The driving force for transport of water in the unsaturated zone is the gradient of the hydraulic head, h, which includes a gravitational component, z, and a pressure component, y. Thus,
(28.25)
The gravitational head at a point is the elevation of the point above the datum (z is positive upwards). The reference level for the pressure head component is the atmospheric pressure. Under unsaturated conditions the pressure head, y, is negative due to capillary forces and short range adsorptive forces between the water molecules and the soil matrix. However, in the gravity flow module, the pressure head term is ignored and the driving force is due entirely to gravity.
Thus for vertical flow, the vertical gradient of the hydraulic head becomes,
(28.26) 
The volumetric flux is then obtained from Darcy's law:
where K(q) is the unsaturated hydraulic conductivity. Assuming that the soil matrix is incompressible and the soil water has a constant density, the continuity equation will be:
where S is the root extraction sink term.
