Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Laminar and turbulent flow in pipes, Darcy–Weisbach and Hazen–Williams equations
Question Statement:
A piston with 50 mm diameter and length 50 mm is to be moved at a velocity of 0.25 m s⁻¹ in a hydraulic cylinder with 50.2 mm diameter. The cylinder is full of oil with a kinematic viscosity of 9×10⁻⁴ m² s⁻¹ and a density of 880 kg m⁻³. Assuming pressure difference between inside and outside of the cylinder as zero, the force required to move the piston is
Options:
(A) 7.772 N
(B) 15.543 N
(C) 76.243 N
(D) 152.476 N
Official Answer Key:
B
Step-by-Step Solution & Explanation
With zero pressure difference, flow in the thin annular gap is simple Couette (drag) flow: F = μAV/t, where t = radial gap = (50.2−50.0)/2 = 0.10 mm, A = π·D_piston·L = π(0.05)(0.05) = 7.854×10⁻³ m². μ = ν·ρ = 9×10⁻⁴ × 880 = 0.792 Pa·s. F = 0.792 × 7.854×10⁻³ × 0.25 / (1.0×10⁻⁴) = 15.543 N. (D) results from using the diameter directly as the gap rather than the (dia. difference)/2.
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