Fluid Mechanics and Hydraulic Machinery
Fluid Mechanics and Hydraulic Machinery
The exam tests pressure at depth, continuity, Bernoulli applications, and the selection of pumps and turbines.
Core rules
- Density ρ; specific gravity = ρ/1000; dynamic viscosity μ; kinematic viscosity ν = μ/ρ.
- Hydrostatic pressure p = ρgh and acts equally in all directions (Pascal's law).
- Continuity for incompressible flow: A₁V₁ = A₂V₂ = Q.
- Bernoulli: p/ρg + V²/2g + z = constant along a streamline for steady ideal flow.
- Reynolds number Re = ρVD/μ; below 2000 laminar, above 4000 turbulent in pipes.
- Discharge measured with a venturimeter, orifice meter or notch.
- Pumps add energy: centrifugal (large discharge, low head) and reciprocating (high head, small discharge). Turbines extract energy: Pelton (impulse, high head), Francis (reaction, medium head), Kaplan (reaction, low head, large flow). A draft tube recovers pressure; cavitation occurs when local pressure drops below vapour pressure.
Worked example
Water flows at 2 m/s in a 150 mm pipe that reduces to 100 mm. Q = A₁V₁ = (π/4 × 0.15²) × 2 = 0.01767 × 2 = 0.0353 m³/s (35.3 L/s). V₂ = V₁ × (D₁/D₂)² = 2 × (150/100)² = 2 × 2.25 = 4.5 m/s. Velocity changes with the square of the diameter ratio.
Traps
- Scaling velocity by the diameter ratio instead of its square.
- Giving head in metres as if it were pressure; 10 m of water ≈ 98.1 kPa.
- Using gauge pressure where absolute is needed in a cavitation check.
- Selecting a Pelton wheel for a low-head installation.
- Saying a draft tube increases head; it recovers pressure and cuts exit loss.