Important Dimensionless Numbers in Fluid Mechanics
Dimensionless Number | Symbol | Formula | Numerator | Denominator | Importance |
Reynolds number | NRe | \[Dv (\frac {\rho}{\mu})\] | Inertial force | Viscous force | Fluid flow involving viscous and inertial forces |
Froude number | NFr | \[\frac{u^2}{gD}\] | Inertial force | Gravitational force | Fluid flow with free surface |
Weber number | NWe | \[u^2 \rho \frac{D}{\sigma}\] | Inertial force | Surface force | Fluid flow with interfacial forces |
Mach number | NMa | \[\frac{u}{c}\] | Local velocity | Sonic velocity | Gas flow at high velocity |
Drag coefficient | CD | \[\frac{F_D}{(\rho \frac{u^2}{2})}\] | Total drag force | Inertial force | Flow around solid bodies |
Friction factor | f | \[\frac{\tau_w}{(\rho \frac{u^2}{2})}\] | Shear force | Inertial force | Flow though closed conduits |
Pressure coefficient | CP | \[\frac{\Delta p}{(\rho \frac{u^2}{2})}\] | Pressure force | Inertial force | Flow though closed conduits. Pressure drop estimation |