In this article we will understand concept of ‘Dimensionless Numbers’. After understanding it we will discuss some important dimensionless (NonDimensional) numbers related to fluid mechanics field.

What is a dimensionless number?
As the name indicates dimensionless numbers are not associated with any dimensions, like m, kg, sec etc.
Nondimensional numbers are the ratios of two numbers which have same dimensions. Hence dimensions get cancelled.
For example:
If we take ratio of pressure to stress then the number obtained will be dimensionless. Because both pressure and stress have same dimensions i.e. N/m^{2}.
Let us now understand some very important dimensionless numbers related to fluid mechanics.
 Five important dimensionless numbers in fluid mechanics
 Mach’s number (M)
 Weber’s number (W_{e})
 Euler’s number (E_{u})
 Froude’s number (F_{e})
 Reynold’s number (R_{e})
2.1. What is Mach’s number (M)?
Mach’s number is defined as square root of ratio of inertia force to elastic force of moving fluid.
M = (Inertia force/Elastic force)^{1/2}
After putting values and solving above equation we will get.
M = V/C
Where
V = Velocity of fluid
C = Velocity of sound in that fluid
Alternatively, many people define Mach’s number as a ratio of velocity of object to velocity of sound.
2.2. What is Weber’s Number (W_{e})?
Weber’s number is defined as square root of ratio of inertia force to surface tension force of moving fluid.
W_{e} = (Inertia force/Surface tension force)^{1/2}
After putting values and solving above equation we will get.
W_{e} = V/(σ/ρ*L)^{1/2}
Where
V = Velocity of fluid
σ = Coefficient of surface tension
ρ = Density of fluid
2.3. What is Euler’s Number (E_{u})?
Euler’s number is defined as square root of ratio of inertia force to pressure force of moving fluid.
E_{u} = (Inertia force/Pressure force)^{1/2}
After putting values and solving above equation we will get.
E_{u} = V/(P/ρ)^{1/2}
Where
V = Velocity of fluid
ρ = Density of fluid
P = Pressure of flowing fluid
2.4. What is Froude’s Number (F_{e})?
Froude’s number is defined as square root of ratio of inertia force to gravity force of moving fluid.
F_{e} = (Inertia force/gravity force)^{1/2}
After putting values and solving above equation we will get.
F_{e} = V/(L*g)^{1/2}
Where
V = Velocity of fluid
g = Gravitational acceleration
2.5. What is Reynold’s Number (R_{e})?
Reynold’s number is defined as ratio of inertia force to viscous force of moving fluid.
R_{e} = Inertia force/viscous force
After putting values and solving above equation we will get.
R_{e} = V*L/ʋ
Where
V = Velocity of fluid
ʋ = Kinematic viscosity

List of other important dimensionless numbers in fluid mechanics
 Zel’dovich number
 Womersley number
 Weissenberg number
 Weaver flame speed number
 Wallis parameter
 Ursell number
 Taylor number
 Stuart number
 Strouhal number
 Stokes number
 Stanton number
 Sommerfeld number
 Sherwood number
 Shape factor
 Schmidt number
 Roshko number
 Richardson number
 Rayleigh number
 Pressure coefficient
 Prandtl number
 Péclet number
 Ohnesorge number
 Nusselt number
 Morton number
 Markstein number
 Marangoni number
 Manning roughness coefficient
 Lockhart–Martinelli parameter
 Lift coefficient
 Lewis number
 Laplace number
 Kutateladze number
 Knudsen number
 Keulegan–Carpenter number
 Karlovitz number
 Iribarren number
 Hagen number
 Hartmann number
 Grashof number
 Graetz number
 Görtler number
 Galilei number
 Fanning friction factor
 Excess temperature coefficient
 Ericksen number
 Eötvös number
 Eckert number
 Drag coefficient
 Deborah number
 Dean number
 Darcy friction factor
 Damkohler number
 Colburn J factors
 Chandrasekhar number
 Capillary number
 Brownell–Katz number
 Brinkman number
 Bond number
 Blake number
 Biot number
 Bingham number
 Bejan number
 Atwood number
 Archimedes number
Featured image attributions: By US Navy – http://www.hnn.navy.mil/Archives/030314/images_031403/originals/Los%20Angeles.JPG (from page http://www.hnn.navy.mil/Archives/030314/losangeles_031403.htm), Public Domain, https://commons.wikimedia.org/w/index.php?curid=647962