Mechanical Engineering - Fluid Mechanics, Turbo-machinery and Machine Design
Fluid Mechanics, Turbo-machinery and Machine Design tests continuity, Bernoulli, pipe friction, pump and turbine similarity, cavitation, and basic stress and fatigue design. Numerical questions are usually power, head, specific speed and shaft diameter.
Fluid flow
Continuity: A₁V₁ = A₂V₂. Bernoulli with losses: p₁/ρg + V₁²/2g + z₁ = p₂/ρg + V₂²/2g + z₂ + h_L. Darcy–Weisbach: h_f = fLV²/(2gD). Reynolds number determines laminar or turbulent regime.
Turbo-machinery
Pump power P = ρgQH/η. Specific speed identifies impeller type: low N_s radial, high N_s axial. Cavitation occurs when local pressure falls below vapour pressure; NPSH_available must exceed NPSH_required. Affinity laws: Q ∝ N, H ∝ N², P ∝ N³.
Machine design
Use maximum shear stress or distortion energy theory for combined stresses. For a circular shaft under torque and bending, equivalent torque T_e = √(M² + T²). Fatigue design uses S–N curves, endurance limit and stress concentration factors.
Worked example
A pump delivers 0.05 m³/s at 30 m head with η = 0.75 and ρ = 1000 kg/m³. P = 1000 × 9.81 × 0.05 × 30/0.75 = 19,620 W ≈ 19.6 kW. If speed is doubled at constant impeller diameter, flow becomes 0.10 m³/s, head becomes 120 m, and power becomes about 156.8 kW, ignoring efficiency change.
Traps
Using gauge instead of absolute pressure; forgetting pump efficiency; mixing manometric head with static head; undersizing NPSH; and applying P ∝ N² instead of N³.