Important Dimensionless Numbers in Fluid Mechanics

Dimensionless Number

Symbol

Formula

Numerator

Denominator

Importance

Reynolds number

NRe

Dvr/m

Inertial force

Viscous force

Fluid flow involving viscous and inertial forces

Froude number

N_Fr

u²/gD

Inertial force

Gravitational force

Fluid flow with free surface

Weber number

N_We

u²rD/s

Inertial force

Surface force

Fluid flow with interfacial forces

Mach number

N_Ma

u/c

Local velocity

Sonic velocity

Gas flow at high velocity

Drag coefficient

C_D

F_D/(ru²/2)

Total drag force

Inertial force

Flow around solid bodies

Friction factor

f

t_w/(ru²/2)

Shear force

Inertial force

Flow though closed conduits

Pressure coefficient

C_P

Dp/(ru²/2)

Pressure force

Inertial force

Flow though closed conduits. Pressure drop estimation