Comprehensive table of dimensionless numbers used in chemistry, fluid flow, and physics engineering
Name	Symbol	Formula	Area of Application
Alfvén number	Al	Al = ν(ρμ)^(1/2) / B	Study of magnetic fields
Cowling number	Co	Co = B² / (μρν²)	Study of magnetic fields
Euler number	Eu	Eu = Δp / (ρν²)	Characterization of energy losses in fluid flows
Fourier number	Fo	Fo = at / l²	Ratio of diffusive/conductive heat transport rate to heat storage rate
Fourier number (mass transfer)	Fo*	Fo* = Dt / l²	Ratio of diffusive mass transport rate to mass storage rate
Froude number	Fr	Fr = ν / (lg)^(1/2)	Resistance of partially submerged objects moving through water
Grashof number	Gr	Gr = l³gαΔTρ² / η²	Natural heat convection situations
Grashof number (mass transfer)	Gr*	Gr* = l³g(∂p/∂x)_(T,p) · (Δxp / η)	Predictions of mass flow patterns
Hartmann number	Ha	Ha = Bl(κ/η)^(1/2)	Ratio of electromagnetic force to viscous force
Knudsen number	Kn	Kn = λ / l	Determines statistical vs continuum mechanics formulation
Lewis number	Le	Le = a / D	Simultaneous heat & mass transfer characterization
Mach number	Ma	Ma = ν / c	Incompressible flow approximation validity
Nusselt number	Nu	Nu = hl / k	Convective to conductive heat transfer ratio across boundary
Nusselt number (mass transfer)	Nu*	Nu* = k_d·l / D	Predicts mass flow patterns
Peclet number	Pe	Pe = νl / a	Advective to diffusive heat transport rates ratio
Peclet number (mass transfer)	Pe*	Pe* = νl / D	Advective to diffusive mass transport rates ratio
Prandtl number	Pr	Pr = η / (ρa)	Thermal conductivity of gases at high temperatures
Rayleigh number	Ra	Ra = l³gαΔTρ / (ηa)	Predicts conduction vs convection heat transfer regime
Reynolds number	Re	Re = ρνl / η	Fluid flow pattern predictions
Magnetic Reynolds number	Re_m	Re_m = νμκl	Advection vs induction effects in magnetic fields
Schmidt number	Sc	Sc = η / (ρD)	Momentum & mass diffusion convection processes
Stanton number	St	St = h / (ρνc_p)	Forced convection heat transfer characterization
Stanton number (mass transfer)	St*	St* = k_d / ν	Forced convection mass transfer characterization
Strouhal number	Sr	Sr = lf / ν	Oscillating flow mechanisms
Weber number	We	We = ρν²l / γ	Fluid flows with interface between two different fluids

Source: engineeringtoolbox.com

Notes on Variable Conventions

The dimensionless numbers in this reference use the following variable conventions:

Symbol	Quantity	SI Unit
$\rho$	Density (mass density)	$\text{kg/m}^3$
$\eta$	Dynamic viscosity	$\text{kg/(m·s)}$
$\nu$	Flow velocity	$\text{m/s}$
$l$	Characteristic length	$\text{m}$
$g$	Acceleration of free fall	$\text{m/s}^2$
$\alpha$	Cubic expansion coefficient	$\text{1/K}$
$\Delta T$	Temperature difference	$\text{K}$
$\Delta p$	Pressure difference	$\text{Pa}$
$a$	Thermal diffusivity	$\text{m}^2/\text{s}$
$D$	Diffusion coefficient	$\text{m}^2/\text{s}$
$h$	Heat transfer coefficient	$\text{W/(m}^2\text{·K)}$
$k$	Thermal conductivity	$\text{W/(m·K)}$
$c_p$	Specific heat capacity (constant pressure)	$\text{J/(kg·K)}$
$c$	Speed of sound	$\text{m/s}$
$B$	Magnetic flux density	$\text{T}$
$\mu$	Permeability	$\text{kg·m/(s}^2\text{·A}^2\text{)}$
$\kappa$	Electrical conductivity	$\text{S/m}$
$\lambda$	Mean free path	$\text{m}$
$f$	Frequency	$\text{Hz}$
$\gamma$	Surface tension	$\text{N/m}$
$k_d$	Mass transfer coefficient	$\text{m/s}$

Dimensionless Number Quantity Symbol Application

Overview

Key Formulas

Ohm's Law

Newton's Second Law

Conservation of Energy

Variables

Complete Reference Table

Notes on Variable Conventions

Interactive Charts

Laminar vs. Turbulent Flow - Reynolds Number Explained with Calculator

References