Research

Designing irrigation pipes

Antonio Fasano^* and Angiolo Farina

• * Corresponding author: Antonio Fasano fasano@math.unifi.it

Author Affiliations

Università degli Studi di Firenze, Dipartimento di Matematica "Ulisse Dini" Viale Morgagni 67/A, I-50134 Firenze, Italy

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Journal of Mathematics in Industry 2011, 1:8 doi:10.1186/2190-5983-1-8

The electronic version of this article is the complete one and can be found online at: http://www.mathematicsinindustry.com/content/1/1/8

Received:	18 April 2011
Accepted:	18 August 2011
Published:	18 August 2011

© 2011 Fasano and Farina; licensee Springer.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).

AMS classification: 76S05, 76D05, 35C20

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