Fluid Mechanics
Governing relations
Continuity (ṁ = ρAV) plus Bernoulli/energy for ideal flow, corrected by head loss, covers most questions. Reynolds number Re = ρVD/μ (≈ 4,000 for transition in pipes) separates laminar from turbulent, and Darcy–Weisbach (h_f = f (L/D)(V²/2g)) or Hazen–Williams gives friction loss. Minor losses use equivalent length or a loss coefficient K, and are negligible in long mains but dominant in short, fitting-heavy runs.
Machines and systems
A pump or fan operates where its curve intersects the system curve (which rises roughly as the square of flow). Affinity laws: Q ∝ N, H ∝ N², P ∝ N³ for a fixed impeller; for a fixed speed, varying diameter behaves similarly. Pumps in series add head at the same flow; in parallel they add flow at the same head. NPSH available must exceed NPSH required, or the pump cavitates - a common exam scenario involving suction lift, fluid temperature, and altitude.
Traps
Using velocity head versus velocity in a loss equation; applying parallel-pump logic to a series arrangement; ignoring that a throttled valve shifts the system curve; and forgetting that a fan's static pressure is measured relative to atmosphere. Duct problems often require the equal-friction chart (typical design ~0.1 in. w.c. per 100 ft) with velocity limits for noise.
Worked example
A fan runs at 1,750 rpm, delivering 10,000 cfm at 2.0 in. w.c. with 5.0 bhp. Speed drops to 1,450 rpm (ratio 0.829). New flow = 8,290 cfm, new pressure = 2.0 × 0.829² = 1.37 in. w.c., new power = 5.0 × 0.829³ = 2.85 bhp.