Question

Water flows through a vertical sand column of cross‐sectional area 4000 mm$^2$ and length 300 mm. For a water head of 600 mm, the seepage quantity is 100 mm$^3$/min. Find the hydraulic conductivity of the sand column (mm/min), rounded to three decimal places.

Hint:

Hydraulic conductivity is proportional to discharge and inversely proportional to hydraulic gradient and area. Use Darcy’s law directly in consistent units.

Answer 1

Correct Answer: 0.012

Using Darcy’s law: \[ Q = k \, A \, \frac{h}{L} \] Given: \[ Q = 100\ \text{mm}^3/\text{min},\quad A = 4000\ \text{mm}^2,\quad h = 600\ \text{mm},\quad L = 300\ \text{mm}. \] Substitute: \[ 100 = k \times 4000 \times \frac{600}{300} \] \[ 100 = k \times 4000 \times 2 = 8000k \] \[ k = \frac{100}{8000} = 0.0125\ \text{mm/min} \] Rounded to three decimal places: \[ \boxed{0.013\ \text{mm/min}} \]