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.
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Name  Symbol  Formula  Areas of application 
Alfvén number  Al  Al = ν(ρ μ)^{½}/B  Study of magnetic fields 
Cowling number  Co  Co = B^{2 }/(μ ρ ν^{2})  Study of magnetic fields 
Euler number  Eu  Eu = Δp /(ρ ν^{2})  Characterization of energy losses in fluid flows 
Fourier number  Fo  Fo = a t / l^{2}  The ratio of diffusive or conductive heat transport rate to the heat storage rate 
Fourier number for mass transfer  Fo*  Fo* = D t / l^{2}  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 = l^{3} g α ΔT ρ^{2 }/ η^{2}  Study situations involving natural heat convection 
Grashof number for mass transfer  Gr*  Gr* = l^{3} 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 = l^{3} 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  Re_{m}  Re_{m }= 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 c_{p})  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 ν^{2 }l / γ  Analysing fluid flows where there is an interface between two different fluids 
where
ν = speed [m/s]
η = viscosity [kg/(m s)]
ρ = density, mass density, [kg/m^{3}]
m = mass [kg]
V = volume [m^{3}]
l = length [m]
a = thermal diffusivity [m^{2}/s]
t = time [s]
μ = permeability [kg m/(s^{2}A^{2})]
B = magnetic flux density [kg/(s^{2}A)]
Δp = pressure difference [kg/(m s^{2})]
g = acceleration of free fall [m/s^{2}]
α = cubic expansion coefficient [1/K]
ΔT = temperature difference
κ = electric conductivity [s^{3} A^{2}/(kg m^{3})]
λ = mean free path [m]
D = diffusion coefficient [m^{2}/s]
c = speed of sound [m/s]
h = coefficient of heat transfer [kg/(s^{3} K)]
k = thermal conductivity [kg m/(s^{3} K)]
c_{p} = specific heat apacity at constant pressure [kg m^{2}/(s^{2} K)]
f = frequency [1/s]
γ = surface tension [kg/s^{2}]
x = mole fraction [1]
k_{d }= mass transfer coefficient [m/s]
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