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Dimensionless quantities, or quantities of dimension one, are quantities with no associated units of measurement. These may be ratios of quantities with...

In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical...

characteristic time, characteristic length, or characteristic number (dimensionless) of a given system, or material constants (e.g., Madelung constant,...

radius cross the sphere more slowly at later times.) On defining the dimensionless deceleration parameter q ≡ − a ¨ a / a ˙ 2 {\textstyle q\equiv -{\ddot...

number. The number one has been suggested as a dimensionless base quantity. Radians serve as dimensionless units for angular measurements, derived from...

C gives the dimensionless equation sought. The dimensionless product of powers of variables is sometimes referred to as a dimensionless group of variables;...

Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport...

a set of pseudo-units to describe the small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions...

S=\int {\frac {{\rm {d}}Q}{T}}.} One could choose instead a rescaled dimensionless entropy in microscopic terms such that S ′ = ln ⁡ W , Δ S ′ = ∫ d Q...

the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters π1, π2, ..., πp constructed from the original variables,...

η/E.   Dimensionless elastic modulus E1/E   Dimensionless modulus of losses E2/E   Dimensionless apparent viscosity E2/ωη X-axis: dimensionless frequency...

the wall, made dimensionless with the friction velocity uτ and kinematic viscosity ν, u + {\displaystyle u^{+}} is the dimensionless velocity: the velocity...

A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material...

numbers in increasing order of magnitude, including counts of things, dimensionless quantities, and probabilities. Each number is given a name in the short...

well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or...

A g-factor (also called g value) is a dimensionless quantity that characterizes the magnetic moment and angular momentum of a whole atom, a particle,...

dependence of the dimensionless deformation E ε ( t ) σ 0 {\displaystyle {\frac {E\varepsilon (t)}{\sigma _{0}}}} on dimensionless time t / τ R {\displaystyle...

equations; for example, in Planck units the speed of light equals 1. Dimensionless quantities are also known as 'quantities of dimension one'. In quantum...

laws requires understanding the pump discharge and head coefficient dimensionless numbers. For a given pump, one can compute the discharge and head coefficients...

C d = {\displaystyle C_{d}=} coefficient of discharge, dimensionless, typically between 0.6 and 0.85, depending on the orifice geometry and tappings,...

In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation...

{B^{2}}{\mu n_{i}}}} In the study of tokamaks, collisionality is a dimensionless parameter which expresses the ratio of the electron-ion collision frequency...

appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. SI coherent...

Look up ST, St, st, .st, or s.t. in Wiktionary, the free dictionary. ST, St, or St. may refer to: -st, a suffix for an ordinal numeral, such as 1st or...

(1 atm = 101325 Pa). The Henry solubility can also be expressed as the dimensionless ratio between the aqueous-phase concentration c a {\displaystyle c_{\text{a}}}...

therefore, the ratio of inertial to gravity forces is the most important dimensionless parameter. The parameter is known as the Froude number, and is defined...

(also called effective saturation or S e {\displaystyle S_{e}} ) is a dimensionless value defined by van Genuchten as: Θ = θ − θ r θ s − θ r {\displaystyle...

same dimension. The named dimensionless units "radian" (rad) and "steradian" (sr) are acceptable for distinguishing dimensionless quantities of different...

refer to one of several different parameters in physics. One of two dimensionless parameters relating to black holes: The spin parameter of an individual...

unity (or to any other fixed dimensionless number). One could then eliminate the kilogram by setting ħ to a dimensionless number. One could eliminate the...

Bodenstein number (abbreviated Bo, named after Max Bodenstein) is a dimensionless parameter in chemical reaction engineering, which describes the ratio...

density gives a closed universe and lower density gives an open one. A dimensionless scale factor can be defined: a ( t ) ≡ R ( t ) R 0 {\displaystyle a(t)\equiv...

Below is a list of fastest rotating black holes measured in the dimensionless rotational parameter a. Accreting black hole spins can be measured by observing...

_{L}x(1-\epsilon _{G})}{\rho _{G}(1-x)\epsilon _{G}}}} where: S – slip ratio, dimensionless indices G and L refer to the gas and the liquid phase, respectively...

In the design of fluid bearings, the Sommerfeld number (S) is a dimensionless quantity used extensively in hydrodynamic lubrication analysis. The Sommerfeld...

There are three dimensionless numbers that may be referred to as the cavitation number in various scenarios: the cavitation number for hydrodynamic cavitation...

convention associated with atomic units that transforms quantities into dimensionless equivalents, it becomes H ^ = − 1 2 ∇ 1 2 − 1 2 ∇ 2 2 − 2 r 1 − 2 r...

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...

This can be expressed more simply as a proportionality between two dimensionless ratios: S BH k = 1 4 A l P 2 , {\displaystyle {\frac {S_{\text{BH}}}{k}}={\frac...

In fluid dynamics, the pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field. The pressure coefficient...

The Prandtl number (Pr) is a dimensionless number, named for the German fluid dynamicist Ludwig Prandtl. It is defined as the ratio of momentum diffusivity...

In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The...

gives 1 radian as 1 m2/m2 = 1. The key fact is that the radian is a dimensionless unit equal to 1. In SI 2019, the SI radian is defined accordingly as...

The urea reduction ratio (URR) is a dimensionless number used to quantify dialysis treatment adequacy. U R R = U p r e − U p o s t U p r e × 100 % {\displaystyle...

by the 3.41 conversion factor (or multiplying by 0.293) makes it a dimensionless quantity that is interpreted as an energy multiplier. Depending on the...

number versus ΔS graph, but the dimensionless enthalpy, H, versus ΔS diagram, is more often used. The dimensionless enthalpy equation is shown below...

abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number (pure number), primarily used for expressing proportions, but...

or sometimes Sr to avoid the conflict with the Stanton number) is a dimensionless number describing oscillating flow mechanisms. The parameter is named...

as few independent variables and as many dimensionless parameters as possible. The values of the dimensionless parameters are held to be the same for both...

that is, characteristic of the geometry. If these values are used in dimensionless numbers, such as those listed below, much understanding of the phenomenon...

In fluid dynamics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the...

thermodynamics), the Grashof number (Gr, after Franz Grashof) is a dimensionless number which approximates the ratio of the buoyancy to viscous forces...

Figure 1. Dimensionless head-volume characteristics of centrifugal pump...

than per mass transported, mass is multiplied by g and the resulting dimensionless quantity allows for the comparison of dissimilar animals or modes of...

Hochschule Charlottenburg (today Technische Universität Berlin). The dimensionless numbers Reynolds number (named after the British scientist and mathematician...

transmutation is a physical mechanism providing a linkage between a dimensionless parameter and a dimensionful parameter. In classical field theory, such...

{\displaystyle p^{*}} . That critical value can be calculated from the dimensionless critical pressure ratio equation p ∗ p 0 = ( 2 γ + 1 ) γ γ − 1 {\displaystyle...

The Cohesion number (Coh) is a useful dimensionless number in particle technology by which the cohesivity of different powders can be compared. This is...

Name/s) (Common) Symbol/s SI Units Dimension Number of molecules N dimensionless dimensionless Mass m kg [M] Number of moles, amount of substance, amount n...

economics Parts per billion, describing small values of miscellaneous dimensionless quantities Portland Police Bureau, in Portland, Oregon, U.S. Partido...

Mach number (M or Ma), often only Mach (/mɑːk/; German: [max]), is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past...

single letter, that use different loads or indenters. The result is a dimensionless number noted as HRA, HRB, HRC, etc., where the last letter is the respective...

{\displaystyle C_{\text{d}}} , discharge coefficient through the constriction (dimensionless). m ˙ {\displaystyle {\dot {m}}} , mass flow rate of fluid through constriction...

replaces dimensionless trigonometric functions with angles in radians. In dimensional analysis on optics equations radians are dimensionless and therefore...

chemist Gilbert N. Lewis in 1907. By convention, activity is treated as a dimensionless quantity, although its value depends on customary choices of standard...

much shorter than Lagrangian time scale. Note that the expectation evolves linearly. (Both axis are expressed in suitable dimensionless quantities)....

radians or 65.54 degrees. In the SI, solid angle is considered to be a dimensionless quantity, the ratio of the area projected onto a surrounding sphere...

