Part 11: Characteristic Numbers

Dimensionless numbers for transport phenomena

115 entries· Edition 2019FR→ About this part

11-4Reynolds number

R e

quotient of inertial forces and viscous forces in a fluid flow, expressed by ; where is mass density (iso80000-4), is speed (iso80000-3),…

11-4.2

Euler number

E u

relationship between pressure drop in a flow and the kinetic energy per volume for flow of fluids in a pipe, expressed by ; where is drop…

11-4.3

Froude number

F r

quotient of a body's inertial forces and its gravitational forces for flow of fluids, expressed by ; where is speed (iso80000-3) of flow,…

11-4.4

Grashof number

G r

quotient of buoyancy forces due to thermal expansion which results in a change of mass density and viscous forces for free convection due…

11-4.5

Weber number

W e

relation between inertial forces and capillary forces due to surface tension at the interface between two different fluids, expressed by ;…

11-4.6

Mach number

M a

quotient of the speed of flow and the speed of sound, expressed by ; where is speed (iso80000-3) of the body, and is speed of sound…

11-4.7

Knudsen number

K n

quotient of free path length of a particle and a characteristic length, expressed by ; where is mean free path (iso80000-9), and is…

11-4.8

Strouhal number, Thomson number

S r

S h

relation between a characteristic frequency and a characteristic speed for unsteady flow with periodic behaviour, expressed by ; where is…

11-4.9

drag coefficient

c_{D}

relation between the effective drag force and inertial forces for a body moving in a fluid, expressed by ; where is drag force (iso80000-4)…

11-4.10

Bagnold number

B g

quotient of drag force and gravitational force for a body moving in a fluid, expressed by ; where is drag coefficient (t11-4.9) of the…

11-4.11

Bagnold number

B a_{2}

quotient of drag force and viscous force in a fluid transferring solid particles, expressed by ; where is mass density (iso80000-4) of…

11-4.12

lift coefficient

c_{l}

c_{A}

quotient of the lift force available from a wing at a given angle and the inertial force for a wing shaped body moving in a fluid,…

11-4.13

thrust coefficient

c_{t}

quotient of the effective thrust force available from a propeller and the inertial force in a fluid, expressed by ; where is thrust force…

11-4.14

Dean number

D n

relation between centrifugal force and inertial force, for flows of fluids in curved pipes, expressed by ; where is (axial) speed…

11-4.15

Bejan number

B e

quotient of mechanical work and frictional energy loss in fluid dynamics in a pipe, expressed by ; where is drop of pressure (iso80000-4)…

11-4.16

Lagrange number

L g

quotient of mechanical work and frictional energy loss in fluid dynamics in a pipe, expressed by ; where is length (iso80000-3) of the…

11-4.17

Bingham number, plasticity number

B m

B n

quotient of yield stress and viscous stress in a viscous material for flow of viscoplastic material in channels, expressed by ; where is…

11-4.18

Hedström number

H e

H d

quotient of yield stress and viscous stress of a viscous material at flow limit for visco-plastic material in a channel, expressed by ;…

11-4.19

Bodenstein number

B d

mathematical expression of the transfer of matter by convection in reactors with respect to diffusion, ; where is speed (iso80000-3), is…

11-4.20

Rossby number, Kiebel number

R o

quotient of inertial forces and Coriolis forces in the context of transfer of matter in geophysics, expressed by ; where is speed…

11-4.21

Ekman number

E k

quotient of viscous forces and Coriolis forces in the context of transfer of matter for the flow of a rotating fluid, expressed by ; where…

11-4.22

elasticity number

E l

relation between relaxation time and diffusion time in viscoelastic flows, expressed by ; where is relaxation time (iso80000-12), is…

11-4.23

Darcy friction factor, Moody friction factor

f_{D}

representation of pressure loss in a pipe due to friction within a laminar or turbulent flow of a fluid in a pipe, expressed by ; where is…

11-4.24

Fanning number

f_{n}

f

relation between shear stress and dynamic pressure in the flow of a fluid in a containment, expressed by ; where is shear stress…

11-4.25

Goertler number, Goertler parameter

G o

characterization of the stability of laminar boundary layer flows in transfer of matter in a boundary layer on curved surfaces, expressed…

11-4.26

Hagen number

H g

H a

generalization of the Grashof number for forced or free convection in laminar flow, expressed by ; where is mass density (iso80000-4) of…

11-4.27

Laval number

L a

quotient of speed and the (critical) sound speed at the throat of a nozzle, expressed by ; where is speed (iso80000-3), is specific gas…

11-4.28

Poiseuille number

P o i

quotient of propulsive force by pressure and viscous force for a flow of fluids in a pipe, expressed by ; where is drop of pressure…

11-4.29

power number

P n

quotient of power consumption by agitators due to drag and rotational inertial power in fluids, expressed by ; where is active power…

