Fluids engineering formula sheet
| Formula | Equation | Symbols | Conditions |
|---|---|---|---|
| Fluid Dynamics | |||
| Reynolds Number | Re = ρ vD / μ | Re Reynolds Number; ρ Density (kg/m³); v Velocity (m/s); D Characteristic Length (m); μ Dynamic Viscosity (Pa·s) | Internal flow in circular pipes: laminar <~ 2300, turbulent >~ 4000 |
| Continuity Equation | A₁ v₁ = A₂ v₂ | A₁ Area 1 (m²); v₁ Velocity 1 (m/s); A₂ Area 2 (m²); v₂ Velocity 2 (m/s) | Incompressible, steady flow |
| Bernoulli Equation | P₁ + (1/2)ρ v₁² + ρ g h₁ = P₂ + (1/2)ρ v₂² + ρ g h₂ | P Pressure (Pa); ρ Density (kg/m³); v Velocity (m/s); g Gravity (m/s²); h Height (m) | Steady, incompressible, inviscid flow along streamline |
| Torricelli's Theorem | v = √(2gh) | v Exit Velocity (m/s); g Gravity (m/s²); h Height Above Orifice (m) | Large tank with small orifice |
| Drag Force 1 | F_D = (1/2) ρ v² C_D A | Fᴅ Drag Force (N); ρ Fluid Density (kg/m³); v Velocity (m/s); Cᴅ Drag Coefficient; A Frontal Area (m²) | not defined |
| Lift Force 1 | F_L = (1/2) ρ v² C_L A | Fₗ Lift Force (N); ρ Fluid Density (kg/m³); v Velocity (m/s); Cₗ Lift Coefficient; A Wing Area (m²) | not defined |
| Froude Number | Fr = v / (√(gL)) | Fr Froude Number; v Velocity (m/s); g Gravity (m/s²); L Characteristic Length (m) | Important for open channel and ship hydrodynamics |
| Mach Number | Ma = v / a | Ma Mach Number; v Flow Velocity (m/s); a Speed of Sound (m/s) | Ma < 0.3 incompressible, Ma > 1 supersonic |
Equations are rendered from the library's own typeset source with no term reordered, dropped or simplified. Symbol legends and validity conditions are the library's; an equation is a model, not a guarantee — confirm its assumptions hold before you rely on a result.
- The formula library records no validity conditions for this entry. An absent condition line is not a statement that the formula is unconditional — check the source before applying it outside the obvious case.
Reference values are provided for study and quick reference. Verify against current standards and manufacturer data before safety-critical design.