Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Dimensionless Numbers

Physical and chemical dimensionless quantities - Reynolds number, Euler, Nusselt, and Prandtl number - and many more.

The table shows the definitions of a lot of dimensionless quantities used in chemistry, fluid flow and physics engineering. Below the table, the symbols used in the formulas are explained and given with SI units.

For full table - rotate the screen!

Dimensionless Numbers Used in Chemistry, Fluid Flow and Physics Engineering
Name Symbol Formula Areas of application
Alfvén number Al Al = ν(ρ μ) ½ /B Study of magnetic fields
Cowling number Co Co = B2/(μ ρ ν2) Study of magnetic fields
Euler number Eu Eu = Δp /(ρ ν2) Characterization of energy losses in fluid flows
Fourier number Fo Fo = a t / l2 The ratio of diffusive or conductive heat transport rate to the heat storage rate
Fourier number for mass transfer Fo* Fo* = D t / l2 The ratio of diffusive mass transport rate to the mass storage rate
Froude number Fr Fr = ν /(l g) ½ Determine the resistance of a partially submerged object moving through water
Grashof number Gr Gr = l3 g α ΔT ρ2/ η2 Study situations involving natural heat convection
Grashof number for mass transfer Gr* Gr* = l3 g (∂p/∂x) T,p (Δx p / η) Predictions of mass flow patterns
Hartmann number Ha Ha = B l (κ/η) 1/2 Describes the ratio of electromagnetic force to the viscous force
Knudsen number Kn Kn = λ / l Determine whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used to model a situation
Lewis number Le Le = a / D Characterize fluid flows where there is simultaneous heat and mass transfer
Mach number Ma Ma = ν / c Determine the approximation with which a flow can be treated as an incompressible flow
Nusselt number Nu Nu = h l / k The ratio of convective to conductive heat transfer across (normal to) a boundary surface, predicts flow patterns.
Nusselt number for mass transfer Nu* Nu* = k d l / D
Predicts mass flow patterns
Peclet number Pe Pe = ν l / a For transport phenomena in a continuum, the ratio of advective to diffusive heat transport rates, to decide the simplicity/complexity of computational models
Peclet number for mass transfer Pe* Pe* = ν l / D The ratio of advective to diffusive mass transport rates
Prandtl number Pr Pr = η / (ρ a) Determine the thermal conductivity of gases at high temperatures
Rayleigh number Ra Ra = l3 g α ΔT ρ /(η a) Predict if heat transfer appear as conduction or convection
Reynolds number Re Re = p ν l / η Predictions of fluid flow patterns
Magnetic Reynolds number Rem Rem = ν μ κ l Estimates of the relative effects of advection or induction of a magnetic field
Schmidt number Sc Sc = η /(ρ D) Characterization of fluid flows in which there are simultaneous momentum and mass diffusion convection processes
Stanton number St St = h /(ρ ν cp ) Characterization of heat transfer in forced convection flows, the ratio of heat transferred into a fluid to the thermal capacity of fluid
Stanton number for mass transfer St* St* = k d / ν To characterize mass transfer in forced convection flows
Strouhal number Sr Sr = l f / ν Describing oscillating flow mechanisms
Weber number We We = ρ ν2l / γ Analysing fluid flows where there is an interface between two different fluids


ν = speed  [m/s]
η = viscosity  [kg/(m s)]
ρ = density, mass density, [kg/m3 ]
m = mass [kg]
V = volume [m3 ]
l = length [m]
a = thermal diffusivity  [m2/s]
t = time [s]
μ = permeability [kg m/(s2A2)]
B = magnetic flux density [kg/(s2A)]
Δp = pressure difference  [kg/(m s2)]
g = acceleration of free fall [m/s2]
α = cubic expansion coefficient [1/K]
ΔT = temperature difference
κ = electric conductivity [s3 A2/(kg m3 )]
λ = mean free path [m]
D = diffusion coefficient [m2/s]
c = speed of sound [m/s]
h = coefficient of heat transfer [kg/(s3 K)]
k = thermal conductivity [kg m/(s3 K)]
cp = specific heat apacity at constant pressure  [kg m2/(s2K)]
f = frequency [1/s]
γ = surface tension [kg/s2]
x = mole fraction [1]
k d = mass transfer coefficient  [m/s]

Related Topics

  • Basics

    Basic engineering data. SI-system, unit converters, physical constants, drawing scales and more.
  • Miscellaneous

    Engineering related topics like Beaufort Wind Scale, CE-marking, drawing standards and more.

Related Documents


Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .


This page can be cited as

  • The Engineering ToolBox (2017). Dimensionless Numbers. [online] Available at: [Accessed Day Month Year].

Modify the access date according your visit.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter