Fluid Mechanics and Hydraulic Systems
Fluid Mechanics and Hydraulic Systems covers continuity, energy and momentum, pipe friction, pump selection, cavitation, and hydraulic circuit behaviour. The exam often combines a Bernoulli balance with a pump power or NPSH check, so keep units and datum consistent.
Core rules
- Continuity: Q = A1V1 = A2V2 for steady incompressible flow.
- Energy: p1/ρg + V1²/2g + z1 + hp = p2/ρg + V2²/2g + z2 + hf + hm.
- Reynolds number Re = ρVD/μ; laminar below about 2000, turbulent above about 4000 in pipes.
- Darcy–Weisbach: hf = f(L/D)(V²/2g); minor losses hm = K(V²/2g).
- Pump shaft power = ρgQH/η; system head curves set the operating point.
- NPSH available must exceed NPSH required with margin to avoid cavitation.
Worked example
Water (ρ = 1000 kg/m³) is pumped at 0.01 m³/s through 100 m of 0.1 m diameter pipe with f = 0.02 and pump efficiency 0.70. Find friction head and shaft power. Area A = π(0.05)² = 0.007854 m², so V = 0.01/0.007854 = 1.273 m/s. Then hf = 0.02 × (100/0.1) × (1.273²/(2 × 9.81)) = 1.65 m. Shaft power = ρgQH/η = 1000 × 9.81 × 0.01 × 1.65/0.70 = 231 W. If minor losses exist, add them before calculating power.
Traps
- Using pipe diameter as radius in the area term.
- Mixing gauge and absolute pressures in NPSH calculations.
- Omitting minor losses in short, fittings-heavy systems.
- Using pump efficiency upside down in the power equation.
- Ignoring that cavitation risk rises with temperature and suction lift.