# Comparison of the water movement by Richard and Darcy

### Abstract

Simulations of water movement in the soil are pervasive, Darcy’s law, Darcy- Buckingham’s law and Richard’s equation are all approved equations for this purpose. The Richard’s equation is the most reliable model which is introduced by Lewis Richardson who was the first one to propose that Darcy’s law was originally fabricated for flow in the saturated zone while for flow in vadose zone Darcy-Buckingham’s law can be used in case of steady state condition. Since it is impossible in nature for flow to be steady, Richard proposed a highly nonlinear partial differential equation (PDE) equation which a combination of Darcy’s law and continuity equation. Hydraulic conductivity K(LT^{-1}) and moisture content θ (L ^{3}L ^{3}) are two important variables of Richard’s equation. Considering the nonlinearity of its variables Richard’s equation lacks a general closed form solution. For this purpose, many researchers derived numerical and analytical models to solve Richard’s equation. In this paper, Green Ampt Infiltration Equation is presented to solve Richard’s equation which is one of the most widely used analytical methods.

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*Zanco Journal of Pure and Applied Sciences*, 32(1), pp. 1-6. doi: 10.21271/zjpas.32.1.1.

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