## A numerical investigation of the effect of curvature and Reynolds number to radial velocity in a curved porous pipe.(English)Zbl 1444.76108

Summary: Different irrigation methods are being used in agriculture. However, due to scarcity of water, irrigation methods that use water efficiently are needed. The motivation of this study is the increasing use of porous pipes to meet this requirement. The objective of this study is to investigate the effect of curvature and Reynolds number on radial velocity profile of water across a porous wall of a curved pipe with circular cross-section, constant permeability $$k$$ and porosity $$\varphi$$. The momentum equations of the two dimensional flow are written in toroidal coordinates. The main flow in the pipe is only characterized by $$\delta$$ and $$Re$$ as the only non-dimensional groups of numbers. We also considered the flow to be fully developed, unsteady, laminar and irrotational. Darcy law is used to analyse the flow across the porous membrane. The main flow was coupled with the flow through the porous wall of the pipe. The equations were solved using finite difference method. It was observed that effect of curvature on the velocity across the pipe wall is negligible while an increase in Reynolds number leads to an increase in the radial velocity. The findings of this study are important in the design of porous pipes and also in their use during irrigation.

### MSC:

 76S05 Flows in porous media; filtration; seepage 76D05 Navier-Stokes equations for incompressible viscous fluids 35Q35 PDEs in connection with fluid mechanics

### Keywords:

unsteady; incompressible; curved porous; Darcy law
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### References:

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