Fluid Mechanics and Hydraulic Machinery
Fluid Mechanics and Hydraulic Machinery tests properties of fluids, pressure measurement, flow continuity and energy, and the selection of pumps and turbines for a given head and discharge.
Core rules
- Density ρ = m/V; specific gravity = ρfluid ÷ ρwater; viscosity is resistance to shear (dynamic μ in Pa·s, kinematic ν = μ/ρ).
- Hydrostatic pressure p = ρgh, acting equally in all directions (Pascal's law). Gauge pressure = absolute − atmospheric.
- Continuity for incompressible flow: A₁V₁ = A₂V₂.
- Bernoulli (steady, incompressible, frictionless, along a streamline): p/ρg + V²/2g + z = constant.
- Reynolds number Re = ρVD/μ; below about 2000 the flow is laminar, above about 4000 turbulent.
- Pumps add energy: centrifugal pumps suit large discharge at moderate head and must be primed; reciprocating pumps suit high head and small discharge. Cavitation occurs when local pressure falls below vapour pressure.
- Turbines: Pelton (impulse, high head, low flow), Francis (reaction, medium head), Kaplan (reaction, low head, high flow). A draft tube recovers kinetic energy at runner exit.
Worked example
Water stands 5 m deep in a tank. Take ρ = 1000 kg/m³ and g = 9.81 m/s². p = 1000 × 9.81 × 5 = 49,050 Pa ≈ 49 kPa gauge. A pipe of 100 mm bore carries water at 1 m/s and reduces to 50 mm bore. Since A₁/A₂ = 4, continuity gives V₂ = 4 m/s.
Traps that cost marks
Using 1000 kg/m³ for oil or mercury; quoting gauge pressure as absolute; applying Bernoulli across a pump or ignoring friction losses; choosing a Kaplan turbine for a high-head site; forgetting that a centrifugal pump loses prime if air enters the suction.