12:166, Zhang

 Spring, 2002

Lecture on

Groundwater Flow Equations

·        Hydraulic Gradient

 

 

 

·       

Hydraulic Conductivity Tensor

Note: In most cases, the off-diagonal terms are zeros

 

·        Darcy’s Law in Three Dimensions

 

 

 

·        Steady-State Flow vs. Unsteady-State Flow or Transient Flow

Steady–state flow is the flow where v does not change with time

(but it may change spatially)

Unstead-state or transient flow is the flow where v change with time

 

·        Groundwater Flow Equations

In a heterogeneous and anisotropic medium in 3-D

·         For unsteady-state flow:

 

·         For steady-state flow:

 

 

 

      In a homogeneous and isotropic medium in 3-D

·        For unsteady-state flow:     

 

·        For steady-state flow:

 

·        Boundary Conditions

Head boundary, e.g., a constant head boundary

Flux boundary, e.g., a no-flow boundary

Reading:     Section 4.7 – 4.10 of the text (p.125 - 132). Optional homework on the back.

 
 
Optional Homework
(We will correct it if you submit it before or on Mon., Feb. 25.
But sorry no bonus for this homework)

 

1.      A. Under what assumptions can groundwater flow be described by the following mathematical model?

                       

 

 

h(0) = h1

h(L) = h2

 

      B. Solve about equation with the boundary conditions.

 

 

2.      A. Under what assumptions can groundwater flow be described by the following mathematical model?

                       

 

 

h(0) = h1

h(L) = h2

 

      B. Solve about equation with the boundary conditions.

 

 

3.      A. Under what assumptions can groundwater flow be described by the following mathematical model?

                       

 

 

h(0) = h1

h(L) = h2

 

      B. Solve about equation with the boundary conditions