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# Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned. [1]

120 relations: Alcohol by volume, Alcoholic drink, Angular velocity, Arbitrary unit, Average, Avogadro constant, Beta (plasma physics), Boltzmann constant, Boyle's law, Buckingham π theorem, Coefficient of variation, Conversion of units, Cost of transport, Coulomb's constant, Damköhler numbers, Data, Decibel, Deformation (mechanics), Degree (angle), Density, Dependent and independent variables, Design, Diameter, Dimension, Dimensional analysis, Dozen, E (mathematical constant), Economics, Edgar Buckingham, Efficiency, Electric charge, Electric power, Electromagnetism, Electron, Elementary particle, Engineering, Equilibrium constant, Ethanol, Fine-structure constant, Fluid mechanics, Fresnel number, Function (mathematics), Golden ratio, Googol, Gradian, Gravitational constant, Gravitational coupling constant, Gravity, Gross (unit), Heat transfer, ... Expand index (70 more) »

## Alcohol by volume

Alcohol by volume (abbreviated as ABV, abv, or alc/vol) is a standard measure of how much alcohol (ethanol) is contained in a given volume of an alcoholic beverage (expressed as a volume percent).

## Alcoholic drink

An alcoholic drink (or alcoholic beverage) is a drink that contains ethanol, a type of alcohol produced by fermentation of grains, fruits, or other sources of sugar.

## Angular velocity

In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin.

## Arbitrary unit

In science and technology, an arbitrary unit (abbreviated arb. unit, see below) or procedure defined unit (p.d.u.) is a relative unit of measurement to show the ratio of amount of substance, intensity, or other quantities, to a predetermined reference measurement.

## Average

In colloquial language, an average is a middle or typical number of a list of numbers.

In chemistry and physics, the Avogadro constant (named after scientist Amedeo Avogadro) is the number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole.

## Beta (plasma physics)

The beta of a plasma, symbolized by β, is the ratio of the plasma pressure (p.

## Boltzmann constant

The Boltzmann constant, which is named after Ludwig Boltzmann, is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas.

## Boyle's law

Boyle's law (sometimes referred to as the Boyle–Mariotte law, or Mariotte's law) is an experimental gas law that describes how the pressure of a gas tends to increase as the volume of the container decreases.

## Buckingham π theorem

In engineering, applied mathematics, and physics, the Buckingham theorem is a key theorem in dimensional analysis.

## Coefficient of variation

In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.

## Conversion of units

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

## Cost of transport

The energy cost of transport quantifies the energy efficiency of transporting an animal or vehicle from one place to another.

## Coulomb's constant

Coulomb's constant, the electric force constant, or the electrostatic constant (denoted) is a proportionality constant in electrodynamics equations.

## Damköhler numbers

The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale (reaction rate) to the transport phenomena rate occurring in a system.

## Data

Data is a set of values of qualitative or quantitative variables.

## Decibel

The decibel (symbol: dB) is a unit of measurement used to express the ratio of one value of a physical property to another on a logarithmic scale.

## Deformation (mechanics)

Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration.

## Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

## Density

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume.

## Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

## Design

Design is the creation of a plan or convention for the construction of an object, system or measurable human interaction (as in architectural blueprints, engineering drawings, business processes, circuit diagrams, and sewing patterns).

## Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Dimensional analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed.

## Dozen

A dozen (commonly abbreviated doz or dz) is a grouping of twelve.

## E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.

## Economics

Economics is the social science that studies the production, distribution, and consumption of goods and services.

## Edgar Buckingham

Edgar Buckingham (July 8, 1867 in Philadelphia, Pennsylvania &ndash; April 29, 1940 in Washington DC) was an American physicist.

## Efficiency

Efficiency is the (often measurable) ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result.

## Electric charge

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

## Electric power

Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit.

## Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

## Electron

The electron is a subatomic particle, symbol or, whose electric charge is negative one elementary charge.

## Elementary particle

In particle physics, an elementary particle or fundamental particle is a particle with no substructure, thus not composed of other particles.

## Engineering

Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.

## Equilibrium constant

The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change.

## Ethanol

Ethanol, also called alcohol, ethyl alcohol, grain alcohol, and drinking alcohol, is a chemical compound, a simple alcohol with the chemical formula.

## Fine-structure constant

In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted (the Greek letter ''alpha''), is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles.

## Fluid mechanics

Fluid mechanics is a branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.

## Fresnel number

The Fresnel number (F), named after the physicist Augustin-Jean Fresnel, is a dimensionless number occurring in optics, in particular in scalar diffraction theory.

## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

## Googol

A googol is the large number 10100.

The gradian is a unit of measurement of an angle, equivalent to \frac of a turn, \frac of a degree, or \frac of a radian.

## Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

## Gravitational coupling constant

In physics, a gravitational coupling constant is a constant characterizing the gravitational attraction between a given pair of elementary particles.

## Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

## Gross (unit)

In English and related languages, several terms involving the words "great" or "gross" (possibly, from grosse thick) relate to numbers involving multiples of exponents of twelve (dozen).

## Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems.

## Identity (mathematics)

In mathematics an identity is an equality relation A.

## Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

## International Bureau of Weights and Measures

The International Bureau of Weights and Measures (Bureau international des poids et mesures) is an intergovernmental organization established by the Metre Convention, through which Member States act together on matters related to measurement science and measurement standards.

## International Committee for Weights and Measures

The International Committee for Weights and Measures (abbreviated CIPM from the French Comité international des poids et mesures) consists of eighteen persons, each of a different nationality, from Member States of the Metre Convention (Convention du Mètre) appointed by the General Conference on Weights and Measures (CGPM) whose principal task is to promote worldwide uniformity in units of measurement by taking direct action or by submitting proposals to the CGPM.

