This is a list of well-known
dimensionless quantities
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1 ...
illustrating their variety of forms and applications. The tables also include
pure numbers, dimensionless ratios, or
dimensionless physical constant
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 value that is independent of whatever system of units may be used.
For example, if one c ...
s; these topics are discussed in the article.
Biology and medicine
Chemistry
Physics
Physical constants
Fluids and heat transfer
, ,
gas dynamics
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ...
(
compressible flow
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ...
; dimensionless
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
)
, -
,
Magnetic Reynolds number
In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the magn ...
, , R
m , ,
, ,
magnetohydrodynamics
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals ...
(ratio of magnetic
advection
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is a ...
to magnetic
diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
)
, -
,
Manning roughness coefficient , , ''n'' , , , ,
open channel flow
In fluid mechanics and hydraulics, open-channel flow is a type of liquid flow within a conduit with a free surface, known as a channel. The other type of flow within a conduit is pipe flow. These two types of flow are similar in many ways but dif ...
(flow driven by
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...
)
, -
,
Marangoni number The Marangoni number (Ma) is, as usually defined, the dimensionless number that compares the rate of transport due to Marangoni flows, with the rate of transport of diffusion. The Marangoni effect is flow of a liquid due to gradients in the surface ...
, , Mg , ,
, ,
fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...
(
Marangoni flow
The Marangoni effect (also called the Gibbs–Marangoni effect) is the mass transfer along an interface between two phases due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermo-capi ...
; thermal
surface tension forces over
viscous
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
forces)
, -
,
Markstein number In combustion engineering and explosion studies, the Markstein number characterizes the effect of local heat release of a propagating flame on variations in the surface topology along the flame and the associated local flame front curvature. The ...
, ,
, ,
, ,
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
,
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combust ...
(turbulent combustion flames)
, -
,
Morton number , , Mo , ,
, ,
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(determination of
bubble
Bubble, Bubbles or The Bubble may refer to:
Common uses
* Bubble (physics), a globule of one substance in another, usually gas in a liquid
** Soap bubble
* Economic bubble, a situation where asset prices are much higher than underlying fundame ...
/
drop
Drop, DROP, drops or DROPS may refer to:
* Drop (liquid) or droplet, a small volume of liquid
** Eye drops, saline (sometimes mydriatic) drops used as medication for the eyes
* Drop (unit), a unit of measure of volume
* Falling (physics), allowi ...
shape)
, -
,
Nusselt number
In thermal fluid dynamics, the Nusselt number (, after Wilhelm Nusselt) is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection (fluid motion) and diffusion (conduction). The conducti ...
, , Nu , ,
, ,
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. Heat transfer is classified into various mechanisms, such as thermal conduction ...
(forced
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...
; ratio of
convective
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
to
conductive
In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. Electric current is gen ...
heat transfer)
, -
,
Ohnesorge number
The Ohnesorge number (Oh) is a dimensionless number that relates the viscous forces to inertial and surface tension forces. The number was defined by Wolfgang von Ohnesorge in his 1936 doctoral thesis.
It is defined as:
: \mathrm = \frac = \fra ...
, , Oh , ,
, ,
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(atomization of liquids,
Marangoni flow
The Marangoni effect (also called the Gibbs–Marangoni effect) is the mass transfer along an interface between two phases due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermo-capi ...
)
, -
,
Péclet number
In continuum mechanics, the Péclet number (, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is defined to be the ratio of the rate of advection of a physical ...
, , Pe , ,
, ,
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. Heat transfer is classified into various mechanisms, such as thermal conduction ...
(
advection
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is a ...
–
diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
problems; total
momentum transfer
In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics.
In the ...
to molecular heat transfer)
, -
,
Péclet number
In continuum mechanics, the Péclet number (, after Jean Claude Eugène Péclet) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is defined to be the ratio of the rate of advection of a physical ...
, , Pe , ,
, ,
mass transfer
Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtra ...
(
advection
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is a ...
–
diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
problems; total
momentum transfer
In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics.
