Fluid Mechanics and Fluid Machinery
Fluid Mechanics and Fluid Machinery tests conservation laws, pipe and duct flow, turbomachinery performance, cavitation, and pump or fan selection.
Core rules and concepts
- Continuity: rho A V=m_dot is constant for steady flow; incompressible flow gives Q=AV.
- Bernoulli applies along a streamline for steady, incompressible, inviscid flow; add pump head and subtract friction and component losses for real systems.
- Reynolds number Re=rho V D/mu classifies flow; Darcy-Weisbach h_f=f(L/D)(V^2/2g), with f from the Moody chart or Colebrook equation.
- Pump power P=rho g Q H/eta; affinity laws give Q proportional to N, H proportional to N^2, and P proportional to N^3 for geometrically similar machines.
- NPSH available must exceed NPSH required to avoid cavitation; vapor pressure sets the limit.
Worked example
A pump moves 0.02 m^3/s of water (rho=1000 kg/m^3) against 20 m head at 75% efficiency. Hydraulic power is rho g Q H=1000 x 9.81 x 0.02 x 20=3924 W. Shaft power is 3924/0.75=5232 W, about 5.2 kW. The calculation uses total head, not pressure rise alone; with a slurry, density would change the power but not the volumetric affinity relations.
Traps
Mixing gauge and absolute pressure in NPSH, applying Bernoulli across a pump without a head term, using diameter instead of hydraulic diameter in non-circular ducts, and ignoring minor losses at low flow all cost marks. Check whether efficiency is given as a fraction or a percent.