Permeability MCQ with answer and solution

Concept

Seepage Velocity

Formula

n = e / (1 + e) and Vs = V / n

Step-by-step solution

1. Calculate porosity: n = 0.5 / (1 + 0.5) = 1/3 2. Calculate seepage velocity: Vs = 0.01 / (1/3) = 0.03 cm/s

Explanation

To find the seepage velocity, we first calculate porosity (n) using the void ratio (e = 0.5): n = e / (1 + e) = 0.5 / 1.5 = 1/3. Seepage velocity (Vs) is equal to the superficial/discharge velocity (V) divided by porosity (n): Vs = 0.01 / (1/3) = 0.03 cm/s. Since water only flows through the open gaps (voids) instead of the total area, it moves faster than the superficial velocity.

Shortcut

Use the shortcut formula Vs = V × (1 + 1/e). When void ratio e = 0.5, 1/e = 2, so seepage velocity is simply 3 times the superficial velocity (Vs = 3 × V).

Common mistake

Students often mistakenly use the void ratio (e) directly instead of converting it to porosity (n), incorrectly calculating seepage velocity as Vs = V / e (0.01 / 0.5 = 0.02 cm/s) or Vs = V × e (0.005 cm/s).