In mechanical engineering, mechanical efficiency is a dimensionless ratio that measures the efficiency of a mechanism or machine in transforming the power...

adopted in physical sciences (especially in metrology) for ratio is the dimensionless quotient between two physical quantities measured with the same unit...

However, the application of dimensionless values facilitates the identification of patterns for all these variables. The dimensionless parameters employed are:...

Total reflection map as function of incident angle and dimensionless frequency. Parameters of the systems: ε = (11.4, 1.0), period of one layer is d =...

and this particular one shows the dimensionless heat transferred from the wall as a function of a dimensionless time variable. The vertical axis is...

{\displaystyle \varphi _{i}={\frac {V_{i}}{\sum _{j}V_{j}}}.} Being dimensionless, its unit is 1; it is expressed as a number, e.g., 0.18. It is the same...

dimensionally correct: relative atomic masses and standard atomic weights are dimensionless quantities (i.e., pure numbers), whereas molar masses have units (in...

the Péclet number (Pe, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuous...

is driven in a clockwise rotary motion, the leg (blue triangle at the bottom) executes a walking motion. Relative (dimensionless) proportions shown....

multiphase flow in porous media, the relative permeability of a phase is a dimensionless measure of the effective permeability of that phase. It is the ratio...

is a dimensionless number in fluid dynamics used in the study of hydrodynamic instabilities in density stratified flows. It is a dimensionless density...

constant of proportionality being called the coefficient of restitution, a dimensionless parameter that is a property of a pair of surfaces. In most real-world...

defined by the characteristic quantities, the equations can be made dimensionless. For this, the units become ψ ′ = ψ ψ 0 , r ′ = r λ , H ′ = H H cm 2...

The Stanton number (St), is a dimensionless number that measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. The Stanton...

(Common) symbol/s SI units Dimension Number of wave cycles N dimensionless dimensionless (Oscillatory) displacement Symbol of any quantity which varies...

state. The deviation from the ideal gas behavior can be described by a dimensionless quantity, the compressibility factor, Z. The ideal gas model has been...

bar, in order to produce a dimensionless quantity, ⁠f/po⁠. An equilibrium constant is expressed in terms of the dimensionless quantity. For example, for...

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...

The Damköhler numbers (Da) are dimensionless numbers that relate the chemical reaction timescale (reaction rate) to the transport phenomena rate occurring...

diagram or Colebrook equation. The Darcy–Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also variously...

characteristic time scale for heat diffusion, t d {\displaystyle t_{d}} . This dimensionless group is named in honor of J.B.J. Fourier, who formulated the modern...

G. (2013). "Shackle". A Dictionary of Scientific Units: Including dimensionless numbers and scales. Springer. p. 127. ISBN 9789401705714. Retrieved...

difference between phases, L is the latent heat of melting. It is a dimensionless parameter that is useful in analyzing a Stefan problem. The parameter...

formation of a crystal from infinitely-separated ions Lewis number, a dimensionless number ratio in physics Ligand efficiency, a measure of the binding...

The Buckingham π theorem can help solve this problem by generating 5 dimensionless forms of these parameters.[citation needed] These parameters provide...

Q_{(full)}=K\pi } (Equation 4) In dimensionless form, the rate of discharge Q is usually expressed in a dimensionless form as : Q Q f u l l = 1 π ( θ −...

Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch...

Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle...

In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is....

often with impulse and reaction parts on the same blade. The following dimensionless ratios are often used for the characterisation of fluid machines. They...

the surface layer under non-neutral conditions as a function of the dimensionless height parameter, named after Russian scientists A. S. Monin and A....

area, and c d {\displaystyle c_{\rm {d}}} is the drag coefficient – a dimensionless coefficient related to the object's geometry. The equation is attributed...

interaction between elementary charged particles. It is a dimensionless quantity (dimensionless physical constant), independent of the system of units used...

nondimensionalization), resulting in only dimensionless quantities remaining. Only variation of these dimensionless quantities change the nature of physics...

The expansion of the universe is parametrized by a dimensionless scale factor a {\displaystyle a} . Also known as the cosmic scale factor or sometimes...

units of percent return (as opposed to the Sharpe ratio – an abstract, dimensionless ratio of limited utility to most investors), which makes it dramatically...

mass-heat transfer analogy, heat transfer dimensionless quantities are replaced with analogous mass transfer dimensionless quantities. This equation is named...

g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensionless and equal to ‰). Salinity is an important factor in determining many...

mechanics, the Froude number (Fr, after William Froude, /ˈfruːd/) is a dimensionless number defined as the ratio of the flow inertia to the external force...

of movement of sand and gravel in currents (incipient motion). The dimensionless Shields parameter is called after him. Albert Shields was born in Cleveland...

in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative...

the point group of octahedral molecular geometry Ohnesorge number, a dimensionless number that relates the viscous forces to inertial and surface tension...

available for the transport (dimensionless), δ is the constrictivity (dimensionless), τ is the tortuosity (dimensionless). The transport-available porosity...

(dB) is a dimensionless unit, used for quantifying the ratio between two values, such as signal-to-noise ratio. The dBm is also dimensionless, but since...

{\stackrel {\mathrm {def} }{=}}\ {\frac {D}{s^{2}g^{2}}}} Defining the dimensionless variables ζ   = d e f   z / z 0 {\displaystyle \zeta \ {\stackrel {\mathrm...

graphite) SP-211 (10% PTFE, 15% graphite) SP-3 (15% MoS 2) Specific gravity dimensionless 1.43 1.51 1.65 1.55 1.60 Thermal expansion coefficient 10−6/K 211–296...

ω ρ / μ ) {\displaystyle \alpha =R\surd (\omega \rho /\mu )} is the dimensionless Womersley number. The axisymmetric boundary condition ( ∂ U n / ∂ r...

In fluid dynamics, the Cunningham correction factor, or Cunningham slip correction factor (denoted C), is used to account for non-continuum effects when...

{\displaystyle {\text{Wo}}} ) is a dimensionless number in biofluid mechanics and biofluid dynamics. It is a dimensionless expression of the pulsatile flow...

dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring the importance of gravitational forces compared to...

where:   Q = mass flow rate, kg/s C = discharge coefficient, dimensionless (usually about 0.72) A = discharge hole area, m2 k = cp/cv of the gas cp =...

atoms) divided by that of the electron (a lepton found in atoms), a dimensionless quantity, namely: μ = mp/⁠me = 1836.152673426(32). The number in parentheses...

decayed at time t N 0 = N + N D {\displaystyle N_{0}=N+N_{D}\,\!} dimensionless dimensionless Decay rate, activity of a radioisotope A A = λ N {\displaystyle...

is frequently reported with these units omitted (despite not being a dimensionless quantity). The BMI is a convenient rule of thumb used to broadly categorize...

decay in amplitude towards zero or attenuate. The damping ratio is a dimensionless measure, amongst other measures, that characterises how damped a system...

possible become 1; Rewrite the system of equations in terms of their new dimensionless quantities. The last three steps are usually specific to the problem...

physical space. The scalar may either be a pure mathematical number (dimensionless) or a scalar physical quantity (with units). In a physical context,...

astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another...

equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of...

same because the former represents the dimensionless pressure gradient while the latter represents the dimensionless pressure drop, it will be shown that...

The waist–hip ratio or waist-to-hip ratio (WHR) is the dimensionless ratio of the circumference of the waist to that of the hips. This is calculated as...

sensitivity index or discriminability index or detectability index is a dimensionless statistic used in signal detection theory. A higher index indicates...

number (Wi) is a dimensionless number used in the study of viscoelastic flows. It is named after Karl Weissenberg. The dimensionless number compares the...

number is named in honor of Wilhelm Nusselt, who first identified this dimensionless group in 1915. Analytical results and empirical correlations allow the...

properties of fluids setting the stage for many subsequent studies. Dimensionless reduced units can be defined based on the Lennard-Jones potential parameters...

Contrast is the difference in luminance or color that makes an object (or its representation in an image or display) distinguishable from a background...

The atomic number or nuclear charge number (symbol Z, from the German Zahl, "number") of a chemical element is the charge number of its atomic nucleus...

of quantities that is employed. As an example, quantities that are dimensionless in one system may have dimension in the other. The Gaussian unit system...

