Fluid Mechanics — Cheat Sheet
Continuity, Bernoulli, Reynolds, Darcy-Weisbach, hydrostatics, pump power.
Flow basics
| Volumetric flow | Q = A·v |
| Continuity | A₁v₁ = A₂v₂ |
| Mass flow | ṁ = ρ·Q |
Energy
| Bernoulli | p/ρg + v²/2g + z = const |
| Dynamic pressure | q = ½ρv² |
Pipe flow
| Reynolds number | Re = ρvD/µ = vD/ν |
| Regime | laminar Re < 2300, turbulent > 4000 |
| Friction (laminar) | f = 64 / Re |
| Head loss | h_f = f (L/D)(v²/2g) |
| Pressure drop | Δp = f (L/D)(ρv²/2) |
Hydrostatics
| Pressure at depth | p = ρ·g·h |
| Force on surface | F = ρ·g·h_c·A |
Devices & power
| Orifice / meter | Q = C_d·A·√(2Δp/ρ) |
| Pump hydraulic power | P = ρ·g·Q·H = Q·Δp |
| Kinematic viscosity | ν = µ / ρ |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.