Fluid Dynamics Reference
Bernoulli, continuity, Reynolds number, and key fluid dimensionless groups.
Reference
Conservation laws
- Continuity
- ρ₁A₁v₁ = ρ₂A₂v₂ (incompressible: A₁v₁ = A₂v₂)
- Bernoulli
- P + ½ρv² + ρgh = constant (inviscid, incompressible)
- Momentum
- F = ρQΔv for control volume
Dimensionless numbers
| Name | Formula | Physical meaning |
|---|---|---|
| Reynolds Re | ρvL / μ | Inertial / viscous — turbulence indicator |
| Mach M | v / c | Flow speed / sound speed — compressibility |
| Froude Fr | v / √(gL) | Inertia / gravity — open-channel flow |
| Weber We | ρv²L / σ | Inertia / surface tension — droplets |
| Prandtl Pr | μc_p / k | Momentum / thermal diffusion |
| Nusselt Nu | hL / k | Convective / conductive heat transfer |
| Péclet Pe | Re · Pr | Advection / diffusion |
| Drag coefficient C_D | F_D / (½ρv²A) | Dimensionless drag |
Pipe flow regime
- Re < 2 300
- Laminar
- 2 300 < Re < 4 000
- Transition
- Re > 4 000
- Turbulent
Darcy-Weisbach friction loss
- Head loss
- h_f = f · (L/D) · v² / (2g)
- Pressure drop
- ΔP = f · (L/D) · ρv² / 2
- f (laminar)
- = 64 / Re
- f (turbulent)
- Moody chart or Colebrook eqn
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