overflow. Depending on the designer's objectives, channel design involves numerous parameters, including the characteristics of construction materials and earthwork. Traditional methods such as Langrage multipliers, Sequential Quadratic Programming (SQP), Differential Evolution Algorithm (DEA), genetic algorithms, ant-colony optimization, and lately, metaheuristic algorithms are often used to minimize a cost function subject to channel cross-section. In this paper, using only the mathematical hydraulic efficiency criterion (other factors assumed optimum), a direct integro-differential John Wahome et al. technique is applied to determine the optimum trapezoidal channel design that additionally minimizes velocity fluctuations during excessive discharge.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (16)

  1. R.K. Rajput, Fluid Mechanics and Hydraulic Machines, S. Chand and Company, New Delhi, (2006).
  2. D. C.Froehlich, Width and Depth-Constrained Best Trapezoidal Section, Journal of Irrigation and Drainage Engineering, 4 (1994) 828-835
  3. B. Aksoy, Optimal Channel Design, MSc. thesis, Middle East Technical University.(2003)
  4. A.T.Hameed, Optimal Design of Round Bottomed Triangle Channels, Tikrit Journal of Eng.Sciences 3 (2010) 31-43.
  5. S. M. Easa, A. R. Vatankhah b and A. O. Abd El Halim, A simplified di- rect method for finding optimal stable trapezoidal channels, International Journal of River Basin Management 2 (2011), 85-29
  6. E.T. Mustafa,Yurdusev M.A., Optimization of Open Channels by Dif- ferential Evolution Algorithm, Mathematical and Computational Applica- tions Journal 1 (2011), 77-86.
  7. J.N. Wahome, An Investigation Of Free Surface Fluid Flow Topologies Using an Inverse Conformal Mapping Inferencing Technique, PhD thesis, University of Eldoret.(2014)
  8. B. Massey, J.W. Smith, Mechanics of fluids, Stanley Thornes.. 182 (1998), 131-137.
  9. Doughlas, J.F., Gasiorek, J.M., Swaffield, J.A., Fluid Mechanics, Prentice Hall.. 182 (2001), 514-558.
  10. V.T. Chow, P. Open Channel Hydraulics, McGraw-Hill, New York, (1959)
  11. R.H.French, Open Channel Hydraulics, McGraw-Hill, New York, (1985)
  12. F.M. Henderson, Open Channel Flow, McGraw-Hill, New York,(1966)
  13. F.M. Henderson, Open Channel Flow, Macmillan, New York,(1996)
  14. D. Stephenson, Stormwater Hydrology and Drainage, Elsevier, Amster- dam,(1981)
  15. J.A. Swaffield and L.S. Galowin, The Engineered Design of Building Drainage Systems Ashgate, Aldershot,(2011)
  16. H. Rouse, Critical Analysis of Open Channel Roughness, J.Hydraul.Div. ASCE, 91 (1965), 1-15.