Nonlinear Differential Equation of Drain Spacing

by William T. Moody,

Serial Information: Journal of the Irrigation and Drainage Division, 1966, Vol. 92, Issue 2, Pg. 1-10

Document Type: Journal Paper


The nonlinear partial differential equation governing spacing of horizontal, parallel, subsurface, agricultural drains is solved numerically by finite difference methods. The differential equation is based on the Dupuit-Forchheimer assumption. Since use of Hooghoudt's equivalent depth is suggested as a means of accounting for the effect of convergence, a simplified formula is derived from computing that quantity. Solutions are presented in the form of dimensionless curve families whose abscissas are a time parameter and whose ordinates represent: (1) Maximum water table height between drains, (2) rate of discharge, and (3) volume of water removed. Individual curve parameters establish the depth from drains to an impermeable barrier which can vary from zero to infinity. An example of application is given.

Subject Headings: Water discharge | Drainage | Differential equations | Subsurface drainage | Curvature | Parameters (statistics) | Water table | Nonlinear analysis

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