11-4.30

Richardson number

R i

quotient of potential energy and kinetic energy for a falling body, expressed by ; where is acceleration of free fall (iso80000-3), is…

11-4.31

Reech number

R e e

relation between the speed of an object submerged in water relative to the water, and wave propagation speed, expressed by ; where is…

11-4.32

Stokes number

S t k

quotient of friction and inertia forces for particles in a fluid or in a plasma, expressed by ; where is relaxation time (iso80000-12) of…

11-4.33

Stokes number

S t k_{1}

quotient of friction and inertia forces for the special case of particles vibrating in a fluid or plasma, expressed by ; where is kinematic…

11-4.34

Stokes number , power coefficient

S t k_{2}

Stokes number for calibration of rotameters metering vertical flows of fluids by means of a floating body, expressed by ; where is ratio of…

11-4.35

Stokes number

S t k_{3}

relation between viscous forces and gravity forces for particles falling in a fluid, expressed by ; where is characteristic speed…

11-4.36

Stokes number

S t k_{4}

quotient of drag force and internal friction forces for particles dragged in a fluid ; where is drag force (iso80000-4), is dynamic…

11-4.37

Laplace number, Suratman number

L a

S u

relation between capillary forces and viscous forces when characterizing free surface flow, expressed by ; where is surface tension…

11-4.38

Blake number

B l

relation between inertial forces and viscous forces in a porous material, expressed by ; where is speed (iso80000-3) of the fluid, is mass…

11-4.39

Sommerfeld number

S o

S m

relation between viscous force and load force in a lubrication boundary, expressed by ; where is dynamic viscosity (iso80000-4) of the…

11-4.40

Taylor number

T a

relation between centrifugal force and viscous force of a rotating shaft, expressed by ; where is angular velocity (iso80000-3) of…

11-4.41

Galilei number

G a

relation between gravitational force and viscous force in fluid films flowing over walls, expressed by ; where is acceleration of free fall…

11-4.42

Womersley number

W o

α

relation between inertial forces and viscous forces in oscillating flows of fluids in pipes, expressed by ; where is (effective) radius…

11-5Fourier number <heat transfer>

11-5.1

Fourier number

F o

relation between heat conduction rate and the rate of thermal energy storage in a body for conductive heat transfer into a body, expressed…

11-5.2

Péclet number

P e

relation between convective heat transfer rate and conductive heat transfer rate, expressed by ; where is speed (iso80000-3), is length…

11-5.3

Rayleigh number

R a

relation between buoyancy forces due to thermal expansion and viscous forces in free convection in buoyancy driven flow near a heated…

11-5.4

Froude number

F r *

quotient of gravitational forces and thermodiffusion forces for heat transfer in forced convection of fluids, expressed by ; where is…

11-5.5

Nusselt number

N u

relation between the internal thermal resistance of a body and its surface thermal resistance in a body transferring heat from a surface…

11-5.6

Biot number

B i

special case of the Nusselt number for heat transfer (item t11-5.5) in case of conductive heat transfer in a solid body, expressed by ;…

11-5.7

Stanton number

S t

relation between heat transfer into a fluid from a surface and its heat transfer by convection, expressed by ; where is coefficient of heat…

11-5.8

j-factor , heat transfer factor, Colburn number

j

C o

J q

relation between heat transfer and mass transfer in a fluid, expressed by ; where is coefficient of heat transfer (iso80000-5), is specific…

11-5.9

Bejan number

B e_{1}

quotient of mechanical work and frictional and thermal diffusion energy losses for a forced flow, expressed by ; where is drop of pressure…

11-5.10

Bejan number

B e_{S}

efficiency of heat transfer by a fluid, expressed by ; where is entropy generation contributed by heat transfer, and is entropy generation…

11-5.11

Stefan number

S t e

S t f

relation between heat content and latent heat content in a binary mixture undergoing a phase transition, expressed by ; where is specific…

11-5.12

Brinkman number

B r

N_{B r}

relation between heat produced by viscosity and heat conducted from a wall adjacent to a fluid moving relative to it, expressed by ; where…

11-5.13

Clausius number

C l

relation between energy transfer associated with fluid momentum and energy transfer by thermal conduction in forced heating, expressed by ;…

11-5.14

Carnot number

C a

theoretical maximum efficiency (iso80000-5) of a Carnot cycle operating between temperature reservoirs ; where is thermodynamic temperature…

11-5.15

Eckert number, Dulong number

E c

relation between the kinetic energy of a flow and its enthalpy change in fluid dynamics exhibiting dissipation, expressed by ; where is…

11-5.16

Graetz number

G z

relation between heat transferred by convection and heat transferred by conduction in a laminar flow in a pipe, expressed by ; where is…

11-5.17

heat transfer number

K_{Q}

relation between heat transferred by a flow and its kinetic energy, expressed by ; where is heat flow rate (iso80000-5), is characteristic…

