Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Laminar and turbulent flow in pipes, Darcy–Weisbach and Hazen–Williams equations
Question Statement:
The apparent wall shear stress in a 0.6 m long pipe line carrying refined oil is 12.5 Pa. If the pressure drop along the length is 300 Pa and flow rate is 0.25 m³ s⁻¹, the absolute viscosity of oil in 10⁻³ Pa s is ______________ (rounded off to 3 decimal places).
Official Answer Key:
4.902 to 4.908
Step-by-Step Solution & Explanation
For fully developed pipe flow, wall shear stress relates to pressure drop and pipe radius by τ_w = ΔP·R/(2L). Solving for the pipe radius: R = 2×τ_w×L/ΔP = 2×12.5×0.6/300 = 15/300 = 0.05 m → D = 0.10 m.
Mean velocity: V = Q/A = 0.25/[π(0.05)²] = 0.25/0.007854 = 31.85 m/s.
For laminar Newtonian pipe flow, wall shear also equals τ_w = 4μV/R (Hagen-Poiseuille relation), so:
μ = τ_w×R/(4V) = 12.5×0.05/(4×31.85) = 0.625/127.39 = 0.004906 Pa·s = 4.906 × 10⁻³ Pa·s. (Cross-checked independently via the Hagen-Poiseuille pressure-drop form ΔP=32μLV/D², which gives the identical result.) Within official range 4.902–4.908.
Section 5 — Irrigation and Drainage Engineering
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