Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Permeability and seepage analysis
Question Statement:
A soil sample of diameter 70 mm was used for constant head permeability test. The observed head loss was 80 mm in the soil sample length of 100 mm and water collected in one minute was 60 mL. The coefficient of permeability, in mm·s⁻¹, is __________. (Rounded off to 2 decimal places)
Official Answer Key:
0.31 to 0.33
Step-by-Step Solution & Explanation
For a constant head permeability test, Darcy’s law gives:
Q = k · i · A · t, where i = h/L
Rearranged:
k = (Q × L)/(A × h × t)
Step 1 — convert to consistent units (mm, s):
Volume collected Q = 60 mL = 60,000 mm³ in t = 60 s
Sample area A = (π/4)(70)² = 3848.45 mm²
L = 100 mm ; h = 80 mm
Step 2 — discharge rate:
q = 60,000/60 = 1000 mm³·s⁻¹
Step 3 — coefficient of permeability:
k = (q × L)/(A × h) = (1000 × 100)/(3848.45 × 80)
= 100,000/307,876
= 0.32 mm·s⁻¹
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