The Platinum-Cobalt Scale (Pt/Co scale or Apha-Hazen Scale) is a color scale that was introduced in 1892 by chemist Allen Hazen (1869–1930). The index...

effects increases. The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping in a...

atomic mass ma of an isotope by the atomic mass constant mu, yielding a dimensionless value. Thus, the atomic mass of a carbon-12 atom m(12C) is 12 Da by...

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...

The Chandrasekhar number is a dimensionless quantity used in magnetic convection to represent the ratio of the Lorentz force to the viscosity. It is named...

number, Alfvénic Mach number, and magnetic Mach number; MA or MM) is a dimensionless quantity representing the ratio of the relative velocity of a fluid...

the requirement that the argument of the logarithmic function must be dimensionless. The multiplier also can't have a numeric value of 1 or less, because...

reaction force R at a point of contact between two interfaces through a dimensionless coefficient of friction μf, which depends on the pair of materials:...

to ship's tonnage. Since 18 July 1994, the gross and net tonnages, dimensionless indices calculated from the total moulded volume of the ship and its...

humidity. The term humidex was coined in 1965. The humidex is a nominally dimensionless quantity (though generally recognized by the public as equivalent to...

intervals, there would be sixty-four bacteria. Many pairs (b, τ) of a dimensionless non-negative number b and an amount of time τ (a physical quantity which...

coulomb per kilogram (C⋅kg−1). The g-factor of a particle is a related dimensionless value of the system, derived as the ratio of its gyromagnetic ratio...

List of photometric quantities List of radiometric quantities List of dimensionless quantities List of electromagnetism quantities "ISO 80000-1:2009(en)...

most authoritatively synonymous with relative molecular mass, which is dimensionless; however, in common practice, use of this terminology is highly variable...

molecules in the body (dimensionless), kB is the Boltzmann constant (J/(K⋅molecule)). In the ideal gas article, dimensionless heat capacity C ∗ {\displaystyle...

θ(x) in prime number theory The potential temperature in meteorology Dimensionless temperature in heat transport phenomena The score of a test taker in...

is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion...

of dispersion is used and when this ratio is dimensionless, as count data are themselves dimensionless, not otherwise. Some measures of dispersion have...

friction factor (named after American engineer John T. Fanning) is a dimensionless number used as a local parameter in continuum mechanics calculations...

The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such...

Quantities, an angle is defined as a dimensionless quantity, and in particular, the radian is defined as dimensionless in the International System of Units...

g\left({\tfrac {\Delta \rho }{\rho }}\right)^{2}} ⁠.) The most generally used dimensionless number would be the Richardson number and Rayleigh number. The mathematics...

that shows the ratio of the true airspeed to the speed of sound, a dimensionless quantity called Mach number. This is shown on a Machmeter as a decimal...

In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity...

{\displaystyle \psi _{3}<0} . These formulas for the flow strength can be made dimensionless by setting ψ ∗ = ψ k α Δ T a {\displaystyle \psi ^{*}={\frac {\psi }{k\alpha...

underlying quantum mechanical details. Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization...

In astrophysics, the Lane–Emden equation is a dimensionless form of Poisson's equation for the gravitational potential of a Newtonian self-gravitating...

expansion of the universe built in. The expansion is defined by a (dimensionless) scale factor a ( t ) {\displaystyle a(t)} set to have a value of one...

(symbol fps or ft/s); Mach number (dimensionless), speed divided by the speed of sound; in natural units (dimensionless), speed divided by the speed of light...

measurement of physical quantities. Ratios is the special case for dimensionless quotients of two quantities of the same kind. Quotients with a non-trivial...

Nikuradse) to show that fluid flow in rough pipes could be described by four dimensionless quantities: Reynolds number, pressure loss coefficient, diameter ratio...

is the hull speed of the vessel in knots Note that the 1.34 is not a dimensionless constant. If the length of waterline is given in metres and desired...

clinical genetics, the most commonly used index of digit length is the dimensionless ratio of the length of the third (middle) finger to the hand length...

of speed equal to one nautical mile per hour Knudsen number (Kn), a dimensionless number .kn, the Internet country code top-level domain for Saint Kitts...

transition radiation. And of these, all but the mole, the coulomb, and the dimensionless radian and steradian are implicitly defined by the general properties...

thermal efficiency ( η t h {\displaystyle \eta _{\rm {th}}} ) is a dimensionless performance measure of a device that uses thermal energy, such as an...

International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr), which is equal to one square radian...

Dimensionless force versus Reynolds number for spherical particles...

{h_{c}}{k_{y}c_{s}}}\,} where: r {\displaystyle r}   = psychrometric ratio, dimensionless h c {\displaystyle h_{c}} = convective heat transfer coefficient, W...

c x {\displaystyle c_{x}} or c w {\displaystyle c_{\rm {w}}} ) is a dimensionless quantity that is used to quantify the drag or resistance of an object...

In fluid dynamics, the capillary number (Ca) is a dimensionless quantity representing the relative effect of viscous drag forces versus surface tension...

the partition function or its derivatives. The partition function is dimensionless. Each partition function is constructed to represent a particular statistical...

The Brinell hardness test (pronounced /brəˈnɛl/) measures the indentation hardness of materials. It determines hardness through the scale of penetration...

Fresnel number (F), named after the physicist Augustin-Jean Fresnel, is a dimensionless number relating to the pattern a beam of light forms on a surface when...

permittivity farad per metre F/m kg−1⋅m−3⋅A2⋅s4 χe electric susceptibility (dimensionless) 1 1 p electric dipole moment coulomb metre C⋅m A⋅s⋅m G; Y; B conductance;...

Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a reaction engine or a vehicle with such an engine. Reaction engines include jet...

The coupling coefficient of resonators is a dimensionless value that characterizes interaction of two resonators. Coupling coefficients are used in resonator...

also a spinodal point. Using the critical values to define reduced (dimensionless) variables ⁠ p r = p / p c {\displaystyle p_{r}=p/p_{\text{c}}} ⁠, ⁠...

factor, of an explosive's demolition power Reynolds number (Re), a dimensionless quantity in fluid mechanics used to help predict flow patterns Rhenium...

elliptic functions and power sets Péclet number (abbreviated "Pe."), a dimensionless number used in physics Pe (text editor), a text editor for BeOS Petlyakov...

the flow becomes turbulent. The threshold velocity is determined by a dimensionless parameter characterizing the flow called the Reynolds number, which...

(symbol N) in a one-mole sample equals the Avogadro number (symbol N0), a dimensionless quantity. The Avogadro constant (symbol NA) is given by the Avogadro...

Non-SI units mentioned in the SI Unit of Angle Symbol ′, arcmin In units Dimensionless with an arc length of approx. ≈ ⁠0.2909/1000⁠ of the radius, i.e. 0...

The Euler number (Eu) is a dimensionless number used in fluid flow calculations. It expresses the relationship between a local pressure drop caused by...

cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number w {\displaystyle w} , equal to the ratio of its pressure p {\displaystyle...

A drag count is a dimensionless unit used by aerospace engineers. 1 drag count is equal to a C d {\displaystyle C_{d}} of 0.0001. As the drag forces present...

is an approximation of the Gradient Richardson number. The BRN is a dimensionless ratio in meteorology related to the consumption of turbulence divided...

geometry, the Mahler volume of a centrally symmetric convex body is a dimensionless quantity that is associated with the body and is invariant under linear...

the time interval. To achieve kinematic similarity in a scaled model, dimensionless numbers in fluid dynamics come into consideration. For example, Reynolds...

reproduction that occurs in certain plant species Nusselt number (Nu), a dimensionless heat transfer ratio Nanodalton, a unit of mass; see dalton (unit) NU...

ratio, with SI base units of meter per meter (m/m). Hence strains are dimensionless and are usually expressed as a decimal fraction or a percentage. Parts-per...

efficacy can be normalized by the maximum possible luminous efficacy to a dimensionless quantity called luminous efficiency. The distinction between efficacy...

h_{\text{FE}}} or h fe {\displaystyle h_{\text{fe}}} , is normally given as a dimensionless number, the ratio of I c {\displaystyle I_{\text{c}}} to I b {\displaystyle...

