Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow through orifices, weirs and notches
Question Statement:
A cylindrical tank of 1.5 m diameter and 4 m height is filled with a liquid by a pipe of 2.5 cm internal diameter. The density and dynamic viscosity of the liquid are 1050 kg m⁻³ and 1.6×10⁻³ N s m⁻², respectively. If flow in the pipe is turbulent, the maximum time required to fill the tank is _______ hours.
Official Answer Key:
16.30 to 16.50
Step-by-Step Solution & Explanation
“Maximum time” ⇒ minimum velocity that still keeps the flow turbulent ⇒ Re = 4000.
Re = ρVD/μ ⇒ V = 4000 × 1.6×10⁻³/(1050 × 0.025) = 6.4/26.25 = 0.2438 m s⁻¹.
Pipe area a = (π/4)(0.025)² = 4.909×10⁻⁴ m² ⇒ Q = aV = 1.1968×10⁻⁴ m³ s⁻¹.
Tank volume V_t = (π/4)(1.5)²(4) = 7.0686 m³.
t = 7.0686/1.1968×10⁻⁴ = 59 062 s = 16.41 h — within the official range 16.30–16.50.
Common error: using Re = 2000 (laminar limit), which gives 32.8 h.
Section 5 — Irrigation and Drainage Engineering
10 questions · 15 marks
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