Summary of Groundwater Flow Equations

I. 3-Dimensional Transient Flow (assuming constant )

a. Heterogeneous, Anisotropic:

b. Heterogeneous, Isotropic:

c. Homogeneous, Anisotropic:

d. Homogeneous, Isotropic (flow of heat and diffusion of solutes also follow this equation):

II. 3-Dimensional Steady State flow: Homogeneous, Isotropic Conditions (assumes constant ). This is also called Laplace's equation:

III. 3-Dimensional Transient flow in the unsaturated zone (Richard's equation)

where C() = d /d is the specific moisture capacity, the slope of the characteristic curve.

IV. 2-Dimensional, Horizontal Flow Equations for Confined Aquifer (including source/sink term for recharge/leakage)

a. Heterogeneous, Anisotropic

b. Heterogeneous, Isotropic

c. Homogeneous, Anisotropic

d. Homogeneous, Isotropic

V. 2-Dimensional Steady State Flow in a Homogeneous, Isotropic Aquifer (no source/sink term) (Laplace Equation in 2-D)

VI. 2-Dimensional, Horizontal Flow for Unconfined Aquifer (including source/sink term for recharge/leakage)

a. Heterogeneous, Anisotropic: nonhorizontal base, saturated thickness equal to b

b Heterogeneous, Anisotropic, Dupuit Assumptions: horizontal base at z=0, gradient equal to slope of water table (h = b)

where T_x = K_x(x,y) h(x,y,t) and T_y = K_y(x,y) h(x,y,t) are pseudotransmissivities.

c. Heterogeneous, Isotropic, Dupuit Assumptions

where T = K(x,y) h(x,y,t) and T = K(x,y) h(x,y,t) are pseudotransmissivities.

d. Homogeneous, Anisotropic, Dupuit Assumptions

e. Homogeneous, Isotropic, Dupuit Assumptions (The Boussinesq equation)

f. Linearized form of the Boussinesq equation, h approximately constant (i.e. small gradients)

where T = Kh

g. Linearized form of the Boussinesq equation, h approximately constant (i.e. small gradients) and large saturated thickness

where T = Kh

Steady State Forms for Unconfined: Left side as above, Right side = 0