Question

In a field test of a formation having a porosity of 25%, the hydraulic gradient was found to be 0.04, and the velocity of a tracer added to the ground water was 6 cm/h. The permeability of the aquifer is about:

• A. 1 cm/s
• B. 4 cm/s
• C. 0.004 cm/s
• D. 0.01 cm/s

Hint:

For calculating permeability using Darcy’s Law, the relationship between the velocity, hydraulic gradient, and permeability is key. Ensure the units are consistent.

Answer 1

The Correct Option is C

The permeability of the aquifer \( k \) can be calculated using Darcy's Law: \[ V = \frac{k \cdot i}{\mu} \] Where: - \( V \) = velocity of the tracer (6 cm/h) - \( i \) = hydraulic gradient (0.04) - \( k \) = permeability of the aquifer - \( \mu \) = unit length (since this is a typical field test, it can be assumed as 1) Rearranging the equation to solve for \( k \), we get: \[ k = \frac{V}{i} = \frac{6 \, \text{cm/h}}{0.04} \] Converting cm/h to cm/s, we get: \[ k = 0.004 \, \text{cm/s} \]
Final Answer: \[ \boxed{0.004 \, \text{cm/s}} \]