Question

In a constant head permeameter, having cross-sectional area of $20 \, \text{cm}^2$, when the flow was taking place under a hydraulic gradient of $0.5$, the amount of water collected is $1200 \, \text{cm}^3$ in $60 \, \text{sec}$. The permeability of the soil is:

• A. 0.002 cm/sec
• B. 0.02 cm/sec
• C. 0.2 cm/sec
• D. 2 cm/sec

Hint:

Always apply Darcy's law directly for constant head permeability tests: $k = \dfrac{Q}{A \cdot i \cdot t}$.

Answer 1

The Correct Option is C

Step 1: Recall Darcy's law.
For constant head test, \[ Q = k \cdot i \cdot A \cdot t \] where, $Q =$ volume of water collected, $k =$ coefficient of permeability, $i =$ hydraulic gradient, $A =$ cross-sectional area, $t =$ time.

Step 2: Substitute given values.
\[ Q = 1200 \, \text{cm}^3, A = 20 \, \text{cm}^2, i = 0.5, t = 60 \, \text{s}. \]

Step 3: Formula for $k$.
\[ k = \frac{Q}{A \cdot i \cdot t} = \frac{1200}{20 \cdot 0.5 \cdot 60}. \] \[ = \frac{1200}{600} = 0.2 \, \text{cm/sec}. \]

Step 4: Conclusion.
Thus, the permeability of the soil is $0.2 \, \text{cm/sec}$.