Designing irrigation pipes

Abstract

The use of porous ducts to deliver water to agricultural fields is an old technique which helps saving water and prevents ground erosion. Designing porous duct is not as a simple task as it looks and apparently has never been the subject of mathematical research. Here the problem is addressed making use of a double rescaling of space and velocity variables, which allows the derivation of the governing equations starting from the study of the classical Navier Stokes equations in a pipe. Such equations are then solved obtaining results of practical interest in design of irrigation pipes, both for low discharge pipes (small plants) and for high discharge pipes (large plants).

Steady flow through a slender tapered vessel with a partially permeable wall and closed end

“…Numerical examples are provided. The mathematical technique employed generalizes the one adopted in [6] for the study of flows in cylindrical tubes with porous walls. Our analysis reveals that the behavior of pressure near the tip is critically dependent on the tip shape.…”

Numerical Investigation of the Effect of Curvature and Reynold's Number to Radial Velocity in a Curved Porous Pipe

“…Fasano and Farina [9] mentions more recent technical studies in this area and also appreciates that this technique is today used to such a large extent that periodic international conferences are held.…”

“…Fasano and Farina [9] in their study that sought to design irrigation pipes applied the fundamental laws of dynamics of fluids in a pipe (Navier stokes equations) and through porous media (Darcy's law) in incompressible laminar flow through hollow fibers with porous walls in a dead end configuration. One of the key points was to obtain at the far end of the pipe a water delivery rate similar to the one close to the inlet.…”