# Dimensionless Numbers in Fluid Mechanics | Definition & List

By | January 25, 2019

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

1. ## What is a dimensionless number?

As the name indicates dimensionless numbers are not associated with any dimensions, like m, kg, sec etc.

Non-dimensional 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/m2.

Let us now understand some very important dimensionless numbers related to fluid mechanics.

1. Five important dimensionless numbers in fluid mechanics
• Mach’s number (M)
• Weber’s number (We)
• Euler’s number (Eu)
• Froude’s number (Fe)
• Reynold’s number (Re)

## 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 (We)?

Weber’s number is defined as square root of ratio of inertia force to surface tension force of moving fluid.

We = (Inertia force/Surface tension force)1/2

After putting values and solving above equation we will get.

We = V/(σ/ρ*L)1/2

Where

V = Velocity of fluid

## 2.3. What is Euler’s Number (Eu)?

Euler’s number is defined as square root of ratio of inertia force to pressure force of moving fluid.

Eu = (Inertia force/Pressure force)1/2

After putting values and solving above equation we will get.

Eu = 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 (Fe)?

Froude’s number is defined as square root of ratio of inertia force to gravity force of moving fluid.

Fe = (Inertia force/gravity force)1/2

After putting values and solving above equation we will get.

Fe = V/(L*g)1/2

Where

V = Velocity of fluid

g = Gravitational acceleration

## 2.5. What is Reynold’s Number (Re)?

Reynold’s number is defined as ratio of inertia force to viscous force of moving fluid.

Re = Inertia force/viscous force

After putting values and solving above equation we will get.

Re = V*L/ʋ

Where

V = Velocity of fluid

ʋ = Kinematic viscosity

1. ## 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
• 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

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