GEO 435
Introduction to Groundwater Modeling
Problem Set 1 – Darcy’s Law Review
Due Jan. 22, 2016
1. Explain why fine-grained granular materials have lower hydraulic conductivity than
coarse-grained granular materials. (3)
2. A farm overlies a sandstone aquifer. In map area, the farm is 1 mile square with sides
oriented N-S and E-W. The aquifer underneath it is 65 ft thick in the vertical direction
and has an average horizontal hydraulic conductivity of Kx=Ky=25 ft/day and an effective
porosity of 0.16. Layers above and below the sandstone have K values several orders of
magnitude smaller. Flow in the aquifer is horizontal, and the magnitude of the average
hydraulic gradient in the area is |dh/dx|=0.006. Groundwater flow is about due east.
a. Estimate the discharge rate of water (Q) under the farm property in the aquifer.
(5)
b. Estimate the specific discharge (q). (3)
c. Estimate the average linear velocity (𝑣̅ ). (3)
3. Calculate ground water flow rate per unit width (m3/(s*m)) between the river and the
drainage channel shown in Figure 1 below. The average elevation of the water surface in
the river is 144.60 meters, and in the channel 142.20 meters. The hydraulic conductivity
of the confined intergranualr aquifer developed in medium alluvial sand is 3.5x10-4 m/s.
The hydrogeologic cross-section in Figure 2 shows the relationship between the aquifer,
the overlying silty clay (aquitard) and the underlying dense (impermeable) clay. Also
calculate the position of the potentiometric surface at a midpoint between the river and
the channel. Use appropriate significant figures. (10)
Figure 1: Plan view of
the river and the
drainage channel
Figure 2: Hydrogeologic crosssection between the river and the
drainage channel shown in Figure 1
4. Consider the map of three well locations shown in Figure 3. The hydraulic conductivity
in the north-south direction is 20 m/day, and the hydraulic conductivity in the east-west
direction is 5 m/day. Each well is screened in the same horizontal aquifer. The ground
surface elevations and water depths at these wells are listed in Table 1.
a. Complete the table, listing the hydraulic head at each well. (3)
b. Calculate the components of the specific discharge in the north-south and the eastwest directions. (4)
c. Make a scaled sketch of the N-S and E-W components of the specific discharge
and draw their vector sum to show the total specific discharge vector |𝑞⃗|. (2)
d. Calculate the magnitude of the specific discharge vector |𝑞⃗|. (5)
Figure 3
Table 1: Well data for problem 4.
Ground Elevation
Well
(m)
A
102.45
B
98.73
C
105.65
Depth to Water
(m)
11.59
10.23
13.19
REMINDER: PROJECT TOPICS ARE DUE JANUARY 29.
Head
(m)