Question

A constant-head permeability test was performed on a vertical sand column of height 40 cm and cross-sectional area of 25 cm². During the test, when the loss of head was 50 cm, the volume of water collected in 2 minutes was 300 cm³. Applying Darcy's law, the calculated coefficient of permeability of the sand column is \(\underline{\hspace{0cm}}\) cm/sec. (round off to 2 decimal places).

Hint:

Darcy's law relates the volume of water passed through a soil sample to its permeability. It can be used to calculate the coefficient of permeability.

Answer 1

Correct Answer: 0.08

Darcy's law is given by: \[ Q = K A \frac{\Delta h}{L} t, \] where:
- \( Q \) = volume of water (300 cm³),
- \( A \) = cross-sectional area of the column (25 cm²),
- \( \Delta h \) = head loss (50 cm),
- \( L \) = height of the column (40 cm),
- \( t \) = time (2 minutes = 120 seconds),
- \( K \) = coefficient of permeability.
Rearranging to solve for \( K \): \[ K = \frac{Q L}{A \Delta h t} = \frac{300 \times 40}{25 \times 50 \times 120} = 0.08 \, \text{cm/sec}. \] Thus, the coefficient of permeability is \( \boxed{0.08} \) cm/sec.