In the ...
to diffusive mass transfer)
, -
,
Prandtl number
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:
: \mathrm = \frac = \fra ...
, , Pr , ,
, ,
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. Heat transfer is classified into various mechanisms, such as thermal conduction ...
(ratio of
viscous diffusion rate over
thermal diffusion Thermal diffusion may refer to:
* A thermal force on a gas due to a temperature gradient, also called ''thermal diffusion'' or Thermal transpiration.
** It is used to drive a gas pump with no moving parts called a Knudsen pump.
** It is the currentl ...
rate)
, -
,
Pressure coefficient The pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field in fluid dynamics. The pressure coefficient is used in aerodynamics and hydrodynamics. Every point in a fluid flow field has its own ...
, , ''C
P'' , ,
, ,
aerodynamics
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...
,
hydrodynamics (
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
experienced at a point on an
airfoil
An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or tur ...
; dimensionless pressure variable)
, -
,
Rayleigh number
In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain ...
, , Ra , ,
, ,
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. Heat transfer is classified into various mechanisms, such as thermal conduction ...
(
buoyancy
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the p ...
versus
viscous forces
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inter ...
in
free convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the conv ...
)
, -
,
Reynolds number , , Re , ,
, ,
fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...
(ratio of fluid
inertia
Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law o ...
l and
viscous
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
forces)
, -
,
Richardson number The Richardson number (Ri) is named after Lewis Fry Richardson (1881–1953). It is the dimensionless number that expresses the ratio of the buoyancy term to the flow shear term:
:
\mathrm = \frac = \frac \frac
where g is gravity, \rho is dens ...
, , Ri , ,
, ,
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(effect of
buoyancy
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the p ...
on flow stability; ratio of
potential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...
over
kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its a ...
)
, -
,
Roshko number In fluid mechanics, the Roshko number (Ro) is a dimensionless number describing oscillating flow mechanisms. It is named after the American Professor of Aeronautics Anatol Roshko. It is defined as
: \mathrm = =\mathrm\,\mathrm
: \mathrm= ,
: ...
, , Ro , ,
, ,
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(oscillating flow,
vortex
In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in t ...
shedding)
, -
,
Schmidt number
Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convect ...
, , Sc , ,
, ,
mass transfer
Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtra ...
(
viscous
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
over molecular
diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
rate)
, -
,
Shape factor , , ''H'' , ,
, ,
boundary layer flow (ratio of displacement thickness to momentum thickness)
, -
,
Sherwood number
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the convective mass transfer to the rate of diffusive mass transport, and is named in h ...
, , Sh , ,
, ,
mass transfer
Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtra ...
(
forced convection
Forced convection is a mechanism, or type of transport, in which fluid motion is generated by an external source (like a pump, fan, suction device, etc.). Alongside natural convection, thermal radiation, and thermal conduction it is one of the me ...
; ratio of
convective
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
to
diffusive
Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of ...
mass transport)
, -
,
Sommerfeld number , , S , ,
, ,
hydrodynamic lubrication
Fluid bearings are bearings in which the load is supported by a thin layer of rapidly moving pressurized liquid or gas between the bearing surfaces. Since there is no contact between the moving parts, there is no sliding friction, allowing flu ...
(boundary
lubrication
Lubrication is the process or technique of using a lubricant to reduce friction and wear and tear in a contact between two surfaces. The study of lubrication is a discipline in the field of tribology.
Lubrication mechanisms such as fluid-lubric ...
)
, -
,
Stanton number , , St , ,
, ,
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. Heat transfer is classified into various mechanisms, such as thermal conduction ...
and
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(forced
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...
)
, -
,
Stokes number
The Stokes number (Stk), named after George Gabriel Stokes, is a dimensionless number characterising the behavior of particles suspended in a fluid flow. The Stokes number is defined as the ratio of the characteristic time of a particle (or drop ...
, , Stk or S
k , ,
, ,
particles suspensions (ratio of characteristic
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, t ...
of particle to time of flow)
, -
,
Strouhal number , , St or Sr , ,
, ,
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(continuous and pulsating flow; nondimensional
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...
