Question

A well fully penetrates a \(30\) m thick confined aquifer. After a long period of pumping at a constant rate of \(0.06\) m\(^3\)/s, drawdowns of \(3.6\) m and \(2.0\) m are found at distances \(60\) m and \(120\) m away from the well, respectively. The hydraulic conductivity of the aquifer is \(n \times 10^{-4}\) m/s. The value of \(n\) is ________ (Rounded off to two decimal places)

Hint:

Apply the Thiem equation for a confined aquifer using the two drawdown observations.

Answer 1

Correct Answer: 1.38

Step 1: Write the Thiem equation for steady radial flow in a confined aquifer.
\[ Q = \frac{2\pi K b (s_1-s_2)}{\ln(r_2/r_1)} \] where \(b\) is the aquifer thickness, and \(s_1\), \(s_2\) are the drawdowns at radii \(r_1\), \(r_2\).

Step 2: List the given values.
\(Q=0.06\) m\(^3\)/s, \(b=30\) m, \(s_1=3.6\) m at \(r_1=60\) m, \(s_2=2.0\) m at \(r_2=120\) m.

Step 3: Rearrange for \(K\) and substitute.
\[ K = \frac{Q\ln(r_2/r_1)}{2\pi b(s_1-s_2)} = \frac{0.06 \times \ln(2)}{2\pi \times 30 \times (3.6-2.0)} \] \[ K = \frac{0.06\times0.6931}{2\pi\times30\times1.6} = \frac{0.04159}{301.59} \]
Step 4: Compute the numeric value.
\[ K \approx 1.38\times10^{-4}\ \text{m/s} \]
Final Answer:
The aquifer's hydraulic conductivity works out close to \(1.38\times10^{-4}\) m/s. \[ \boxed{n \approx 1.38} \]