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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