Fluid Mechanics
Fluid Mechanics
ESE Prelims Paper II tests property definitions, hydrostatics, control-volume analysis, pipe losses, dimensional analysis, and turbomachinery selection. Most numerical items reduce to one conservation equation plus a loss model.
Core rules
- Hydrostatic pressure: p = p₀ + ρgh; gauge pressure excludes atmospheric. The centre of pressure lies below the centroid for a submerged vertical plane.
- Continuity for steady flow: ρAV = constant. Bernoulli along a streamline for steady, incompressible, inviscid flow: p/ρg + V²/2g + z = constant. In real flow add head loss and pump head; do not apply Bernoulli across a lossy component without them.
- Reynolds number Re = ρVD/μ. Laminar pipe friction f = 64/Re; turbulent f from the Moody chart or Colebrook equation. Darcy–Weisbach loss h_f = fLV²/(2gD).
- Pump affinity laws: Q ∝ N, H ∝ N², P ∝ N³. NPSH available must exceed NPSH required to avoid cavitation.
Worked example
Water flows at V = 2 m/s through a 100 m long, 0.1 m diameter pipe with f = 0.02. Head loss h_f = fLV²/(2gD) = 0.02 × 100 × 4 / (2 × 9.81 × 0.1) = 8 / 1.962 = 4.08 m. Check Re: with ρ = 1000 kg/m³ and μ = 10⁻³ Pa·s, Re = 1000 × 2 × 0.1 / 10⁻³ = 2 × 10⁵, so turbulent flow is consistent with the assumed f.
Traps
Using gauge and absolute pressures interchangeably; forgetting the kinetic-energy correction factor α; using radius instead of diameter in A and D; applying Bernoulli across a pump or valve without head terms; and confusing NPSH margin with suction lift.