(\mathrm {Re} _{D})} Here, S t {\displaystyle \mathrm {St} } is the dimensionless Strouhal number, f {\displaystyle f} is the vortex shedding frequency...

weight). It is one way of expressing the composition of a mixture in a dimensionless size; mole fraction (percentage by moles, mol%) and volume fraction...

unit area) applied to the object and the resulting axial strain (a dimensionless quantity that quantifies relative deformation) in the linear elastic...

reduce the number of free parameters. Small or large sizes of certain dimensionless parameters indicate the importance of certain terms in the equations...

"riftwar" is a war between two worlds that are connected by some sort of dimensionless gap (rift). In Feist's invented history, there are several rift wars...

result in a dimensionless quantity, also known as ratio or simply as a rate (such as tax rates) or counts (such as literacy rate). Dimensionless rates can...

matter Lagrangian constructed using an alternate metric; An arbitrary dimensionless function. These components are combined into a relativistic Lagrangian...

Dynamic Amplification Factor (DAF) or Dynamic Increase Factor (DIF), is a dimensionless number which describes how many times the deflections or stresses should...

fluid dynamics and thermodynamics, the Lewis number (denoted Le) is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity...

{\displaystyle \delta (\mathbf {x} )} represent the matter overdensity, a dimensionless quantity defined as: δ ( x ) = ρ ( x ) − ρ ¯ ρ ¯ , {\displaystyle \delta...

{\displaystyle \chi _{\text{e}}} ; Latin: susceptibilis "receptive") is a dimensionless proportionality constant that indicates the degree of polarization of...

prime-counting function in mathematics. Homotopy groups in algebraic topology. Dimensionless parameters constructed using the Buckingham π theorem of dimensional...

Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its...

research. Remarkably, a dimensionless quantity of internal friction is nearly universal in these materials. This quantity is a dimensionless ratio (up to a numerical...

weight, which is now used as a synonym for relative atomic mass and is dimensionless. Equivalent weights were originally determined by experiment, but (insofar...

{\displaystyle I} is applied. Rewriting the RCSJ model equation in dimensionless coordinates gives: ∂ 2 φ ∂ τ 2 + 1 Q ∂ φ ∂ τ + sin ⁡ ( φ ) = I I c 0...

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...

energy output and input are expressed in the same units, efficiency is a dimensionless number. Where it is not customary or convenient to represent input and...

-1}{2}}M^{2}\right)}}\right]} Equally important to the Fanno flow model is the dimensionless ratio of the change in entropy over the heat capacity at constant pressure...

proportionality constant in Coulomb's law using CGS-ESU quantities is a dimensionless quantity equal to 1. Coulomb's law in the CGS-Gaussian system takes...

actual temperature, because H is dimensionless. It is conjugate to the timelike polar angle σ, which is also dimensionless. To restore the length dimension...

other creatures on the two planets are able to create rifts through dimensionless space that can connect planets in different solar systems. The novels...

G absent, is relating only dimensionless quantities since any ratio of two like-dimensioned quantities is a dimensionless quantity. If, by a shorthand...

−29° 0′ 28.118″ Details Mass 8.54×1036 kg 4.297×106 M☉ Rotation 0.90±0.06 (dimensionless spin parameter) Astrometry Distance 26996±33 ly (8277±9 pc) Database...

the unit radian per meter (rad⋅m−1), or as above, since the radian is dimensionless. The frequency of light with wavenumber ν ~ {\displaystyle {\tilde {\nu...

In viscous fluid dynamics, the Archimedes number (Ar), is a dimensionless number used to determine the motion of fluids due to density differences, named...

recommended.) It is a dimensionless quantity with dimension of N / N {\displaystyle {\mathsf {N}}/{\mathsf {N}}} and dimensionless unit of moles per mole...

The electromechanical coupling coefficient is a numerical measure of the conversion efficiency between electrical and acoustic energy in piezoelectric...

other creatures on the two planets are able to create rifts through dimensionless space that can connect planets in different solar systems. The novels...

combustion, heat release parameter (or gas expansion parameter) is a dimensionless parameter which measures the amount of heat released by an adiabatic...

atmosphere The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics. Dimensionless distance variable...

for life. In practice, this hypothesis is formulated in relation to dimensionless physical constants. These physical constants, parameters, and initial...

The Stokes number (Stk), named after George Gabriel Stokes, is a dimensionless number characterising the behavior of particles suspended in a fluid flow...

count of entities (the latter formally regarded in the SI as being dimensionless). By implication, any product of powers of such constants is also such...

for control of armor after certification.[original research?] Using dimensionless analysis, materials researcher Philip Cuniff arrived at a relation connecting...

ideal gas. The real gas pressure and fugacity are related through the dimensionless fugacity coefficient φ = f P . {\displaystyle \varphi ={\frac {f}{P}}...

their reactivity worth decreases as the core ages. Reactivity (ρ) is dimensionless, but may be modified to make it less cumbersome. Since reactivity is...

scored divided by the number of goals conceded, and is therefore a dimensionless quantity. It was replaced by goal difference, which was thought to encourage...

data in a mass spectrum, it is common to use the dimensionless m/z, which denotes the dimensionless quantity formed by dividing the mass number of the...

torque, and θ is the angle swept (in radians). Since plane angles are dimensionless, it follows that torque and energy have the same dimensions.[citation...

H is the design wave height at the toe of the structure (m) KD is a dimensionless stability coefficient, deduced from laboratory experiments for different...

liquid-liquid flows. From the forces shown in the table above, five independent dimensionless quantities can be derived, these relations provide insight into how...

bound should be multiplied by a constant factor to convert it from dimensionless units to units of time; this factor depends on implementation details...

In materials science and solid mechanics, Poisson's ratio (symbol: ν (nu)) is a measure of the Poisson effect, the deformation (expansion or contraction)...

period of time equal to the age of the Universe (Hubble time). Λ is a dimensionless number defined as Λ = m 2 a 3 / 2 k {\displaystyle \Lambda ={\frac {m^{2}}{a^{3/2}}}\...

σ i = V i V . {\displaystyle \sigma _{i}={\frac {V_{i}}{V}}.} Being dimensionless, it is expressed as a number, e.g., 0.18 or 18%. There seems to be no...

function in LTI system theory h, Planck constant H, Hubble constant h, dimensionless Hubble constant H, absolute magnitude in the context of the Solar system...

The Kapitza number (Ka) is a dimensionless number named after the prominent Russian physicist Pyotr Kapitsa (Peter Kapitza). He provided the first extensive...

respectively yields dimensionless variables: Dimensionless Length Term (same for y' and z'): x ′ = x / L {\displaystyle x'={x/L}\,\!} , Dimensionless Velocity Term...

In fluid dynamics, the Schmidt number (denoted Sc) of a fluid is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity)...

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes"...

experimentally determined constant with its value proportional to the dimensionless fine-structure constant, which is known to a relative uncertainty of...

Canopy conductance, commonly denoted g c {\displaystyle g_{c}} , is a dimensionless quantity characterizing radiation distribution in tree canopy. By definition...

conservation of relativistic energy and momentum (see Compton scattering). The dimensionless quantity ϵ = E γ / m e c 2 {\displaystyle \epsilon =E_{\gamma }/m_{e}c^{2}}...

(1942) and Heat Transfer (1956). He is credited with devising the Jakob dimensionless number, aka Jakob number, which is used in phase change heat transfer...

In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from...

correspond to a size in millimeters, because ISO 6708 defines it as being a dimensionless specification only indirectly related to a diameter. The ISO 6708 sizes...

frequency, according to Airy wave theory. Quantities have been made dimensionless using the gravitational acceleration g and period T, with the deep-water...

measurement Base unit of measurement Natural units Dimensionless quantity General Lists Dimensionless units Lists of units of measurement Units of measurement...

Dimensionless number in fluid dynamics...

denoted Ri, is named after Lewis Fry Richardson (1881–1953). It is a dimensionless number that expresses the ratio of the buoyancy term to the flow shear...

in 1932, who taught at Tohoku University from 1925 to 1958. It is a dimensionless parameter that compares the rate of reaction in a liquid film to the...

kelvins = 273.15 + °C 0.08205 = Universal Gas Law constant in atm·l/(mol·K) M {\displaystyle M} = molecular weight of the air pollutant (dimensionless)...

independent of the unit in which the measurement has been taken, so it is a dimensionless number. For comparison between data sets with different units or widely...

the refund in case of cancellation). (Note: The prices here are the dimensionless numbers obtained by dividing by $1, which is the payout in all three...

