Fluid Mechanics and Hydraulic Machinery
What you must command
Fluid properties (density, viscosity, surface tension), hydrostatics, continuity, Bernoulli and energy equations, momentum principles, laminar and turbulent flow, Reynolds number, friction factor and head loss, flow measurement, and the operation of pumps and turbines (centrifugal, reciprocating, Pelton, Francis, Kaplan), including specific speed and cavitation.
Traps that appear in questions
- Bernoulli assumptions: steady, incompressible, frictionless, along a streamline. Adding a pump head changes the equation.
- Reynolds number: Re = ρVD/μ = VD/ν. Laminar below about 2000 in pipes, turbulent above about 4000.
- Head loss: Darcy–Weisbach h_f = fLV²/(2gD); friction factor depends on relative roughness and Re (Moody chart).
- Continuity: A₁V₁ = A₂V₂ for incompressible flow; velocity rises where area falls.
- Pump curves: operating point is the intersection of pump and system curves; cavitation occurs when NPSH available falls below NPSH required.
- Unit confusion: gauge vs. absolute pressure; head in metres of the flowing fluid.
Worked rule of thumb
For a venturi meter, Q = A₂·√(2gΔh/(1 − (A₂/A₁)²)). Example: A₁ = 0.01 m², A₂ = 0.005 m², Δh = 0.5 m. Ratio squared = 0.25, so denominator = 0.75; √(2·9.81·0.5/0.75) = √13.08 ≈ 3.62 m/s; Q = 0.005 × 3.62 ≈ 0.0181 m³/s. Note the discharge coefficient would reduce this in practice.
For pumps in series, heads add at the same flow; in parallel, flows add at the same head. This is a frequent qualitative question.