)
, -
,
Stuart number The Stuart number (N), also known as magnetic interaction parameter, is a dimensionless number of fluids, i.e. gases or liquids.
It is defined as the ratio of electromagnetic to inertial forces, which gives an estimate of the relative importance of ...
, , N , ,
, ,
magnetohydrodynamics
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals ...
(ratio of
electromagnetic
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
to inertial forces)
, -
,
Taylor number
In fluid dynamics, the Taylor number (Ta) is a dimensionless quantity that characterizes the importance of centrifugal "forces" or so-called inertial forces due to rotation of a fluid about an axis, relative to viscous forces.
In 1923 Geoffrey In ...
, , Ta , ,
, ,
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
(rotating fluid flows; inertial forces due to
rotation
Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
of a
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shea ...
versus
viscous forces
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inter ...
)
, -
,
Ursell number
In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953.
The Ursell number is derived from t ...
, , U , ,
, ,
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (r ...
mechanics (nonlinearity of
surface gravity waves on a shallow fluid layer)
, -
,
Vadasz number , , Va , ,
, ,
porous media
A porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usu ...
(governs the effects of
porosity
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...
, the
Prandtl number
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:
: \mathrm = \frac = \fra ...
and the
Darcy number In fluid dynamics through porous media, the Darcy number (Da) represents the relative effect of the permeability of the medium versus its cross-sectional area—commonly the diameter squared. The number is named after Henry Darcy and is found fro ...
on flow in a
porous medium
A porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is us ...
)
, -
,
Wallis parameter , , ''j''
* , ,
, ,
multiphase flow
In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve so ...
s (nondimensional
superficial velocity Superficial velocity (or superficial flow velocity), in engineering of multiphase flows and flows in porous media, is a hypothetical (artificial) flow velocity calculated as if the given phase or fluid were the only one flowing or present in a give ...
)
, -
,
Weber number
The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is named ...
, , We , ,
, ,
multiphase flow
In fluid mechanics, multiphase flow is the simultaneous flow of materials with two or more thermodynamic phases. Virtually all processing technologies from cavitating pumps and turbines to paper-making and the construction of plastics involve so ...
(strongly curved surfaces; ratio of
inertia
Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law o ...
to
surface tension)
, -
,
Weissenberg number
The Weissenberg number (Wi) is a dimensionless number used in the study of viscoelastic flows. It is named after Karl Weissenberg. The dimensionless number compares the elastic forces to the viscous forces. It can be variously defined, but it is us ...
, , Wi , ,
, ,
viscoelastic
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linear ...
flows (
shear rate
In physics, shear rate is the rate at which a progressive shearing deformation is applied to some material.
Simple shear
The shear rate for a fluid flowing between two parallel plates, one moving at a constant speed and the other one stationary ...
times the relaxation time)
, -
,
Womersley number
The Womersley number (\alpha or \text) is a dimensionless number in biofluid mechanics and biofluid dynamics. It is a dimensionless expression of the pulsatile flow frequency in relation to viscosity, viscous effects. It is named after John R. Wom ...
, ,
, ,
, ,
biofluid mechanics (continuous and pulsating flows; ratio of
pulsatile flow
In fluid dynamics, a flow with periodic variations is known as pulsatile flow, or as Womersley flow. The flow profiles was first derived by John R. Womersley (1907–1958) in his work with blood flow in arteries. The cardiovascular system of chord ...
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...
to
viscous effects)
Womersley number
, -
, Zel'dovich number The Zel'dovich number is a dimensionless number which provides a quantitative measure for the activation energy of a chemical reaction which appears in the Arrhenius exponent, named after the Russian scientist Yakov Borisovich Zel'dovich, who along ...
, , , , , , fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
, Combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combust ...
(Measure of activation energy
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules p ...
)
Solids
Optics
Mathematics and statistics
Geography, geology and geophysics
Sport
Other fields
References
{{Reflist, 30em
*