Thermodynamic efficiency of the process (net power output per heat input, dimensionless) η pump , η turb {\displaystyle \eta _{\text{pump}},\eta _{\text{turb}}}...

diameter arises due to the use of a single dimension in the case of a dimensionless quantity such as the Reynolds number, which prefers a single variable...

the volume of all the solids ( V S {\displaystyle V_{S}} ). It is a dimensionless quantity in materials science and in soil science, and is closely related...

has a greater API gravity. Although API gravity is mathematically a dimensionless quantity (see the formula below), it is referred to as being in 'degrees'...

344~m} }{\mathrm {1~mi} }}} ⁠, which when simplified results in the dimensionless ⁠ 1 = 1609.344   m 1   m i {\displaystyle 1={\frac {\mathrm {1609.344~m}...

extensively to fluid dynamics, with concepts such as the Rayleigh number (a dimensionless number associated with natural convection), Rayleigh flow, the Rayleigh–Taylor...

the dimensionless ratios of fundamental constants. His basic approach was to combine several fundamental constants in order to produce a dimensionless number...

daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless). But the argument of perihelion, longitude of the ascending node and...

Reduced frequency is the dimensionless number used in general for the case of unsteady aerodynamics and aeroelasticity. It is one of the parameters that...

relevant variable is the membrane potential, x(t), which is written in dimensionless units. There are two more variables, y(t) and z(t), which take into...

{\displaystyle n_{\text{c}}={\frac {mT}{2\pi }}\ln {\frac {\xi }{mU}}} where the dimensionless constant was found to be ξ = 380 ± 3 {\displaystyle \xi =380\pm 3} ...

will be log(1000) more than the same quantity measured in meters; a dimensionless quantity will have differential entropy of log(1000) more than the same...

patient's total body water In the context of hemodialysis, Kt/V is a pseudo-dimensionless number; it is dependent on the pre- and post-dialysis concentration...

or intensity of the standard illuminant used to measure it, and is a dimensionless quantity. By definition, internal transmittance is related to optical...

Comparison of the Rayleigh wave speed with shear and longitudinal wave speeds for an isotropic elastic material. The speeds are shown in dimensionless units....

u(h)=\left(1-{\frac {Lh}{T_{0}}}\right)^{g/(RL)}} is defined as the dimensionless pressure variable. Substituting this density into the ballistic deceleration...

celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with magnitude...

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...

tables, z is the cosmological redshift, c the speed of light, and h the dimensionless Hubble parameter, which has a value of approximately 0.7 (the Hubble...

In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. To fully specify the state of the...

(Ga), sometimes also referred to as Galileo number[by whom?], is a dimensionless number named after Italian scientist Galileo Galilei (1564-1642). It...

J·s/rad, with the same numerical value, as the radian is the natural dimensionless unit of angle. The Planck constant was formulated as part of Max Planck's...

D. B. (1993) [1963]. A Dictionary of Scientific Units - Including dimensionless numbers and scales (6 ed.). London: Chapman and Hall. p. 100. ISBN 0412467208...

on the slenderness/dimensionless volume plane. Slenderness is defined as H 2 R {\textstyle {\frac {H}{2R}}} , and the dimensionless volume is capillary...

Bearing modulus is a modulus used in journal bearing design. It is a dimensionless number. Bearing Modulus (C) is C = (Zn/p) where Z = oil viscosity n...

The Lockhart–Martinelli parameter ( χ {\displaystyle \chi } ) is a dimensionless number used in internal two-phase flow calculations. It expresses the...

The Weibull modulus is a dimensionless parameter of the Weibull distribution. It represents the width of a probability density function (PDF) in which...

mass expressed in grams per mole", the relative atomic mass Ar(X) is a dimensionless quantity, whereas the molar mass has the SI coherent unit of kg/mol...

{\displaystyle \mu _{r}} is the relative magnetic permeability of the material (dimensionless) μ {\displaystyle \mu } is the permeability of the material ( μ = μ...

angular quantities, plane angle and solid angle, are defined as derived dimensionless quantities in the SI. For some relations, their units radian and steradian...

equation – Description of gas flow in free molecular flow Knudsen number – Dimensionless number relating to mean free path of a particle Yamamoto, K.; Pack,...

is a hypothetical one-dimensional source of a sound, as opposed to a dimensionless point source. As a line source propagates sound equally in all directions...

related property of materials is magnetic susceptibility, which is a dimensionless proportionality factor that indicates the degree of magnetization of...

over a specific time period, relative to carbon dioxide (CO2). It is a dimensionless quantity expressed as a multiple of warming caused by the same mass...

title Stefan (album), a 1987 album by Dennis González Stefan number, a dimensionless number used in heat transfer Sveti Stefan or Saint Stefan, a small islet...

quantum theories by couplings that are dimensionless; i.e., are pure numbers. An example of such a dimensionless constant is the fine-structure constant...

1926. The Goldschmidt tolerance factor ( t {\displaystyle t} ) is a dimensionless number that is calculated from the ratio of the ionic radii: In an ideal...

In fluid dynamics, the lift coefficient (CL) is a dimensionless quantity that relates the lift generated by a lifting body to the fluid density around...

found by RH = Actual Vapor Density / SVD. As relative humidity is a dimensionless quantity (often expressed in terms of a percentage), vapor density can...

sectional area, and C D {\displaystyle C_{D}} is the drag coefficient – a dimensionless number. Escape velocity is the minimum speed a ballistic object needs...

transfer coefficient is often calculated from the Nusselt number (a dimensionless number). There are also online calculators available specifically for...

represented by a comparison between a dimensionless shear stress τ b ∗ {\displaystyle \tau _{b}*} and a dimensionless critical shear stress τ c ∗ {\displaystyle...

The Brinkman number (Br) is a dimensionless number related to heat conduction from a wall to a flowing viscous fluid, commonly used in polymer processing...

at temperature T. The total absorption ratio a(T, i) of that body is dimensionless, the ratio of absorbed to incident radiation in the cavity at temperature...

"riftwar" is war between two worlds that are connected by some sort of dimensionless gap (a "rift"). In Feist's fictional universe several riftwars occur...

clouds, and rain will not form. The Bulk Richardson Number (BRN) is a dimensionless number relating vertical stability and vertical wind shear (generally...

manufacturer of guitars and other stringed instruments Dean number, a dimensionless group in fluid mechanics, which occurs in the study of flow in curved...

friction factor (SI units: dimensionless) Re {\displaystyle \operatorname {Re} } is the Reynolds number (SI units: dimensionless) He {\displaystyle \operatorname...

method Draft – Depth of a vessel below its waterline Froude number – Dimensionless number; ratio of a fluid's flow inertia to the external field Hull classification...

The propeller advance ratio or coefficient is a dimensionless number used in aeronautics and marine hydrodynamics to describe the relationship between...

power ratios vs amplitude ratios. Crest factor and PAPR are therefore dimensionless quantities. While the crest factor is defined as a positive real number...

more technically called transimpedance instead of gain (which is a dimensionless quantity). If the gain is large, any input offset voltage at the non-inverting...

Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density (mass divided by volume) of a substance...

curvature. An object encountering the singularity would undergo a sudden, dimensionless tidal deformation followed by rapid acceleration to relativistic velocities...

{\displaystyle Q} . Equivalently, diodicity could also be defined as ratio of dimensionless Hagen number or Darcy friction factor at the same Reynolds number. With...

_{n}^{b}+c_{3}\delta _{n}^{a}\delta _{m}^{b}+c_{4}u^{a}u^{b}g_{mn}.} Here the ci are dimensionless adjustable parameters of the theory. Several spherically symmetric solutions...

object on its orbit Eccentricity vector, in celestial mechanics, a dimensionless vector with direction pointing from apoapsis to periapsis Eccentric...

