Subtopic: Steady and unsteady flow in confined and unconfined aquifers
Question Statement:
A fully penetrating well of diameter $30\text{ cm}$ penetrates a confined aquifer of thickness $20\text{ m}$. Under steady pumping at a rate of $2400\text{ m}^3/\text{day}$, the drawdowns measured in two observation wells located at radial distances of $15\text{ m}$ and $60\text{ m}$ from the pumping well are $2.4\text{ m}$ and $0.8\text{ m}$ respectively. The hydraulic conductivity of the aquifer is ________ $\text{m/day}$ (round off to two decimal places).
Answer Key:
16.55
Step-by-Step Solution & Explanation
For steady radial flow to a well in a confined aquifer, Thiem's equation is:
$Q = \frac{2 \pi k b (s_1 - s_2)}{\ln(r_2 / r_1)}$
Rearranging for hydraulic conductivity $k$:
$k = \frac{Q \ln(r_2 / r_1)}{2 \pi b (s_1 - s_2)}$
Given values:
- $Q = 2400\text{ m}^3/\text{day}$
- $b = 20\text{ m}$
- $r_1 = 15\text{ m}, \quad s_1 = 2.4\text{ m}$
- $r_2 = 60\text{ m}, \quad s_2 = 0.8\text{ m}$
- $\ln(r_2/r_1) = \ln(60/15) = \ln(4) = 1.38629$
Substituting:
$k = \frac{2400 \times 1.38629}{2 \times \pi \times 20 \times (2.4 - 0.8)} = \frac{3327.106}{201.062} = 16.547\text{ m/day} \approx 16.55\text{ m/day}$