11-5.18

Pomerantsev number

P o

P o v

relation between heat generated in a body and conducted heat in the body, expressed by ; where is (constant) volumic heat generation rate,…

11-5.19

Boltzmann number

B z

B o l

B o

relation between convective heat and radiant heat for a fluid in a channel, expressed by ; where is mass density (iso80000-4) of the fluid,…

11-5.20

Stark number, DEPRECATED: Stefan number, DEPRECATED: Biot radiation number

S k

relation between radiant heat and conductive heat multiplied by the relative temperature difference for a body, expressed by ; where is…

11-6Fourier number <mass transfer>

11-6.1

Fourier number

F o *

relation between diffusive mass transfer within a given duration and mass storage rate in transient mass transfer, expressed by ; where is…

11-6.2

Péclet number , Bodenstein number

P e *

B d

B o d

relation between advective mass transfer rate and longitudinal diffusive mass transfer rate for mass transfer in reactors, expressed by ;…

11-6.3

Grashof number

G r *

relation between buoyancy forces and viscous forces in natural convection of fluids, expressed by ; where is characteristic length…

11-6.4

Nusselt number

N u *

relation between mass flux at an interface and specific flux by pure molecular diffusion in a layer of thickness for mass transfer at the…

11-6.5

Stanton number

S t *

relation between mass transfer perpendicular to the surface of a fluid flow and mass transfer parallel to the surface in a free surface…

11-6.6

Graetz number

G z *

quotient of advective mass transfer rate and radial diffusive mass transfer rate for mass transfer in pipes, expressed by ; where is…

11-6.7

mass transfer factor, j-factor

j *

relation between mass transfer perpendicular to the surface of a fluid and mass transfer parallel to the surface in an open flow of fluids,…

11-6.8

Atwood number

A t

scaled density difference of heavier and lighter fluids, expressed by ; where is density of heavier fluid, and is density of lighter fluid

11-6.9

Biot number

B i *

relation between mass transfer rate at the interface and mass transfer rate in the interior of a body, expressed by ; where is the mass…

11-6.10

Morton number

M o

quotient of gravitational forces and viscous forces for gas bubbles in a liquid, or liquid drops in a gas, expressed by ; where is…

11-6.11

Bond number, Eötvös number

B o

E o

quotient of inertial force and capillary force for gas bubbles or liquid drops in a fluid, expressed by ; where is the acceleration of the…

11-6.12

Archimedes number

A r

quotient of buoyancy forces and viscous forces in fluids motion due to density differences for a body in a fluid, expressed by ; where is…

11-6.13

expansion number

E x

quotient of buoyancy force and inertial force in moving fluids due to density differences for gas bubbles rising in a liquid, expressed by…

11-6.14

Marangoni number

M g

M a r

quotient of heat transferred by Marangoni convection and heat transferred by thermal diffusivity in thermo-capillary convection of liquid…

11-6.15

Lockhart-Martinelli parameter

L p

quotient of mass flow rates multiplied by the square root of density in a two-phase flow, expressed by ; where is liquid phase mass flow…

11-6.16

Bejan number

B e *

B e_{2}

quotient of mechanical work and frictional and diffusion energy loss in viscous flow of fluids in pipes, expressed by ; where is drop of…

11-6.17

cavitation number

C a

C n

quotient of the excess of local static head over vapour pressure head and velocity head for fast flow in liquids, expressed by ; where is…

11-6.18

absorption number

A b

relation between mass flow rate and surface area for gas absorption at wetted walls, expressed by ; where is the mass transfer coefficient…

11-6.19

capillary number

C a

quotient of gravitational forces and capillary forces for fluids in narrow pipes, expressed by ; where is diameter (iso80000-3) of the…

11-6.20

dynamic capillary number

C a *

C n

quotient of viscous force and capillary force acting across an interface between a liquid and a gas, or between two immiscible liquids for…

11-7Prandtl number

11-7.1

Prandtl number

P r

quotient of kinematic viscosity and thermal diffusivity for a fluid, expressed by ; where is kinematic viscosity (iso80000-4), and is…

11-7.2

Schmidt number, DEPRECATED: Colburn number

S c

quotient of kinematic viscosity and diffusion coefficient for a fluid, expressed by ; where is kinematic viscosity (iso80000-4), and is…

11-7.3

Lewis number

L e

quotient of thermal diffusivity and diffusion coefficient for heat transfer in a fluid, expressed by ; where is thermal diffusivity…

11-7.4

Ohnesorge number

O h

relation between viscous force and the square root of the product of inertia force and capillary force for atomization of liquids,…

11-7.5

Cauchy number, aeroelasticity parameter

C y

relation between inertia forces and compression forces in compressible fluids, expressed by ; where is mass density (iso80000-4), is speed…