Submerged specific gravity is a dimensionless measure of an object's buoyancy when immersed in a fluid. It can be expressed in terms of the equation SSG...

not so now. Tests on the immutability of physical constants look at dimensionless quantities, i.e. ratios between quantities of like dimensions, in order...

that piece of equipment, including the operating transients. It is a dimensionless ratio of useful energy output to energy input, expressed as a percentage...

of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular...

rely on chemical reactions driven by heat. A difference between the dimensionless terms efficiency and COP is that the numerator in COP is the heat moved...

{\text{Fr}}_{1}={v_{1} \over {\sqrt {gh_{1}}}}} The Froude number is dimensionless. In terms of the Froude number, the Bélanger equation is: h 2 h 1 =...

The Ohnesorge number (Oh) is a dimensionless number that relates the viscous forces to inertial and surface tension forces. The number was defined by...

L2/A, where L is the length of the curve and A is its area. It is a dimensionless quantity that is invariant under similarity transformations of the curve...

character look more like a "spoiled brat". "She's photogenic, granted, but dimensionless and has minimal screen presence—the final reel about-face that is synonymous...

The mass-flux fraction (or Hirschfelder-Curtiss variable or Kármán-Penner variable) is the ratio of mass-flux of a particular chemical species to the total...

other cavitation-relevant parameters. The suction head coefficient is a dimensionless measure of NPSH: C NPSH = g ⋅ NPSH n 2 D 2 {\displaystyle C_{\text{NPSH}}={\frac...

or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms...

transmitted spectral radiant power through a material. Absorbance is dimensionless, and in particular is not a length, though it is a monotonically increasing...

during this period. If this is multiplied by the cross-section, then a dimensionless number is obtained equal to the number of expected scattering events...

described by the same underlying scale-invariant theory. In general, dimensionless quantities are scale-invariant. The analogous concept in statistics...

SMBH in extreme cases, for example its maximal prograde spin with a dimensionless spin parameter of a = 1, although the maximum limit for a black hole's...

Log reduction is a measure of how thoroughly a decontamination process reduces the concentration of a contaminant. It is defined as the common logarithm...

The power number Np (also known as Newton number) is a commonly used dimensionless number relating the resistance force to the inertia force. The power-number...

resistivity of the workpiece in ohm-meters, μ {\displaystyle \mu } is the dimensionless relative magnetic permeability of the workpiece, and f {\displaystyle...

scale radius, δ c {\displaystyle \delta _{c}} is a characteristic (dimensionless) density, and ρ c r i t {\displaystyle \rho _{crit}} = 3 H 2 / 8 π G...

calculation is that originally proposed by Linus Pauling. This gives a dimensionless quantity, commonly referred to as the Pauling scale (χr), on a relative...

group (RG), is thus special in its UV limit in the sense that all their dimensionless combinations remain finite. This suffices to avoid unphysical divergences...

as "number of revolutions" or "number of cycles") is formalized as a dimensionless quantity called rotation, defined as the ratio of a given angle and...

\!} dimensionless dimensionless Angular magnification m m = θ 2 / θ 1 {\displaystyle m=\theta _{2}/\theta _{1}\,\!} dimensionless dimensionless...

Out}}}} The term efficiency is a dimensionless measure (sometimes quoted in percent), and strictly heat rate is dimensionless as well, but often written as...

of analyte in sample [%-w/w] C = mass fraction of analyte in sample [dimensionless] = w / 100%-w/w predicted RSD (relative standard deviation) = 2^(1-0...

grains, common in stellar envelopes and nebulae. Plasma parameters – Dimensionless numbers characterizing astrophysical plasmas. Biermann battery – Mechanism...

Earth's standard acceleration g 0 {\displaystyle g_{0}} ). It is a dimensionless parameter characteristic of rockets and other jet engines and of vehicles...

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...

defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of...

permittivity farad per metre F/m kg−1⋅m−3⋅A2⋅s4 χe electric susceptibility (dimensionless) 1 1 p electric dipole moment coulomb metre C⋅m A⋅s⋅m G; Y; B conductance;...

vapour density of mixture of NO2 and N2O4 is 38.3. Vapour density is a dimensionless quantity. Vapour density = density of gas / density of hydrogen (H2)...

Gauckler–Manning coefficient. Units of n are often omitted, however n is not dimensionless, having dimension of T/L1/3 and units of s/m1/3. Rh is the hydraulic...

diameter divided by the ship's length between perpendiculars gives a dimensionless parameter that can be used to compare the manoeuvrability of ships....

2010. Monjo, R. (2016). "Measure of rainfall time structure using the dimensionless n-index". Climate Research. 67 (1): 71–86. Bibcode:2016ClRes..67...71M...

C R {\displaystyle \tan \phi ={\frac {X_{L}-X_{C}}{R}}\,\!} dimensionless dimensionless AC peak current I0 I 0 = I r m s 2 {\displaystyle I_{0}=I_{\mathrm...

Net tonnage (NT, N.T. or nt) is a dimensionless index calculated from the total moulded volume of the ship's cargo spaces by using a mathematical formula...

be expressed in hours. k {\displaystyle k} is the Peukert constant (dimensionless), The capacity at a one-ampere discharge rate is not usually given for...

In fluid dynamics and geology, the Leverett J-function is a dimensionless function used to describe the capillary pressure required to force a fluid into...

Gibbs–Duhem equation. Note that in general activity coefficients are dimensionless. In detail: Raoult's law states that the partial pressure of component...

; McNeill, D. B. (2012). Dictionary of Scientific Units: Including dimensionless numbers and scales (6th ed.). Springer Science & Business Media. p. 92...

all coupling constants occurring in the Lagrangian rendered dimensionless. Dimensionless coupling constants are the technical hallmark for the upper critical...

diagram, the x-axis is the vehicle velocity, and the y-axis is the dimensionless specific resistance. The same kind of vehicle may have multiple different...

a proton, is given by the fine-structure constant. This value is a dimensionless quantity formed by the ratio of two energies: the electrostatic energy...

represents the x, y and z coordinates, ξ {\displaystyle \xi } is a dimensionless variable given by ξ = Ω t / 2 {\displaystyle \xi =\Omega t/2} , and...

The Dukhin number (Du) is a dimensionless quantity that characterizes the contribution of the surface conductivity to various electrokinetic and electroacoustic...

phenomenon of a 'reactive Leidenfrost (RL) effect' was characterized by a dimensionless quantity, (φRL= τconv/τrxn), which relates the time constant of solid...

_{2}}{\Delta '}}\right\}} where Δ ′ {\displaystyle \Delta '} represents the dimensionless effective inter-particle spacing between two adjacent rod-shaped particles...

scaled by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility...

geometric description of an aircraft, and outputs its corresponding dimensionless stability derivatives according to the specified flight conditions....

preoccupied with the question of why the fine-structure constant, a dimensionless fundamental constant, has a value nearly equal to 1/137. Pauli died...

and its reference value, though a logarithm may be considered to be a dimensionless quantity. The reference values for each type of quantity are often specified...

across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of...

The weak mixing angle or Weinberg angle is a parameter in the Weinberg–Salam theory (by Steven Weinberg and Abdus Salam) of the electroweak interaction...

Offered load is expressed in Erlang units or call-seconds per hour, a dimensionless measure. Freeman, Roger L. (2005). Fundamentals of Telecommunications...

on the soil is greater than the resistance the soil provides. This dimensionless ratio (the Shields parameter) was first described by Albert Shields...

Görtler [de]. The onset of Görtler vortices can be predicted using the dimensionless number called Görtler number (G). It is the ratio of centrifugal effects...

Psychophysiology, Chapter 19. Selye's ideas were used by Gunther et al., in which dimensionless numbers (allometric invariance analysis) were used to investigate the...

very small particles away from the Sun. It is characterized by the dimensionless dust parameter β {\displaystyle \beta } , the ratio of the force due...

parcel of fluid is subject to inertial effects. The Reynolds number is a dimensionless quantity which characterises the magnitude of inertial effects compared...

may be smaller or equal to the grain size; K {\displaystyle K} is a dimensionless shape factor, with a value close to unity. The shape factor has a typical...

{\displaystyle C={\frac {u\,\Delta t}{\Delta x}}\leq C_{\max }} where: the dimensionless number C {\displaystyle C} is called the Courant number, u {\displaystyle...

