23
El rate of change of liquid water to water vapor
[kg-m^n-s'1]
For the range of temperatures generally occurring in the soil, the
density of water may be considered constant. The volumetric flow rate
of water (q|_) can be obtained by dividing the mass flow rate (Ql) by
the density of water (pw). The volumetric flow rate of water in an
unsaturated soil is governed by Darcy's Law as follows:
qL - k gf (2-19)
where:
qL volumetric flow rate of liquid water [m3*m"2*s-1]
k unsaturated hydraulic conductivity [m*s"l]
0 = soil water potential [m]
z = spatial dimension [m]
The relationship between soil water content and soil water potential is
unique for a given soil type. Therefore, the volumetric flux of water
can be expressed in terms of volumetric water content instead of soil
water potential by applying the chain rule of differentiation to
equation (2-19) as follows
q, = k
30 33
W W
(2-20)
The hydraulic diffusivity of the soil is defined as
DL
K
30
W
(2-21)
By substituting the definition for the hydraulic diffusivity (2-21) and
the volumetric flow rate in terms of the soil water content (2-20) the
equation for the conservation of mass for liquid water (2-18) becomes
33
3t
3_
3z
CDl
33
3z
1 E(z,t)
N
(2-22)