11-7.6

Hooke number

H o_{2}

relation between inertia forces and linear stress forces in elastic fluids, expressed by ; where is mass density (iso80000-4), is speed…

11-7.7

Weissenberg number

W i

product of time derivative of shear rate and relaxation time in viscoelastic flows, expressed by ; where is time derivative of shear strain…

11-7.8

Deborah number

D e

quotient of relaxation time of viscoelastic fluids and observation duration in rheology of viscoelastic fluids, expressed by ; where is…

11-7.9

Lorentz number

L o

quotient of electrical conductivity and thermal conductivity, expressed by ; where is electrical conductivity (iec80000-6), is difference…

11-7.10

compressibility number

Z

quotient of isothermal compressibility (iso80000-5) of a gas and that of an ideal gas, expressed by ; where is pressure (iso80000-4), is…

11-8Reynolds magnetic number

11-8.1

Reynolds magnetic number

R m

relation between inertial force and magneto-dynamic viscous force in an electrically conducting fluid, expressed by ; where is speed…

11-8.2

Batchelor number

B t

relation between inertia and magneto-dynamic diffusion in an electrically conducting liquid, expressed by ; where is speed (iso80000-3), is…

11-8.3

Nusselt electric number

N e

relation between convective current and diffusive current of ions in electrochemistry, expressed by ; where is speed (iso80000-3), is…

11-8.4

Alfvén number, Mach magnetic number, Kárman number

A l

relation between speed of a plasma and the Alfvén wave speed, expressed by ; where is speed (iso80000-3), is magnetic flux density…

11-8.5

Hartmann number

H a

relation between magnetically induced stress and hydrodynamic shear stress in an electrically conducting fluid, expressed by ; where is…

11-8.6

Cowling number , Euler magnetic number

C o

quotient of magnetic and kinematic energy density in a plasma, expressed by ; where is magnetic flux density (iec80000-6), is magnetic…

11-8.7

Stuart electrical number

S e

quotient of electric energy density and kinematic energy density in a plasma, expressed by ; where is electric permittivity (iec80000-6),…

11-8.8

magnetic pressure number

N_{m p}

quotient of gas pressure and magnetic pressure in a gas or plasma, expressed by ; where is pressure (iso80000-4), is magnetic permeability…

11-8.9

Chandrasekhar number

Q

C h

quotient of Lorentz force and viscous force in magnetic convection in a fluid, expressed by ; where is magnetic flux density (iec80000-6),…

11-8.10

Prandtl magnetic number

P r_{m}

quotient of kinematic viscosity and magnetic viscosity in an electrically conducting liquid, expressed by ; where is kinematic viscosity…

11-8.11

Roberts number

R o

quotient of thermal diffusivity and magnetic viscosity in an electrically conducting liquid, expressed by ; where is thermal diffusivity…

11-8.12

Stuart number

S t w

quotient of magnetic forces and inertia forces in an electrically conducting liquid, expressed by ; where is magnetic flux density…

11-8.13

magnetic number

N_{m g}

quotient of magnetic forces and viscous forces in an electrically conducting fluid, expressed by ; where is magnetic flux density…

11-8.14

electric field parameter

E f

quotient of Coulomb force and Lorentz force on moving electrically charged material or particles, expressed by ; where is electric field…

11-8.15

Hall number

H_{c}

C_{H}

quotient of gyro frequency and collision frequency in a plasma, expressed by ; where is cyclotron angular frequency (iso80000-10), is mean…

11-8.16

Lundquist number

L u

quotient of Alfvén speed and magneto-dynamic speed in a plasma, expressed by ; where is magnetic flux density (iec80000-6), is…

11-8.17

Joule magnetic number

J o_{m}

quotient of Joule heating energy and magnetic field energy in a plasma, expressed by ; where is mass density (iso80000-4), is magnetic…

11-8.18

Grashof magnetic number

G r_{m}

mathematical expression for the heat transfer by free thermo-magnetic convection of a paramagnetic fluid under gravity, ; where is…

11-8.19

Naze number

N a

quotient of velocity of Alfvén waves and velocity of sound in a plasma, expressed by ; where is magnetic flux density (iec80000-6), is…

11-8.20

Reynolds electric number

R e_{e}

quotient of speed of a fluid and average drift speed of the charged particles in an electrically conducting fluid, expressed by ; where is…

11-8.21

Ampère number

A m

relation between electric surface current and magnetic field strength in an electrically conducting liquid, expressed by ; where is…

11-9Arrhenius number

11-9.1

Arrhenius number

α

quotient of chemical activation energy and thermal energy; in a chemical reaction it is the exponential factor of the reaction rate…

11-9.2

Landau-Ginzburg number

κ

quotient of penetration depth of a magnetic field into a superconductor and the coherence length of thermodynamic fluctuations within a…

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