1. Principles of Groundwater Flow
ESS 454 Hydrogeology
Module 3
Principles of Groundwater Flow
Point water Head, Validity of Darcy’s Law
Diffusion Equation
Flow in Unconfined Aquifers & Refraction of Flow lines
Flownets
Instructor: Michael Brown

2. Outline and Learning Goals
Understand how to quantitatively calculate heads and water fluxes in unconfined aquifers
Be able to qualitatively and quantitatively estimate how flow lines are bent at interfaces between materials having different hydraulic conductivities

3. Unconfined Aquifer q’in=Qin/y q’out=q’in Jules Dupuit’s Contribution:
Assume
Water Table
Hydraulic gradient is slope of water table
Flow is horizontal h1
q’in=Qin/y
q’out=q’in h2 y
x=L
x=0 h x

4. Unconfined Aquifer Qin Qout qout qin w=Infiltration (inches/year)
Water Table
w=Infiltration (inches/year)
Vertical Flux:
Qinfiltration=w dx dy h1
qout
qin h2
Horizontal Flux dy dx
Qin
Qout

5. Unconfined Aquifer Consider unconfined aquifer with infiltration
Consider change in storage caused by flow in x-direction
Quantity change
Over distance dx
Contribution from flow in y-direction

6. Unconfined Aquifer A trick
The steady-state behavior of an unconfined aquifer
Align water table gradient in x-direction

7. Unconfined Aquifer This is easy to solve: Just integrate twice
Two integrations, two integration constants
The value of the head a two points (usually the two boundaries) gives enough information to solve this

8. Unconfined Aquifer x=0 L w h1 w=0 x=0 -> h=h1 x=L -> h=h2 h2
flow
flow
xw.t.divide
At divide q’=0
You can solve for h at water table divide

9. Diffusion Equation for Unconfined Aquifer
Valid for
small draw-down (small ∆h)
Nearly horizontal water table
b is average thickness of saturated zone

10. Refraction of Flow Lines
Derivation given in book i
Imagine flux tube intersecting boundary
Conserve water through boundary K1 K2
Apply Darcy’s Law at interface
Use standard trig. relationships
tan(r)=K2/K1 tan(i) r
Bent away if K2<K1
Bent towards if K2>K1

11. End of
Flow in unconfined Aquifers and Refraction of flow lines
Coming up: The creation of “Flownets”