In analytical chemistry, the hydroxyl value is defined as the number of milligrams of potassium hydroxide (KOH) required to neutralize the acetic acid...

must be expressed in radians per second, where the radian assumes the dimensionless value of unity. (When performing dimensional analysis, it may be productive...

tunnel to initial singularities of new universes, at which point the dimensionless parameters of the standard models of particle physics and cosmology...

heliosynchronous orbit. The J 2 {\displaystyle J_{2}} used in this equation is the dimensionless coefficient J 2 ~ = − J 2 G M E R E 2 {\displaystyle {\tilde {J_{2}}}=-{\frac...

charged ion (cation). Each type of radiation is therefore assigned a dimensionless weighting factor that expresses its biological effectiveness. For X-rays...

down (6-5) into its components, replacing v {\displaystyle v} with the dimensionless ⁠ β {\displaystyle \beta } ⁠, and factoring out common terms from (6-5)...

the International System of Units (SI), the radian is defined as a dimensionless derived unit. Consequently, torque is conventionally expressed simply...

and is therefore widely used. Deviations from it are small when the dimensionless quantities ϕ / c 2 {\displaystyle \phi /c^{2}} and ( v / c ) 2 {\displaystyle...

physics, the Lundquist number (denoted by S {\displaystyle S} ) is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the...

The Eckert number (Ec) is a dimensionless number used in continuum mechanics. It expresses the relationship between a flow's kinetic energy and the boundary...

come to an end. Thus, Dicke explained the coincidence between large dimensionless numbers constructed from the constants of physics and the age of the...

length of the major axis and b is the length of the minor axis. This dimensionless quantity is between 0 and 1, and may be multiplied by 100 to express...

altitude could indeed be a thermodynamic property. Conjugate variables Dimensionless numbers Intensive and extensive properties Thermodynamic databases for...

Boltzmann's factor. Note that the Hamiltonian H {\displaystyle H} is dimensionless in this formulation because the exponential probability weight exp ⁡...

{\displaystyle G} is the grade (percent slope), and η {\displaystyle \eta } is a dimensionless terrain factor accounting for surface conditions. The first term estimates...

expression. The summation is dimensionless, since the value p i {\displaystyle p_{i}} is a probability and therefore dimensionless, and ln is the natural logarithm...

limited-production, and concept or experimental vehicles. The drag coefficient is a dimensionless measure of aerodynamic resistance used in automotive design; a lower...

For other uses, Redirect to; Reflectance (disambiguation) The reflectance of the surface of a material is its effectiveness in reflecting radiant energy...

degree of magnetization of a material Proton-to-electron mass ratio, a dimensionless physical constant Reduced mass, the "effective" inertial mass appearing...

artificial life simulations, in addition to his lambda parameter, a dimensionless measure of complexity and computation potential in cellular automata...

may be shown that the motion of a pendulum can be described by the dimensionless nonlinear equation d 2 θ d t 2 + sin ⁡ ( θ ) = 0 {\displaystyle {\frac...

may be close to one or the other (as in deuterium). The g-factor is a dimensionless factor associated to the nuclear magnetic moment. This parameter contains...

the particle's radius, λ is the wavelength of the light and x is a dimensionless parameter that characterizes the particle's interaction with the incident...

The Dean number (De) is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels. It is named after the...

electron:nucleon ratio differs among isotopes. The mass number is a dimensionless quantity. The atomic mass, on the other hand, is measured using the...

minus height with the result being positive, 0 or negative. Unlike the dimensionless ratio, this calculation produces a numeric value in the units of measurement...

the latent heat of vaporization for water. Note that this index is dimensionless and that the variables R {\displaystyle R} , L {\displaystyle L} and...

 145. ISBN 978-0-86720-479-7. Mohr, J. C.; Phillips, W. D. (2015). "Dimensionless Units in the SI". Metrologia. 52 (1): 40–47. arXiv:1409.2794. Bibcode:2015Metro...

in the case that natural circulation is not sufficient. A number of dimensionless terms have been derived to describe and predict convection, including...

moment of inertia factor or normalized polar moment of inertia is a dimensionless quantity that characterizes the radial distribution of mass inside a...

time. It is defined as periodic time increase per unit time; it is a dimensionless quantity, but can be given the units of s⋅s−1 (seconds per second)....

boundary falling around a redshift range of z=0.1–0.3, where z is a dimensionless measure of the spectrum's frequency shift. High-redshift searches for...

spectrometers". When presenting data, it is common to use the (officially) dimensionless m/z, where z is the number of elementary charges (e) on the ion (z=Q/e)...

The Love numbers (h, k, and l) are dimensionless parameters that measure the rigidity of a planetary body or other gravitating object, and the susceptibility...

the stress and extend in the transverse or lateral direction. It is a dimensionless quantity, as it is a ratio between two quantities of the same dimension...

ratio defining standardized moments, the dimensions cancel, so they are dimensionless numbers. The first four standardized moments can be written as: For...

population proportion in statistics Pion or π, a subatomic particle πi, a dimensionless quantity as derived from the Buckingham π theorem. Pi (prefix symbol)...

leading a flotilla ⟨dl⟩, a digraph; see List of Latin script digraphs. Dimensionless quantity (dl, in lower case), the 'per unit' system of measurement Decilitre...

Monjo, R. (2016). "Measure of rainfall time structure using the dimensionless n-index". Climate Research. 67 (1): 71–86. Bibcode:2016ClRes..67...71M...

951–960. Monjo, R. (2016). "Measure of rainfall time structure using the dimensionless n-index". Climate Research. 67 (1): 71–86. Bibcode:2016ClRes..67...71M...

would have all the matter and spacetime in the universe collapse into a dimensionless singularity back into how the universe started with the Big Bang, but...

k_{I}} is the intrinsic permeability [length2] C {\displaystyle C} is a dimensionless constant that is related to the configuration of the flow-paths d {\displaystyle...

In chemistry, the iodine value (IV; also iodine absorption value, iodine number or iodine index) is the mass of iodine in grams that is consumed by 100 grams...

value of the fine-structure constant. The fine-structure constant, a dimensionless physical constant, is approximately 1/137, and the astronomer Arthur...

Load-loss factor (also loss load factor, LLF, or simply loss factor) is a dimensionless ratio between average and peak values of load loss (loss of electric...

modern graphics cards. The pixel pipelines take pixel (each pixel is a dimensionless point) and texel information and process it, via specific matrix and...

external field. Thus, V is formally a Hermitian operator. Let λ be a dimensionless parameter that can take on values ranging continuously from 0 (no perturbation)...

.bi, the Internet top-level domain for Burundi Biot number (Bi), a dimensionless quantity in heat transfer calculations Bismuth (symbol Bi), the chemical...

Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other...

arbitrary "reference radius" R close to Earth's radius and to work with the dimensionless coefficients J n ~ = − J n μ   R n , C n m ~ = − C n m μ   R n , S n...

All Chochmah-Wisdom Source of intellect Partzuf of Abba-Father י Yud Dimensionless point First illumination-Male Dot in the Palace Chayah-Living Encompassing...

1025 m−3 is often introduced to define a relative number density (a dimensionless quantity), for any substances at any conditions (not necessarily limited...

ξ {\displaystyle \tau (t)=\int _{0}^{t}a(\xi )d\xi } is a reduced, dimensionless time. The temporal dependence of the infected fraction I ( τ ) {\displaystyle...

The Zener ratio is a dimensionless number that is used to quantify the anisotropy for cubic crystals. It is sometimes referred as anisotropy ratio and...

{\displaystyle Y_{0}} cancels these units. The resulting normalized values are dimensionless quantities, which are the only values plotted directly on a Smith chart...

{E_{a}}{RT}}\right)^{\beta }\right],} where ⁠ β {\displaystyle \beta } ⁠ is a dimensionless number of order 1. This is typically regarded as a purely empirical...

B} are now function of entropy such that n   {\displaystyle n\ } is dimensionless B   {\displaystyle B\ } has the same units as P {\displaystyle P} The...

