ENCE 621/489G, Midterm 2

1. Given the arrangement of soil layers in the following figure and the hydraulic conductivity, the thickness and width of layers, and the porosity of each layer in the following table:

   

   Layer No.	Hydraulic conductivity (cm/h)	Thickness (cm)	Width (cm)	Porosity
   1	5.76	10	10	0.45
   2	1.54 × 10-3	10	10	0.05
   3	0.14	10	10	0.25
   4	0.14	10	10	0.25
   5	0.04	10	10	0.15
   6	0.24	50	20	0.35

   Calculate the averaged hydraulic conductivity in the horizontal and vertical directions.
   

2. A graduate student conducted a laboratory experiment in order to determine the hydraulic conductivity of an undisturbed soil sample, using a falling head permeameter (panel (a)) as shown in the following figure.

   

   The following is his measurements:

   • h₀ = 20 cm at time = 0 min
     
     
   • h₁ = 5 cm at time = 60 min
     
     
   • length of soil sample, L = 25 cm
     
     
   • diameter of soil sample, D = 10 cm
     
     
   • diameter of standing pipe, d = 2 cm
     
     

   Please estimate the hydraulic conductivity of the soil for the student. If one were to use a constant head permeameter (panel (b)) and a flow rate equal to the average of that used for the falling head permeameter to measure the hydraulic conductivity of the same soil sample, what would be the minimum length of the tube within which a standing water head of at least L + h will be needed?

3. Assuming steady-state, estimate the annual groundwater discharge from the semi-confined aquifer into the surface stream, Q (m³/m/yr), for the hillslope shown in the following figure:
   
   The annual rainfall of the study area is 1350 mm, of which 5% is estimated to be recharge to the groundwater, namely, semi-confined aquifer. Evapotranspiration is estimated at 55% of annual rainfall. The outcrop area of the semi-confined aquifer, between points A and B, is 100 m²/m. The horizontal distance between points C and D, is 10 km. The groundwater flow in the semi-confined aquifer is considered under steady state. Note that the above figure is vertically exaggerated.

4. The Cartesian coordinate system used by a hydrogeologist is 30^o counterclockwise from the major principal direction of hydraulic conductivity for the area of his interest. Laboratory data suggest that the hydraulic conductivity along the major principal direction is 3 × 10^-8 m/s and that along the minor is 3 × 10^-9 m/s. Determine the conductivity tensor in the hydrogeologist's Cartesian coordinate system. The hydraulic gradient along the x and y directions of the coordinate system are 0.01 and 0.002, respectively. What are the groundwater velocities in these directions?