Darcy’s equation is often used to describe water movement in saturated soils. For one-dimensional water flow, it can be written as ( Hillel, 1982)

where q is the flux density of water passing through the soil, K is the saturated hydraulic conductivity, H is the total potential, and x is the position coordinate.

For unsaturated soils, this equation takes the modified form developed by Buckingham (1907)

where K(q) or K(h) is the unsaturated hydraulic conductivity function ( Brooks and Corey, 1964; Gardner, 1958; vanGenuchten, 1980), q is the volumetric water content and h is the matric potential. The total potential is the sum of the matric potential and gravitational potential.

For uniform saturated soils we can write this equation as

where H₁ and H₂ are the total potentials at the inlet and outlet of the soil system, respectively. The difference in total potential divided by the length of the system is the driving force causing water to flow.

When soils are saturated and homogeneous, the flux density can be easily obtained if the conductivity of the soil is known and the total potential or matric potential at the ends of the soil are specified. However, the problem becomes more difficult when the soil is not homogeneous or when it is unsaturated.

This applet considers one-dimensional flow in a soil. The soil is assumed to be homogeneous. This means that the conductivity will be uniform throughout if the matric potentials at both ends are zero or more since that means the soil is saturated. If one or more matric potentials are less than zero, the conductivity and water content can change with position.

The user can specify the length of the soil, its saturated hydraulic conductivity, the total potental or matric potential at each end of the soil system, and the orientation of the soil. The software then solves the equations above and displays graphs of total potential, matric potential, gravitational potential, conductivity, driving force, or water content as a function of position along the soil column. In this way the user can see the impact of changes in matric potential and water content upon the flow rate and equivalent conductivity of the entire soil system.

Simplifications and assumptions on soil media and flow conditions:

1. This software assumes that flow is strictly one-dimensional.
   
2. Flow-induced deformation in a soil medium affects the shape, size, and connectivity of soil pores, which largely determines the hydraulic properties of a soil system ( Buckingham, 1907). In this program, it is assumed that the soil system simulated in this program is rigid, i.e., no flow-induced deformation occurs.

3. Flow through conduits is classified into laminar flow and turbulent flow dependent on the ratio of inertial to viscous forces exerted on the fluids( Bear, 1972). In a laminar flow, the relationship between flow rate and gradient in total potential is linear, while in a turbulent flow the relationship is nonlinear. The linear relationship of Darcy's law is valid in the range of laminar flow only. Hence, an implicit assumption in this program is that flow conditions inside soil pores are laminar.

4. In fine-grained (especially clayey) soils, a minimum potential gradient called threshold gradient may exist. Below this threshold gradient there is very little flow. This non-Darcy behavior( Swartzendruber, 1962)may be due to the effect of stream potential which generates small countercurrents along the pore walls in a direction opposite that of the main flow( Bear, 1972). Another explanation for the non-Darcy behavior is the non-Newtonian liquid viscosity caused by clay-water interaction. In this program, non-Darcy behavior is ignored.