Mathematical Modelling of Water Flow of Irrigation in a Permeable Pipe of Elliptical Cross-section - Ndegwa, A.W; Kimathi, M.M; Kinyanjui, M.N (British Journal of Mathematics and Computer Science, 2015)
Anunsteadyincompressiblefullydevelopedﬂowinahorizontalﬂexibleandpermeableannularpipe 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.
Keywords: Elliptical cross-section; Mass flow rate; Permeability; Fully developed Flow; Scale separation; Homogenization