List of dimensionless quantities

This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The table does not include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.

Name	Standard symbol	Definition	Field of application
Abbe number	V	$V = \frac{ n_d - 1 }{ n_F - n_C }$	optics (dispersion in optical materials)
Activity coefficient	$\gamma$	$\gamma= \frac {{a}}{{x}}$	chemistry (Proportion of "active" molecules or atoms)
Albedo	$\alpha$	$\alpha= (1-D) \bar \alpha(\theta_i) + D \bar{ \bar \alpha}$	climatology, astronomy (reflectivity of surfaces or bodies)
Archimedes number	Ar	$\mathrm{Ar} = \frac{g L^3 \rho_\ell (\rho - \rho_\ell)}{\mu^2}$	fluid mechanics (motion of fluids due to density differences)
Arrhenius number	$\alpha$	$\alpha = \frac{E_a}{RT}$	chemistry (ratio of activation energy to thermal energy)^[1]
Atomic weight	M		chemistry (mass of atom over one atomic mass unit, u, where carbon-12 is exactly 12 u)
Atwood number	A	$\mathrm{A} = \frac{\rho_1 - \rho_2} {\rho_1 + \rho_2}$	fluid mechanics (onset of instabilities in fluid mixtures due to density differences)
Bagnold number	Ba	$\mathrm{Ba} = \frac{\rho d^2 \lambda^{1/2} \gamma}{\mu}$	fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)^[2]
Bejan number (fluid mechanics)	Be	$\mathrm{Be} = \frac{\Delta P L^2} {\mu \alpha}$	fluid mechanics (dimensionless pressure drop along a channel)^[3]
Bejan number (thermodynamics)	Be	$\mathrm{Be} = \frac{\dot S'_{\mathrm{gen},\, \Delta T}}{\dot S'_{\mathrm{gen},\, \Delta T}+ \dot S'_{\mathrm{gen},\, \Delta p}}$	thermodynamics (ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction)^[4]
Bingham number	Bm	$\mathrm{Bm} = \frac{ \tau_y L }{ \mu V }$	fluid mechanics, rheology (ratio of yield stress to viscous stress)^[1]
Biot number	Bi	$\mathrm{Bi} = \frac{h L_C}{k_b}$	heat transfer (surface vs. volume conductivity of solids)
Blake number	Bl or B	$\mathrm{B} = \frac{u \rho}{\mu (1 - \epsilon) D}$	geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media)
Bodenstein number	Bo or Bd	$\mathrm{Bo} = vL/\mathcal{D} = \mathrm{Re}\, \mathrm{Sc}$	chemistry (residence-time distribution; similar to the axial mass transfer Peclet number)^[5]
Bond number	Bo	$\mathrm{Bo} = \frac{\rho a L^2}{\gamma}$	geology, fluid mechanics, porous media (buoyant versus capillary forces, similar to the Eötvös number) ^[6]
Brinkman number	Br	$\mathrm{Br} = \frac {\mu U^2}{\kappa (T_w - T_0)}$	heat transfer, fluid mechanics (conduction from a wall to a viscous fluid)
Brownell–Katz number	N_BK	$\mathrm{N}_\mathrm{BK} = \frac{u \mu}{k_\mathrm{rw}\sigma}$	fluid mechanics (combination of capillary number and Bond number) ^[7]
Capillary number	Ca	$\mathrm{Ca} = \frac{\mu V}{\gamma}$	porous media, fluid mechanics (viscous forces versus surface tension)
Chandrasekhar number	Q	$\mathrm{Q} = \frac{{B_0}^2 d^2}{\mu_0 \rho \nu \lambda}$	magnetohydrodynamics (ratio of the Lorentz force to the viscosity in magnetic convection)
Colburn J factors	J_M, J_H, J_D		turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients)
Coefficient of kinetic friction	$\mu _{k}$		mechanics (friction of solid bodies in translational motion)
Coefficient of static friction	$\mu _{s}$		mechanics (friction of solid bodies at rest)
Coefficient of determination	$R^{2}$		statistics (proportion of variance explained by a statistical model)
Coefficient of variation	${\frac {\sigma }{\mu }}$	${\frac {\sigma }{\mu }}$	statistics (ratio of standard deviation to expectation)
Cohesion number	Coh	$Coh={\frac {1}{\rho g}}\left({\frac {\Gamma ^{5}}{{E^{}}^{2}{R^{}}^{8}}}\right)^{\frac {1}{3}}$	Chemical engineering, material science, mechanics (A scale to show the energy needed for detaching two solid particles)^[8]^[9]
Correlation	ρ or r	${\frac {\operatorname {E} [(X-\mu _{X})(Y-\mu _{Y})]}{\sigma _{X}\sigma _{Y}}}$	statistics (measure of linear dependence)
