Journal of Mathematics in Industry

, 1:8

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Designing irrigation pipes

  • Antonio FasanoAffiliated withDipartimento di Matematica “Ulisse Dini”, Università degli Studi di Firenze Email author 
  • , Angiolo FarinaAffiliated withDipartimento di Matematica “Ulisse Dini”, Università degli Studi di Firenze


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).

AMS classification: 76S05, 76D05, 35C20

porous pipes Navier-Stokes equations asymptotic expansions irrigation