Question

In a groundwater model, the hydraulic conductivity of the aquifer is 10 m/day and the cross-sectional area perpendicular to the flow is 20 m$^2$. The hydraulic gradient is 0.006. Calculate the flow rate (Q) using the Darcy's Law.

• A. 1 m$^3$/day
• B. 1.2 m$^3$/day
• C. 2 m$^3$/day
• D. 0.12 m$^3$/day

Hint:

• Darcy's Law for groundwater flow: Q = K $\times$ A $\times$ i
• Q = Flow rate
• K = Hydraulic conductivity
• A = Cross-sectional area of flow
• i = Hydraulic gradient (change in head per unit distance)
• Substitute the given values: K = 10 m/day, A = 20 m$^2$, i = 0.006.
• Q = 10 $\times$ 20 $\times$ 0.006 = 200 $\times$ 0.006 = 1.2 m$^3$/day.

Answer 1

The Correct Option is B

To calculate the flow rate (Q) using Darcy's Law, we need to understand the law and the given parameters.

1. Understanding the Concepts:

- Darcy's Law: Describes the flow of a fluid through a porous medium. The equation is: \[ Q = -K \cdot A \cdot i \] Where: - Q is the flow rate (discharge) - K is the hydraulic conductivity - A is the cross-sectional area perpendicular to the flow - i is the hydraulic gradient

2. Given Values:

\( K = 10 \text{ m/day} \)
\( A = 20 \text{ m}^2 \)
\( i = 0.006 \)

3. Calculating the Flow Rate (Q):

Substituting the given values into Darcy's Law: \[ Q = 10 \text{ m/day} \times 20 \text{ m}^2 \times 0.006 = 1.2 \text{ m}^3/\text{day} \]

Final Answer:

The flow rate (Q) is 1.2 m$^3$/day.