Fluid Mechanics
Scope
Incompressible and compressible flow in pipes, pumps and fans, flow measurement, packed beds, and particle motion.
Concepts to own
- Mechanical energy balance: P1/ρ + v1²/2 + g z1 = P2/ρ + v2²/2 + g z2 + hf, with Darcy-Weisbach hf = f (L/D)(v²/2).
- Friction factor: laminar f = 64/Re; turbulent from Colebrook or Swamee-Jain; roughness relative to diameter.
- Minor losses as equivalent length or velocity heads (K).
- Pumps: system curve versus pump curve, operating point, and affinity laws (Q ∝ N, head ∝ N², power ∝ N³).
- NPSH available = (P_atm − P_v)/(ρg) + static head − friction; it must exceed NPSH required.
- Flow meters: orifice and venturi Q = Cd A √(2ΔP/ρ); rotameter; pitot tube.
- Packed beds: Ergun equation, with the laminar term dominating at low Reynolds number.
- Compressible flow chokes at Mach 1 in the throat.
Traps
- Using diameter instead of radius in area, or mixing in² with ft².
- Fanning versus Darcy friction factor, which differ by a factor of 4.
- Reporting NPSH in psi when it is a head in feet or meters of liquid.
- Applying affinity laws across different impeller geometries.
Worked example
Doubling pump speed from 1750 to 3500 rpm doubles flow, quadruples head, and multiplies brake power by eight.
Rule of thumb: a 10% speed increase costs roughly 33% more power; check the motor before changing a sheave.