Flow in Soils

Generalized Darcy Equation
Water flow in soils normally occurs at velocities that are well below the threshold for turbulent flow, and can be described by Darcy's law:

where 	H = the total soil water pressure or potential
		h = piezometric pressure or head
		z = gravitational potential or head

One dimensional forms of Darcy's Equation
For flow in one dimension, Darcy's law is given by 

For horizontal flow

		

For vertical flow

		
Flow in layered soils
An equivalent conductivity can be developed for flow in layered soils. 

Equivalent Conductivity for Vertical Flow

When flow is perpendicular to a series of soil layers, the flux through each layer is the same. 

	

These equations can be rearranged to give:

	
	-----

		

Adding both sides of these equations yield

By rearranging this equation

		

where 	D = D1 + D2 +...+Dn

and 		

Equivalent Conductivity for Lateral Flow

When flow is parallel to a series of soil layers, the discharge through unit thickness of the system is the sum of the discharges through the layers. 

Q = Q1 + Q2 +...+Qn

	

	

where