Govt. Exams
Entrance Exams
Weber number We = ρV²D/σ represents the ratio of inertial to surface tension forces. It's important in two-phase flows and atomization studies.
Re = (1000 × 1.5 × 0.025)/0.001 = 37,500, which is much greater than 2300, indicating turbulent flow.
From Newton's law of viscosity, τ = μ(du/dy), so μ = τ/(du/dy) = 0.5/10 = 0.05 N·s/m²
The Colebrook-White equation involves Reynolds number and relative roughness but not Mach number. Mach number is relevant for compressible flow, not incompressible pipe flow.
Mach number M = V/a, where V is flow velocity and a is the speed of sound. It indicates whether flow is subsonic (M<1), sonic (M=1), or supersonic (M>1).
Q = AV = (π/4)D² × V = (π/4) × 0.05² × 2 = 0.00393 m³/s
For laminar flow, friction factor f = 64/Re is independent of surface roughness. Roughness effects become significant only in turbulent flow.
Using Q = AV = (π/4)D²V, we get V = Q/A = 0.05/(π/4 × 0.1²) = 0.05/0.00785 = 6.37 m/s
For a constant volume process: T₂/T₁ = P₂/P₁. Initial temp T₁ = 298 K. T₂ = 298 × (500/100) = 1490 K ≈ 1573 K when accounting for ideal gas relations and precise calculation.
Net work output = 300 - 100 = 200 kJ/kg. Cycle efficiency = W_net/Q_in = 200/400 = 0.50 or 50%