Question

A confined sandstone aquifer with a uniform cross-sectional area of 7 m² and a hydraulic conductivity of 2 m/s, transmits water across a hydraulic gradient of 3.2. Assuming steady state Darcian flow, the volumetric flow rate through the aquifer is .......... m³/s (answer in one decimal place).

Hint:

In Darcian flow, the flow rate is directly proportional to the hydraulic conductivity, cross-sectional area, and hydraulic gradient.

Answer 1

Correct Answer: 44.8

Step 1: Understand the equation for Darcian flow.
The volumetric flow rate \( Q \) through the aquifer can be calculated using Darcy's law: \[ Q = K \cdot A \cdot i \] where: - \( K \) is the hydraulic conductivity (2 m/s), - \( A \) is the cross-sectional area (7 m²), - \( i \) is the hydraulic gradient (3.2).

Step 2: Substituting the values into Darcy's law.
Substituting the known values into the equation: \[ Q = 2 \, \text{m/s} \times 7 \, \text{m}^2 \times 3.2 \] \[ Q = 44.8 \, \text{m}^3/\text{s} \]

Step 3: Conclusion.
The volumetric flow rate through the aquifer is 44.8 m³/s.