Question

An aquifer has a cross-sectional area of 10 $m^2$ and a hydraulic conductivity of 0.25 cm/s. The volume of water that will flow per second through the aquifer for a hydraulic gradient of 0.04 is _____ $cm^3$. (Round off to three decimal places)

Answer 1

Correct Answer: 1000

Calculating the Volume of Water Flowing Through the Aquifer Using Darcy's Law 

Step 1: Understanding the Formula

Darcy's Law is given by the equation:

\[ Q = K \cdot A \cdot i \]

Where:

• Q is the volume of water per second (discharge).
• K is the hydraulic conductivity (0.25 cm/s).
• A is the cross-sectional area (10 m²).
• i is the hydraulic gradient (0.04).

Step 2: Convert the Cross-Sectional Area

The given cross-sectional area is in square meters (m²). We need to convert it to square centimeters (cm²):

\[ A = 10 \, \text{m}^2 = 10 \times 10^4 \, \text{cm}^2 = 100000 \, \text{cm}^2 \]

Step 3: Substitute the Values into the Formula

Substitute the given values into Darcy's Law:

\[ Q = 0.25 \, \text{cm/s} \cdot 100000 \, \text{cm}^2 \cdot 0.04 \]

Now, calculate the volume of water flowing per second:

\[ Q = 1000 \, \text{cm}^3/\text{s} \]

Final Answer:

The volume of water flowing per second is: 1000 cm³/s (rounded to three decimal places).