Question

The permeability of a soil sample is 2 x 10$^{-4}$ cm/s. If the hydraulic gradient is 0.5, what is the seepage velocity (in cm/s) given a porosity of 0.4?

• A. 1 x 10$^{-4}$
• B. 2 x 10$^{-4}$
• C. 2.5 x 10$^{-4}$
• D. 1 x 10$^{-3}$

Hint:

Seepage velocity accounts for porosity, making it higher than Darcy’s velocity.

Answer 1

The Correct Option is C

Step 1: Understand Darcy’s law 
Darcy’s velocity (q) = Permeability ($k$) $\times$ Hydraulic gradient ($i$). 
Given: $k = 2 \times 10^{-4}$ cm/s, $i = 0.5$. 
Step 2: Calculate Darcy’s velocity 
$q = k \times i = 2 \times 10^{-4} \times 0.5 = 1 \times 10^{-4}$ cm/s. 
Step 3: Relate to seepage velocity 
Seepage velocity ($v_s$) = $\frac{\text{Darcy’s velocity}}{\text{Porosity}}$. 
Given porosity ($n$) = 0.4. 
$v_s = \frac{1 \times 10^{-4}}{0.4} = 2.5 \times 10^{-4}$ cm/s.