A solution in closed form and a series solution to replace the tables for the thickness of the equivalent layer in Hooghoudt's drain spacing formula

• Published in: Agricultural water management 1991, Vol.19 (1), p.1-16
• Main Authors: van der Molen, W.H., Wesseling, J.
• Format: Article
• Language: English
• Subjects: Agricultural and forest climatology and meteorology. Irrigation. Drainage; Agronomy. Soil science and plant productions; APLICACIONES DEL ORDENADOR; APPLICATION DES ORDINATEURS; Biological and medical sciences; COMPUTER APPLICATIONS; DRAINAGE EQUIPMENT; Earth sciences; Earth, ocean, space; EQUIPO DE DRENAJE; ESPACEMENT; ESPACIAMIENTO; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General agronomy. Plant production; Hydrogeology; Hydrology. Hydrogeology; Irrigation. Drainage; MATERIEL DE DRAINAGE; PIPES; SPACING; TUBERIA; TUYAU
• ISSN: 0378-3774; 1873-2283
• DOI: 10.1016/0378-3774(91)90058-Q

Fifty years ago, Hooghoudt presented formulas for obtaining the mutual distance between drains, based on steady-state flow conditions. The “thickness of the equivalent layer, d”, was introduced to account for the radial resistance occurring near the drains. Thus, the solution did not involve Dupuit's Assumption of pseudo-horizontal flow. For a subsoil of infinite thickness, d could be expressed in a closed form. For thin aquifers Hooghoudt gave tables, based on a numerical approximation, and in practice nomographs were extensively used. The use of these tables forms a drawback in design computations with modern electronic devices. This paper describes a general solution in closed form, involving theta-functions. For computer calculations, series solutions are presented, although for thin aquifers their convergency is slow. For this case, however, the formula proposed by Dagan proved to be very accurate. A combination of both types of solutions provides an efficient algorithm.