Question

Two vertical wells penetrating a confined aquifer are 200 m apart. The water surface elevations in these wells are 35 m and 40 m above a common reference datum. The discharge per unit area through the aquifer is 0.05 m/day. Using Darcy’s law, the coefficient of permeability is _________ m/day.

Hint:

Darcy’s law can be used to calculate the coefficient of permeability by rearranging the formula to isolate \(K\). It depends on the discharge per unit area, the distance between the wells, and the difference in water elevations.

Answer 1

Correct Answer: 2

Step 1: Understand Darcy's Law.
Darcy’s law relates the discharge through an aquifer to the hydraulic conductivity (permeability), the cross-sectional area, and the hydraulic gradient. It is given by: \[ Q = K \cdot A \cdot \frac{\Delta h}{L}, \] where: - \(Q\) is the discharge (m\(^3\)/day), - \(K\) is the coefficient of permeability (m/day), - \(A\) is the cross-sectional area of flow (m\(^2\)), - \(\frac{\Delta h}{L}\) is the hydraulic gradient, where \(\Delta h\) is the difference in water surface elevations and \(L\) is the distance between the wells. Step 2: Rearranging Darcy’s Law.
We are given the discharge per unit area (\(Q/A = 0.05\) m/day), so we can solve for \(K\): \[ K = \frac{Q/A \cdot L}{\Delta h}. \] Step 3: Substituting the given values.
We know: - \(Q/A = 0.05\) m/day, - \(L = 200\) m, - \(\Delta h = 40 \, \text{m} - 35 \, \text{m} = 5\) m. Substituting into the equation: \[ K = \frac{0.05 \times 200}{5} = 0.4 \, \text{m/day}. \] Step 4: Conclusion.
The coefficient of permeability is 0.4 m/day.