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Research Article Open access CC BY 4.0

Mathematical Modeling of Water Flow for Irrigation in a Permeable Pipe of Elliptical Cross-section

A. W. Ndegwa, M. M. Kimathi, M. N. Kinyanjui, I. Chepkwony

Journal of Advances in Mathematics and Computer Science · pp. 159–178 · Published 23 Oct 2014

10.9734/BJMCS/2015/13157

Abstract

An unsteady incompressible fully developed flow in a horizontal flexible and permeable annular pipe of elliptic cross-section under the action of gravity is studied. The solution is obtained through a homogenization method by employing a small scale separation parameter that approximates the pipe in the form of a series. The results in terms of velocity and pressure distributions and mass flow rate inside the pipe and through the pipe wall are presented and discussed. It is shown that the pipe thickness has no influence on the water flow through the pores. We also propose that for the efficient use of water for irrigation, the elliptical pipe should be laid in a vertical position.

Elliptical cross-section Mass flow rate, Permeability Fully developed flow Scale separation Homogenization

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