1. Cross Section of Unconfined and Confined Aquifers

2. Unconfined Aquifer Systems
Unconfined aquifer: an aquifer where the water table exists under atmospheric pressure as defined by levels in shallow wells
Water table: the level to which water will rise in a well drilled into the saturated zone

3. Confined Aquifer Systems
Confined aquifer: an aquifer that is overlain by a relatively impermeable unit such that the aquifer is under pressure and the water level rises above the confined unit
Potentiometric surface: in a confined aquifer, the hydrostatic pressure level of water in the aquifer, defined by the water level that occurs in a lined penetrating well

4. Special Aquifer Systems
Leaky confined aquifer: represents a stratum that allows water to flow from above through a leaky confining zone into the underlying aquifer
Perched aquifer: occurs when an unconfined water zone sits on top of a clay lens, separated from the main aquifer below

5. Ground Water Hydraulics
Hydraulic conductivity, K, is an indication of an aquifer’s ability to transmit water
Typical values:
10-2 to 10-3 cm/sec for Sands
10-4 to 10-5 cm/sec for Silts
10-7 to 10-9 cm/sec for Clays

6. Ground Water Hydraulics
Transmissivity (T) of Confined Aquifer
-The product of K and the saturated thickness of the aquifer T = Kb
- Expressed in m2/day or ft2/day
- Major parameter of concern
- Measured thru a number of tests - pump, slug, tracer

7. Ground Water Hydraulics
Intrinsic permeability (k)
Property of the medium only, independent of fluid properties
Can be related to K by:
K = k(g/µ)
where: µ = dynamic viscosity
 = fluid density
g = gravitational constant

8. Storage Coefficient S = Vol/ (AsH)
Relates to the water-yielding capacity of an aquifer
S = Vol/ (AsH)
It is defined as the volume of water that an aquifer releases from or takes into storage per unit surface area per unit change in piezometric head - used extensively in pump tests.
For confined aquifers, S values range between to 0.005
For unconfined aquifers, S values range between 0.07 and 0.25, roughly equal to the specific yield

9. Regional Aquifer Flows are Affected by Pump Centers
Streamlines and Equipotential lines

10. Derivation of the Dupuit Equation - Unconfined Flow

11. Dupuit Assumptions
For unconfined ground water flow Dupuit developed a theory that allows for a simple solution based off the following assumptions:
1) The water table or free surface is only
slightly inclined
2) Streamlines may be considered horizontal
and equipotential lines, vertical
3) Slopes of the free surface and hydraulic
gradient are equal

12. Derivation of the Dupuit Equation
Darcy’s law gives one-dimensional flow per unit width as:
q = -Kh dh/dx
At steady state, the rate of change of q with distance is zero, or
d/dx(-Kh dh/dx) = 0
OR (-K/2) d2h2/dx2 = 0
Which implies that,
d2h2/dx2 = 0

13. Dupuit Equation Integration of d2h2/dx2 = 0 yields h2 = ax + b
Where a and b are constants. Setting the boundary
     condition h = ho at x = 0, we can solve for b
b = ho2
Differentiation of h2 = ax + b allows us to solve for a,
a = 2h dh/dx
And from Darcy’s law,
hdh/dx = -q/K

14. Dupuit Equation So, by substitution h2 = h02 – 2qx/K
Setting h = hL2 = h02 – 2qL/K
Rearrangement gives
q = K/2L (h02- hL2) Dupuit Equation
Then the general equation for the shape of the parabola is
h2 = h02 – x/L(h02- hL2) Dupuit Parabola
However, this example does not consider recharge to the aquifer.

15. Cross Section of Flow q

16. Adding Recharge W - Causes a Mound to Form
Divide

17. Dupuit Example Example: 2 rivers 1000 m apart K is 0.5 m/day
average rainfall is 15 cm/yr
evaporation is 10 cm/yr
water elevation in river 1 is 20 m
water elevation in river 2 is 18 m
Determine the daily discharge per meter width into each
River.

18. Example L = 1000 m Dupuit equation with recharge becomes
h2 = h02 + (hL2 - h02) + W(x - L/2)
If W = 0, this equation will reduce to the parabolic
Equation found in the previous example, and
q = K/2L (h02- hL2) + W(x-L/2)
Given:
L = 1000 m
K = 0.5 m/day
h0 = 20 m
hL= 28 m
W = 5 cm/yr = x 10-4 m/day

19. Example For discharge into River 1, set x = 0 m
q = K/2L (h02- hL2) + W(0-L/2)
= [(0.5 m/day)/(2)(1000 m)] (202 m2 – 18 m2 ) +
(1.369 x 10-4 m/day)(-1000 m / 2)
q = – 0.05 m2 /day
The negative sign indicates that flow is in the opposite direction
From the x direction. Therefore,
q = 0.05 m2 /day into river 1

20. Example For discharge into River 2, set x = L = 1000 m:
q = K/2L (h02- hL2) + W(L-L/2)
= [(0.5 m/day)/(2)(1000 m)] (202 m2 – 18 m2 ) +
(1.369 x 10-4 m/day)(1000 m –(1000 m / 2))
q = m2/day into River 2
By setting q = 0 at the divide and solving for xd, the
water divide is located m from the edge of
River 1 and is 20.9 m high

21. Flow Nets - Graphical Flow Tool
Q = KmH / n
n = # head drops
m= # streamtubes
K = hyd cond
H = total head drop

22. Flow Net in Isotropic Soil
Portion of a flow net is shown below Y
Stream tube F
Curvilinear Squares

23. Flow Net Theory Streamlines Y and Equip. lines  are .
Streamlines Y are parallel to no flow boundaries.
Grids are curvilinear squares, where diagonals cross at right angles.
Each stream tube carries the same flow.

24. Seepage Flow under a Dam