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

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.