1. Groundwater Flow Equations
Groundwater Hydraulics
Daene C. McKinney

2. Summary General Groundwater Flow Confined Aquifer Flow
Control Volume Analysis
General Continuity Equation
Confined Aquifer Flow
Continuity Equation
Integrate over vertical dimension
Transmissivity
Continuity
Examples
Unconfined Aquifer Flow
Darcy Law

3. Control Volume Control volume of dimensions Dx, Dy, Dz
Completely saturated with a fluid of density r x y z
Mass flux in
Mass flux out
Control
volume

4. Mass Flux Mass flux = Mass in - Mass out: Fluid mass in the volume:
mass flux in
mass flux out
Mass flux = Mass in - Mass out:
Fluid mass in the volume:
Continuity: Mass flux = change of mass

5. Aquifer Storage

6. Continuity Equation

7. Confined Aquifer Flow

8. Horizontal Aquifer Flow
Most aquifers are thin compared to horizontal extent
Flow is horizontal, qx and qy
No vertical flow, qz = 0
Average properties over aquifer thickness (b)
Ground surface
Bedrock
Confined aquifer Qx K x y z h
Head in confined aquifer
Confining Layer b

9. Aquifer Transmissivity
Transmissivity (T)
Discharge through thickness of aquifer per unit width per unit head gradient
Product of conductivity and thickness
Hydraulic gradient = 1 m/m
Potentiometric Surface
Confining Bed
Confined Aquifer b
1 m
Transmissivity, T, volume of water flowing an area 1 m x b under hydraulic gradient of 1 m/m
Conductivity, K, volume of water flowing an area 1 m x 1 m under hydraulic gradient of 1 m/m

10. Continuity Equation Continuity equation Darcy’s Law Continuity
Ground surface
Bedrock
Confined aquifer Qx K x y z h
Head in confined aquifer
Confining Layer b
Radial Coordinates

11. Example – Horizontal Flow
Consider steady flow from left to right in a confined aquifer
Find: Head in the aquifer, h(x)
Ground surface
Bedrock
Confined aquifer Qx K x y z hB
Confining Layer b hA L
steady flow
Head in the aquifer

12. Example – Horizontal Flow
L = 1000 m, hA = 100 m, hB = 80 m, K = 20 m/d, f = 0.35
Find: head, specific discharge, and average velocity
Ground surface
Bedrock
Confined aquifer Qx
K=2-m/d x y z
hB=80m
Confining Layer b
hA=100m
L=1000m

13. Unconfined Aquifer Flow

14. Flow in an Unconfined Aquifer
Dupuit approximations
Slope of the water table is small
Velocities are horizontal
Ground surface
Bedrock
Unconfined aquifer
Water table Dx Qx K h x y z

15. Steady Flow in an Unconfined Aquifer
1-D flow
Steady State
K = constant h
Flow hA hB
Water Table
Ground Surface
Bedrock L x

16. Steady Flow in an Unconfined Aquifer
K = 10-1 cm/sec
L = 150 m
hA = 6.5 m
hB = 4 m
x = 150 m
Find Q h
Flow
hA=6.5m
hB=4m
Water Table
Ground Surface
Bedrock
L=150m x
K=0.1cm/s

17. Summary General Groundwater Flow Confined Aquifer Flow
Control Volume Analysis
General Continuity Equation
Confined Aquifer Flow
Continuity Equation
Integrate over vertical dimension
Transmissivity
Continuity
Examples
Unconfined Aquifer Flow
Darcy Law