Richards equation
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The Richards equation represents the movement of water in unsaturated soils, and was formulated by Lorenzo A. Richards in 1931. It is a non-linear partial differential equation, which is often difficult to approximate since it does not have a closed-form analytical solution.
Darcy's law was developed for saturated flow in porous media; to this Richards applied a continuity requirement suggested by Buckingham, and obtained a general partial differential equation describing water movement in unsaturated non-swelling soils. The transient state form of this flow equation, known commonly as Richards equation:
![\frac{\partial \theta}{\partial t}= \frac{\partial}{\partial z} \left[ K(h) \left (\frac{\partial h}{\partial z} + 1 \right) \right]\](../../../math/f/f/a/ffa6d3042ec79584393eb2c51a3c31d4.png)
where
- K is the hydraulic conductivity,
- h is the hydraulic head,
- z is the elevation above a vertical datum,
- θ is the water content, and
- t is time
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