Important Dimensionless Numbers And Their Significance l1y6o

Dimensionless number From Wikipedia, the free encyclopedia. In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units; it does not change if one alters one's system of units of measurement, for example from English units to metric units. Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all units cancel.

List of dimensionless numbers There are infinitely many dimensionless numbers. Some of those that are used most often have been given names, as in the following list of examples (in alphabetical order, indicating their field of use):   

Abbe number: Dispersion in optical materials Archimedes number: Motion of fluids due to density differences Bagnold number: Flow of grain [5] (http://www2.umt.edu/Geology/faculty/hendrix/g432/g432_L6.h

tm)   

Biot number: Surface vs volume conductivity of solids Bodenstein number: Residence-time distribution Bond number: Capillary action driven by buoyancy [6] (http://ising.phys.cwru.edu/plt/PapersInPdf/181BridgeCollap

se.pdf)          

 

Brownell Katz number: Combination of capillary number and Bond number Capillary number: Fluid flow influenced by surface tension Damköhler numbers: Reaction time scales vs transport phenomena Darcy friction factor: Fluid flow Deborah number: Rheology of viscoelastic fluids Drag coefficient: Flow resistance Eckert number: Convective heat transfer Ekman number: Frictional (viscous) forces in geophysics Euler number: Hydrodynamics (pressure forces vs. inertia forces) Fanning friction factor: Fluid flow in

pipes [7] (http://www.engineering.uiowa.edu/~cee081/Exams/Final/Final.h tm) Feigenbaum's delta: Period doubling in chaos theory [8] (http://www.drchaos.net/drchaos/Book/node44.html) Fourier number: Heat transfer



Fresnel number: Diffraction at a slit [9] (http://www.ilt.fraunhofer.de/default.php?web=1&id=100050&lan=e

ng&dat=2)       

Froude number: Wave and surface behaviour Graetz number: Heat flow Grashof number: Free convection Hagen number: Forced convection Knudsen number: Continuum approximation in fluids Laplace number: Free convection with immiscible fluids Lockhart-Martinelli parameter: flow of wet gases [10] (http://www.flowprogramme.co.uk/publications/guidancenotes/

GN40.pdf)  

 



          

   

Lift coefficient: amount of lift available from given airfoil at given angle of attack Courant-Friedrich-Levy number: Non-hydrostatic dynamics [11] (http://www.cnrm.meteo.fr/aladin/newsletters/news22/J_Vi

voda/Texte.html) Mach number: Gas dynamics Magnetic Reynolds number: used to compare the transport of magnetic lines of force in a conducting fluid to the leakage of such lines from the fluid [12] (http://www.inprosys.bizland.com/website/injector.htm) Manning roughness coefficient: see Manning equation [13] (http://www.epa.gov/ORD/NRMRL/pubs/600r01043/600R0104 3chap2.pdf) Nusselt number: Heat transfer with forced convection Ohnesorge number: Atomization of liquids Peclet number: Competition between viscous and Brownian forces Peel number: Adhesion of microstructures with substrate [14] (http://web.imech.ac.cn/efile/2000.htm) Pressure coefficient: Coefficient of pressure experienced at a point on an airfoil Poisson's ratio: Load in transverse and longitudinal direction Power number: Power consumption by agitators Prandtl number: Forced and free convection Rayleigh number: Buoyancy and viscous forces in free convection Reynolds number: Characterizing flow behaviour (laminar or turbulent) Richardson number: Effect of buoyancy on flow stability [15] (http://apollo.lsc.vsc.edu/classes/met455/notes/section4/2.ht ml) Rockwell scale: Mechanical hardness Rossby number: Inertial forces in geophysics Schmidt number: mass transfer, and diffusion in flowing systems [16] (http://www.ent.ohiou.edu/~hbwang/fluidynamics.htm) Sherwood number: Mass transfer with forced convection

 

Sommerfeld number: Boundary lubrication [17] (http://epubl.luth.se/avslutade/0348-8373/41/) Strouhal number: Continuous and pulsating flow [18] (http://www.seas.upenn.edu/courses/belab/LabProjects/2001/be3

10s01m2.doc) 

Coefficient of static friction: Friction of solid bodies at rest



Coefficient of kinetic friction: Friction of solid bodies in translational motion Stokes number: Dynamics of particles Strouhal number: Oscillatory flows Weaver flame speed number: laminar burning velocity relative to hydrogen gas [19] (http://eyrie.shef.ac.uk/will/eee/e630/comfun8.html) Weber number: Characterization of multiphase flow with strongly curved

   

surfaces  

Weissenberg number: Viscoelastic flows [20] (http://physics.ucsd.edu/~des/Shear1999.pdf) Womersley number: continuous and pulsating flows [21] (http://www.seas.upenn.edu/courses/belab/LabProjects/2001/be

310s01m2.doc)

Nusselt number the ratio of convective to conductive heat transfer across (normal to) the boundary.

Reynolds number the ratio of Inertial forces to the Viscous forces.

Primarily used to analyse different flow regimes i.e. Laminar, Turbulent, or Transient Flow.

Prandtl number the ratio of momentum diffusivity to thermal diffusivity.

Graetz number In fluid dynamics, the Graetz number (Gz) is a dimensionless number that characterizes laminar flow in a conduit.

where

DH is the diameter in round tubes or hydraulic diameter in arbitrary cross-section ducts L is the length Re is the Reynolds number and Pr is the Prandtl number.` When used in connection with mass transfer the Prandtl number is replaced by the Schmidt number, Sc, which expresses the ratio of the momentum diffusivity to the mass diffusivity.

The quantity is named after the physicist Leo Graetz.

Grashof number the ratio of the buoyancy to viscous force acting on a fluid, used in fluid dynamics and heat transfer.

Heat transfer Free convection is caused by a change in density of a fluid due to a temperature change or gradient. Usually the density decreases due to an increase in temperature and causes the fluid to rise. This motion is caused by the buoyancy force. The major force that resists the motion is the viscous force. The Grashof number is a way to quantify the opposing forces.[3]

where:

g is acceleration due to Earth's gravity β is the coefficient of thermal expansion (equal to approximately 1/T, for ideal gases) Ts is the surface temperature T∞ is the bulk temperature L is the vertical length D is the diameter`

ν is the kinematic viscosity.

Mass transfer There is an analogous form of the Grashof number used in cases of natural convection mass transfer problems. In the case of mass transfer, natural convection is caused by concentration gradients rather than temperature gradients.

where:

and:

g is acceleration due to Earth's gravity Ca,s is the concentration of species a at surface Ca,a is the concentration of species a in ambient medium L is the characteristic length ν is the kinematic viscosity ρ is the fluid density Ca is the concentration of species a T is the temperature (constant) p is the pressure (constant).