## International Organization for Standardization

The International Organization for Standardization (ISO) is an international standard-setting body composed of representatives from various national standards organizations.

## International System of Units

The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.

## Invariant mass

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system.

## James Clerk Maxwell

James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist in the field of mathematical physics.

## John William Strutt, 3rd Baron Rayleigh

John William Strutt, 3rd Baron Rayleigh, (12 November 1842 – 30 June 1919) was a physicist who, with William Ramsay, discovered argon, an achievement for which he earned the Nobel Prize for Physics in 1904.

## Joseph Bertrand

Joseph Louis François Bertrand (11 March 1822 – 5 April 1900) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics.

## Joseph Fourier

Jean-Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations.

## Kilogram

The kilogram or kilogramme (symbol: kg) is the base unit of mass in the International System of Units (SI), and is defined as being equal to the mass of the International Prototype of the Kilogram (IPK, also known as "Le Grand K" or "Big K"), a cylinder of platinum-iridium alloy stored by the International Bureau of Weights and Measures at Saint-Cloud, France.

## Length

In geometric measurements, length is the most extended dimension of an object.

## Mach number

In fluid dynamics, the Mach number (M or Ma) is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

## Magnetic stirrer

A magnetic stirrer or magnetic mixer is a laboratory device that employs a rotating magnetic field to cause a stir bar (or flea) immersed in a liquid to spin very quickly, thus stirring it.

## Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

## Mass fraction (chemistry)

In chemistry, the mass fraction w_i is the ratio of one substance with mass m_i to the mass of the total mixture m_\text, defined as The symbol Y_i is also used to denote mass fraction.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Metre

The metre (British spelling and BIPM spelling) or meter (American spelling) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in some metric systems, including the International System of Units (SI).

## Metre per second

Metre per second (American English: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector quantity which specifies both magnitude and a specific direction), defined by distance in metres divided by time in seconds.

## Mole (unit)

The mole, symbol mol, is the SI unit of amount of substance.

## Mole fraction

In chemistry, the mole fraction or molar fraction (xi) is defined as the amount of a constituent (expressed in moles), ni, divided by the total amount of all constituents in a mixture (also expressed in moles), ntot: The sum of all the mole fractions is equal to 1: The same concept expressed with a denominator of 100 is the mole percent or molar percentage or molar proportion (mol%).

## Natural units

In physics, natural units are physical units of measurement based only on universal physical constants.

## Nondimensionalization

Nondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables.

## Normalization (statistics)

In statistics and applications of statistics, normalization can have a range of meanings.

## Number

A number is a mathematical object used to count, measure and also label.

## 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.

## Orders of magnitude (numbers)

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities.

## Osborne Reynolds

Osborne Reynolds FRS (23 August 1842 – 21 February 1912) was a prominent Irish innovator in the understanding of fluid dynamics.

## Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

## 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.

## Per mille

A per milleCambridge Dictionary Online.

## Percent sign

The percent (per cent) sign (%) is the symbol used to indicate a percentage, a number or ratio as a fraction of 100.

## Physical constant

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time.

## Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

## Pi

The number is a mathematical constant.

## Planck constant

The Planck constant (denoted, also called Planck's constant) is a physical constant that is the quantum of action, central in quantum mechanics.

## Planck mass

In physics, the Planck mass, denoted by mP, is the unit of mass in the system of natural units known as Planck units.

## Planck units

In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of five universal physical constants, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units.

## Power number

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

## Proton

| magnetic_moment.

## Proton-to-electron mass ratio

In physics, the proton-to-electron mass ratio, μ or β, is simply the rest mass of the proton divided by that of the electron.

## Quantity

Quantity is a property that can exist as a multitude or magnitude.

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

## Ratio

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

## Relative atomic mass

Relative atomic mass (symbol: A) or atomic weight is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to one unified atomic mass unit.

## Relative density

Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material.

## Reynolds number

The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations.

## Schmidt number

Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes.

## Second

The second is the SI base unit of time, commonly understood and historically defined as 1/86,400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each.

## Sherwood number

The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation.

## Similitude (model)

Similitude is a concept applicable to the testing of engineering models.

## Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

## Speed

In everyday use and in kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity.

## Speed of light

The speed of light in vacuum, commonly denoted, is a universal physical constant important in many areas of physics.

## Standard atomic weight

The standard atomic weight (Ar, standard, a relative atomic mass) is the atomic weight (Ar) of a chemical element, as appearing and met in the earthly environment.

## Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

## Standardized moment

In probability theory and statistics, the standardized moment of a probability distribution is a moment (normally a higher degree central moment) that is normalized.

## Statistical dispersion

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

## Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

## Strong interaction

In particle physics, the strong interaction is the mechanism responsible for the strong nuclear force (also called the strong force or nuclear strong force), and is one of the four known fundamental interactions, with the others being electromagnetism, the weak interaction, and gravitation.

## System of measurement

A system of measurement is a collection of units of measurement and rules relating them to each other.

## Temperature

Temperature is a physical quantity expressing hot and cold.

## Thiele modulus

The Thiele modulus was developed by Ernest Thiele in his paper 'Relation between catalytic activity and size of particle' in 1939.

## Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

## Unit of measurement

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

## Variable (mathematics)

In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.

## Viscosity

The viscosity of a fluid is the measure of its resistance to gradual deformation by shear stress or tensile stress.

## Water

Water is a transparent, tasteless, odorless, and nearly colorless chemical substance that is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms.

## 1

1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.

## References

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