# Category: Dimensionless numbers

Heat release parameter
In combustion, heat release parameter (or gas expansion parameter) is a dimensionless parameter which measures the amount of heat released by the combustion process. It is defined as where * is the b
Numerical aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of r
Supersonic airfoils
A supersonic airfoil is a cross-section geometry designed to generate lift efficiently at supersonic speeds. The need for such a design arises when an aircraft is required to operate consistently in t
Dynamic amplification factor
Dynamic Amplification Factor (DAF) or Dynamic Increase Factor (DIF), is a dimensionless number which describes how many times the deflections or stresses should be multiplied to the deflections or str
Ericksen number
In the study of liquid crystals, the Ericksen number (Er) is a dimensionless number used to describe the deformation of the director field under flow. It is defined as the ratio of the viscous to elas
Dynamic similarity (Reynolds and Womersley numbers)
In fluid mechanics, dynamic similarity is the phenomenon that when there are two geometrically similar vessels (same shape, different sizes) with the same boundary conditions (e.g., no-slip, center-li
Blake number
The Blake number in fluid mechanics is a nondimensional number showing the ratio of inertial force to viscous force.It is used in momentum transfer in general and in particular for flow of a fluid thr
Karlovitz number
In combustion, the Karlovitz number is defined as the ratio of chemical time scale to Kolmogorov time scale , named after Béla Karlovitz. The number reads as . In premixed turbulent combustion, the ch
Lockhart–Martinelli parameter
The Lockhart–Martinelli parameter is a dimensionless number used in internal two-phase flow calculations. It expresses the liquid fraction of a flowing fluid. Its main application is in two-phase pres
Passenger load factor, or load factor, measures the capacity utilization of public transport services like airlines, passenger railways, and intercity bus services. It is generally used to assess how
Weinberg angle
The weak mixing angle or Weinberg angle is a parameter in the Weinberg–Salam theory of the electroweak interaction, part of the Standard Model of particle physics, and is usually denoted as θW. It is
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number b
Cunningham correction factor
In fluid dynamics, the Cunningham correction factor or Cunningham slip correction factor is used to account for noncontinuum effects when calculating the drag on small particles. The derivation of Sto
Goodness factor
The goodness factor is a metric developed by Eric Laithwaite to determine the 'goodness' of an electric motor. Using it he was able to develop efficient magnetic levitation induction motors. where G i
Total internal reflection
Total internal reflection (TIR) is the optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("e
Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric func
Proton-to-electron mass ratio
In physics, the proton-to-electron mass ratio, μ or β, is the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, nam
Electromechanical coupling coefficient
The electromechanical coupling coefficient is a numerical measure of the conversion efficiency between electrical and acoustic energy in piezoelectric materials. Qualitatively the electromechanical co
Poisson's ratio
In materials science and solid mechanics, Poisson's ratio (nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific
Shore durometer
The Shore durometer is a device for measuring the hardness of a material, typically of polymers. Higher numbers on the scale indicate a greater resistance to indentation and thus harder materials. Low
Nelson complexity index
The Nelson complexity index (NCI) is a measure to compare the secondary conversion capacity of a petroleum refinery with the primary distillation capacity. The index provides an easy metric for quanti
Log reduction
Log reduction is a measure of how thoroughly a decontamination process reduces the concentration of a contaminant. It is defined as the common logarithm of the ratio of the levels of contamination bef
F-number
In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture"). It is also known as the focal rat
Taylor number
In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about an axis, r
Fine-structure constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the
Refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determi
Zeldovich number
The Zel'dovich number is a dimensionless number which provides a quantitative measure for the activation energy of a chemical reaction which appears in the Arrhenius exponent, named after the Russian
Abbe number
In optics and lens design, the Abbe number, also known as the V-number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index ve
List of dimensionless quantities
This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The table also includes pure numbers, dimensionless ratios, or dimensionless physical consta
Markstein number
In combustion engineering and explosion studies, the Markstein number characterizes the effect of local heat release of a propagating flame on variations in the surface topology along the flame and th
West number
The West number is an empirical parameter used to characterize the performance of Stirling engines and other Stirling systems. It is very similar to the Beale number where a larger number indicates hi
Friction factor
No description available.
Beale number
In mechanical engineering, the Beale number is a parameter that characterizes the performance of Stirling engines. It is often used to estimate the power output of a Stirling engine design. For engine
Rayleigh number
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characteris
Weber number
The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flo
Bagnold number
The Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first identified by Ralph Alger Bagnold. The Bagnold nu
Hagen number
The Hagen number (Hg) is a dimensionless number used in forced flow calculations. It is the forced flow equivalent of the Grashof number and was named after the German hydraulic engineer G. H. L. Hage
Parts-per notation
In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractio
Sherwood number
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the convective mass transfer to the rate o
Reflectance
The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a
Richardson number
The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term: where is gravity, is de
Reynolds number
The Reynolds number (Re) helps predict flow patterns in different fluid flow situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated
Transparency and translucency
In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without appreciable scattering of light. On a macr
Contrast (vision)
Contrast is the contradiction in luminance or colour that makes an object (or its representation in an image or display) distinguishable. In visual perception of the real world, contrast is determined
Characteristic number (fluid dynamics)
Characteristic numbers are dimensionless numbers used in fluid dynamics to describe a character of the flow. To compare a real situation (e.g. an aircraft) with a small-scale model it is necessary to
Shields parameter
The Shields parameter, also called the Shields criterion or Shields number, is a nondimensional number used to calculate the initiation of motion of sediment in a fluid flow. It is a nondimensionaliza
Knudsen number
The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the ra
Lewis number
The Lewis number (Le) is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transf
Rockwell scale
The Rockwell scale is a hardness scale based on indentation hardness of a material. The Rockwell test measures the depth of penetration of an indenter under a large load (major load) compared to the p
Brinell scale
The Brinell scale /brəˈnɛl/ characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece. It is one of several definitions of ha
Lindemann index
The Lindemann index is a simple measure of thermally driven disorder in atoms or molecules. The local Lindemann index is defined as: where angle brackets indicate a time average. The global Lindemann
Rouse number
The Rouse number (P or Z) is a non-dimensional number in fluid dynamics which is used to define a concentration profile of suspended sediment and which also determines how sediment will be transported
Reflection coefficient
In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to
Dimensionless quantity
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corres
Morton number
In fluid dynamics, the Morton number (Mo) is a dimensionless number used together with the Eötvös number or Bond number to characterize the shape of bubbles or drops moving in a surrounding fluid or c
Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of
Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indic
Chandrasekhar number
The Chandrasekhar number is a dimensionless quantity used in magnetic convection to represent ratio of the Lorentz force to the viscosity. It is named after the Indian astrophysicist Subrahmanyan Chan
Van 't Hoff factor
The van 't Hoff factor i (named after Dutch chemist Jacobus Henricus van 't Hoff) is a measure of the effect of a solute on colligative properties such as osmotic pressure, relative lowering in vapor
Quantum number
In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with
Leaf area index
Leaf area index (LAI) is a dimensionless quantity that characterizes plant canopies. It is defined as the one-sided green leaf area per unit ground surface area (LAI = leaf area / ground area, m2 / m2
Sticking coefficient
Sticking coefficient is the term used in surface physics to describe the ratio of the number of adsorbate atoms (or molecules) that adsorb, or "stick", to a surface to the total number of atoms that i