Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Permeability and seepage analysis
Question Statement:
In a falling head permeameter test, the initial head is 0.30 m. The head drops to 0.10 m in 40 min. The permeability of a soil sample, 0.06 m high and 50 × 10⁻⁴ m² in cross-sectional area, is found to be 1.0 × 10⁻⁶ m s⁻¹. The size of the stand pipe in m² is
Options:
(A) 1.82
(B) 1.82 × 10⁻¹
(C) 1.82 × 10⁻²
(D) 1.82 × 10⁻⁴
Official Answer Key:
D
Step-by-Step Solution & Explanation
Falling-head permeability formula: k = (a·L)/(A·t)·ln(h1/h2), where a = standpipe cross-section, A = 50×10⁻⁴ m² (sample area), L = 0.06 m (sample height), t = 40×60 = 2400 s. Solving for a: a = k·A·t / [L·ln(h1/h2)] = (1.0×10⁻⁶ × 50×10⁻⁴ × 2400) / (0.06 × ln(3)) = (1.2×10⁻⁵) / (0.06 × 1.0986) = 1.2×10⁻⁵/0.0659 = 1.82×10⁻⁴ m², matching option (D).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.