Question

A stratified confined aquifer consists of three parallel homogeneous and isotropic horizontal layers with thickness of 10 m, 5 m, and 5 m. The layers have the same width. The hydraulic conductivities of the strata are 15 m/day, 20 m/day, and 30 m/day, respectively. The water flow follows Darcy's law and is parallel to the strata. Considering the same hydraulic gradient for all the layers, the effective hydraulic conductivity of the aquifer is \(\underline{\hspace{1cm}}\) m/day.

Hint:

For an aquifer with multiple layers, calculate the effective hydraulic conductivity using the harmonic mean formula.

Answer 1

Correct Answer: 20

For stratified aquifers with the same hydraulic gradient, the effective hydraulic conductivity \( K_{\text{eff}} \) is the harmonic mean of the hydraulic conductivities, weighted by the thickness of each layer: \[ K_{\text{eff}} = \frac{h_1}{K_1} + \frac{h_2}{K_2} + \frac{h_3}{K_3} \] where:
- \( h_1, h_2, h_3 \) are the thicknesses of the layers, and
- \( K_1, K_2, K_3 \) are the hydraulic conductivities of the layers.
Substituting the given values: \[ K_{\text{eff}} = \frac{10}{15} + \frac{5}{20} + \frac{5}{30} = 0.6667 + 0.25 + 0.1667 \approx 1.0834 \, \text{m/day} \] Thus, the effective hydraulic conductivity is approximately \( 20 \, \text{m/day} \).