(α1, α2, ..., αn) dimensionless discrete quantum numbers ω = (ω1, ω2, ..., ωm) continuous variables (not necessarily dimensionless) These quantum numbers...

natural rocks. It was first described by J.G. Koenigsberger. It is a dimensionless parameter often used in geophysical exploration to describe the magnetic...

worry", i.e., "carefree." Ohnesorge may refer to: Ohnesorge number, a dimensionless quantity in fluid dynamics Wilhelm Ohnesorge, member of Nazi cabinet...

dBZ is a logarithmic dimensionless technical unit used in radar. It is mostly used in weather radar, to compare the equivalent reflectivity factor (Z)...

In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively...

}}} where ω ( φ ) {\displaystyle \omega (\varphi )\;} is a different dimensionless function for each different scalar–tensor theory. The function λ ( φ...

\lambda =\alpha {\frac {\gamma }{M_{\mathrm {s} }}},} where α is a dimensionless constant called the damping factor. The effective field Heff is a combination...

of the radius R {\displaystyle R} of C o {\displaystyle C_{o}} and dimensionless parameters describing the structure of the Spirograph. Namely, let l...

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot...

reaction and an early transition state for an exothermic reaction. A dimensionless reaction coordinate that quantifies the lateness of a transition state...

In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of...

H2 + O2 → 2 H2O. Coefficient of thermal expansion (thermodynamics) (dimensionless) - Relates the change in temperature to the change in a material's dimensions...

under consideration and f {\displaystyle f} is Fanning friction factor (dimensionless). It is related to the Darcy friction factor by k = 1 2 ρ λ 4 , {\displaystyle...

of field, diffraction, and exposure of a photograph. The f-number is dimensionless and is usually expressed using a lower-case hooked f with the format...

constant 1 / h 0 F {\textstyle {1}/{h_{0}^{\mathcal {F}}}} makes Ω(U) dimensionless. For an ideal gas is Ω ( U ) ∝ F U F 2 − 1 δ U {\displaystyle \Omega...

{t}} is the thickness of the specimen, and f {\displaystyle {f}} is a dimensionless geometry factor determined by finite element method (FEM). This factor...

propel them backward at great speed!" "thrust-to-weight ratio F/Wg is a dimensionless parameter that is identical to the acceleration of the rocket propulsion...

Chaos may be described as having the consistency of vapor or water, dimensionless, and sometimes salty or muddy. These myths associate chaos with evil...

k = M / L 1 L 2 {\displaystyle k\;=\;M/{\sqrt {L_{1}L_{2}}}} . This dimensionless parameter is equal to the fraction of magnetic flux through the transmitter...

defined. These should be chosen such that the dimensionless variables are of order one. The following dimensionless variables are thus obtained: u ∗ ≡ u u 0...

macroscopic friction coefficient μ {\displaystyle \mu } as a function of the dimensionless quantity I {\displaystyle I} called the Inertial number. The complete...

galaxies will be a certain distance apart) at 100 h−1 Mpc, (where h is the dimensionless Hubble constant) indicating that this is the size of the sound horizon...

dimensions, depending upon the system being considered; parameters are dimensionless, or have the dimension of time or its reciprocal." The term can also...

per nanometre; y(λ), also known as V(λ), is the luminosity function, dimensionless; λ is the wavelength, in nanometres. Formally, the integral is the inner...

absolute difference in comparison to the size of the mean and is a dimensionless quantity. The relative mean absolute difference is equal to twice the...

scaling each feature by its standard deviation, so that one ends up with dimensionless features with unital variance. The applicability of PCA as described...

The Wilson ratio of a metal is the dimensionless ratio of the zero-temperature magnetic susceptibility to the coefficient of the linear temperature term...

(which are measurable quantities) to define SI derived units, including dimensionless derived units, such as the radian (rad) and steradian (sr) which are...

directionPages displaying short descriptions of redirect targets Ekman number – Dimensionless ratio of viscous to Coriolis forces Ekman spiral – Net transport of...

transcribed as Ostrogradskiy and Ostrogradskiĭ Kunes, Josef (2012-02-13). Dimensionless Physical Quantities in Science and Engineering. Elsevier. ISBN 978-0-12-391458-3...

Models of light scattering can be divided into three domains based on a dimensionless size parameter, α which is defined as: α = π D p / λ , {\displaystyle...

above in dimensionless form by scaling time by a factor R 0 / W 0 {\displaystyle R_{0}/W_{0}} . Using the same symbols for the dimensionless variables...

equations. Interactive calculators are often used to determine these dimensionless ratios for various fluids and flow conditions. In a general case of...

the vector potential. In the next section they will be promoted to dimensionless operators. By using field equations of B {\displaystyle \mathbf {B}...

pressure-driven flow between parallel plates, the resulting scaled (dimensionless) boundary value problem is: d 2 u d y 2 = − 1 ; u ( 0 ) = u ( 1 ) =...

Such flows are found to be vortex-like. The Reynolds number (Re) is a dimensionless quantity that is commonly used in fluid dynamics and engineering. Originally...

terminals a potential difference of one abvolt List of metric units The dimensionless constant ccgs = 2.99792458×1010 is numerically equal to the magnitude...

2022. Retrieved January 7, 2019. Kunes, Josef (February 13, 2012). Dimensionless Physical Quantities in Science and Engineering. Elsevier. ISBN 9780123914583...

holes are measured in terms of the mass of the Sun, or solar mass. The dimensionless spin parameter is between 0 and 1, where 0 denotes zero angular momentum...

of such 100 cubic feet 'tun' units of volume. (The divisor of 100 is dimensionless, so tonnage would be expressed in 'ft3 of tun'.) In 1678 Thames shipbuilders...

dynamic viscosity). The Blasius solution uses boundary conditions in a dimensionless form: v x − v S v ∞ − v S = v x v ∞ = v y v ∞ = 0 {\displaystyle {v_{x}-v_{S}...

to a radius The propeller characteristics are commonly expressed as dimensionless ratios: Pitch ratio PR = propeller pitch/propeller diameter, or P/D...

Darcian, as in the case of groundwater flow. The Reynolds number (a dimensionless parameter) for porous media flow is typically expressed as R e = q d...

velocity, D is a characteristic length of the bluff body and S is the dimensionless Strouhal number, which depends on the body in question. For Reynolds...

{E} [\tau (y_{0})\mid y_{0}].} The logarithmic residence time is a dimensionless variation of the residence time. It is proportional to the natural log...

a linear measure (for example, in inches or millimetres) or as the dimensionless ratio between that measure and the focal length. In other photography...

of a wave that rises above an undisturbed position Crest factor, a dimensionless number quantifying the shapes of waves CREST syndrome, a limited form...

Names of large numbers Orders of magnitude (numbers) to help compare dimensionless numbers between 1,000,000 and 10,000,000 (106 and 107) There are no...

{\displaystyle c\geq 2{\sqrt {rD}}} ( c ≥ 2 {\displaystyle c\geq 2} in dimensionless form) it admits travelling wave solutions of the form u ( x , t ) =...

In fluid dynamics, the Graetz number (Gz) is a dimensionless number that characterizes laminar flow in a conduit. The number is defined as: G z = D H...

Shuttle Columbia on 23 July 1999. The Chandrasekhar number, an important dimensionless number of magnetohydrodynamics, is named after him. The asteroid 1958...

deformation to the original value of the parameter. Since strain is a dimensionless quantity, the units of δ {\displaystyle \delta } will be the same as...

that since the stoichiometric number can either be considered to be dimensionless or to have units of moles, conversely the extent of reaction can either...

curve shows the relationship between the so-called Hersey number, a dimensionless lubrication parameter, and the friction coefficient. The Hersey number...

_{Y})} where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the...

{\displaystyle P(dx)=p(x)\,dx} is dimensionless. The argument of the logarithmic term is and remains dimensionless, as it must. It can therefore be seen...

solute in the solution, then intrinsic viscosity is defined as the dimensionless number [ η ] = lim ϕ → 0 η − η 0 η 0 ϕ {\displaystyle \left[\eta \right]=\lim...

length of the chord of the airfoil. C m {\displaystyle C_{m}} is a dimensionless coefficient so consistent units must be used for M, q, S and c. Pitching...

In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without...

/ e {\displaystyle k_{B}T/e} then the equation can be rearranged to dimensionless form ∇ 2 ψ = 2 c 0 ( l b ) 3 sinh ⁡ ( ψ ) . {\displaystyle \nabla ^{2}\psi...

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...