Cost of transport	COT	$\mathrm {COT} ={\frac {E}{mgd}}$	energy efficiency, economics (ratio of energy input to kinetic motion)
Courant–Friedrich–Levy number	C or 𝜈	$C = \frac {u\,\Delta t} {\Delta x}$	mathematics (numerical solutions of hyperbolic PDEs)^[10]
Damkohler number	Da	$\mathrm{Da} = k \tau$	chemistry (reaction time scales vs. residence time)
Damping ratio	$\zeta$	$\zeta = \frac{c}{2 \sqrt{km}}$	mechanics (the level of damping in a system)
Darcy friction factor	C_f or f_D		fluid mechanics (fraction of pressure losses due to friction in a pipe; four times the Fanning friction factor)
Darcy number	Da	$\mathrm{Da} = \frac{K}{d^2}$	porous media (ratio of permeability to cross-sectional area)
Dean number	D	$\mathrm{D} = \frac{\rho V d}{\mu} \left( \frac{d}{2 R} \right)^{1/2}$	turbulent flow (vortices in curved ducts)
Deborah number	De	$\mathrm{De} = \frac{t_\mathrm{c}}{t_\mathrm{p}}$	rheology (viscoelastic fluids)
Decibel	dB		acoustics, electronics, control theory (ratio of two intensities or powers of a wave)
Drag coefficient	c_d	$c_\mathrm{d} = \dfrac{2 F_\mathrm{d}}{\rho v^2 A}\, ,$	aeronautics, fluid dynamics (resistance to fluid motion)
Dukhin number	Du	$\mathrm{Du} = \frac{\kappa^{\sigma}}{{\Kappa_m} a}$	colloid science (ratio of electric surface conductivity to the electric bulk conductivity in heterogeneous systems)
Eckert number	Ec	$\mathrm{Ec} = \frac{V^2}{c_p\Delta T}$	convective heat transfer (characterizes dissipation of energy; ratio of kinetic energy to enthalpy)
Ekman number	Ek	$\mathrm{Ek} = \frac{\nu}{2D^2\Omega\sin\varphi}$	geophysics (viscous versus Coriolis forces)
Elasticity (economics)	E	$E_{x,y} = \frac{\partial \ln(x)}{\partial \ln(y)} = \frac{\partial x}{\partial y}\frac{y}{x}$	economics (response of demand or supply to price changes)
Eötvös number	Eo	$\mathrm{Eo}=\frac{\Delta\rho \,g \,L^2}{\sigma}$	fluid mechanics (shape of bubbles or drops)
Ericksen number	Er	$\mathrm{Er}=\frac{\mu v L}{K}$	fluid dynamics (liquid crystal flow behavior; viscous over elastic forces)
Euler number	Eu	$\mathrm{Eu}=\frac{\Delta{}p}{\rho V^2}$	hydrodynamics (stream pressure versus inertia forces)
Euler's number	e	$e = \displaystyle\sum\limits_{n = 0}^{ \infty} \dfrac{1}{n!} \approx 2.71828$	mathematics (base of the natural logarithm)
Excess temperature coefficient	$\Theta_r$	$\Theta_r = \frac{c_p (T-T_e)}{U_e^2/2}$	heat transfer, fluid dynamics (change in internal energy versus kinetic energy)^[11]
Fanning friction factor	f		fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)^[12]
Feigenbaum constants	$\alpha$ , $\delta$	$\alpha \approx 2.50290,$ $\ \delta \approx 4.66920$	chaos theory (period doubling)^[13]
Fine-structure constant	$\alpha$	$\alpha ={\frac {e^{2}}{4\pi \varepsilon _{0}hc}}$	quantum electrodynamics (QED) (coupling constant characterizing the strength of the electromagnetic interaction)
f-number	f	$f = \frac {{\ell}}{{D}}$	optics, photography (ratio of focal length to diameter of aperture)
Föppl–von Kármán number	$\gamma$	$\gamma = \frac{Y r^2}{\kappa}$	virology, solid mechanics (thin-shell buckling)
Fourier number	Fo	$\mathrm{Fo} = \frac{\alpha t}{L^2}$	heat transfer, mass transfer (ratio of diffusive rate versus storage rate)
Fresnel number	F	$\mathit{F} = \frac{a^{2}}{L \lambda}$	optics (slit diffraction)^[14]
Froude number	Fr	$\mathrm{Fr} = \frac{v}{\sqrt{g\ell}}$	fluid mechanics (wave and surface behaviour; ratio of a body's inertia to gravitational forces)
Gain	–		electronics (signal output to signal input)
Gain ratio	–		bicycling (system of representing gearing; length traveled over length pedaled)^[15]
Galilei number	Ga	$\mathrm{Ga} = \frac{g\, L^3}{\nu^2}$	fluid mechanics (gravitational over viscous forces)
Golden ratio	$\varphi$	$\varphi = \frac{1+\sqrt{5}}{2} \approx 1.61803$	mathematics, aesthetics (long side length of self-similar rectangle)
Görtler number	G	$\mathrm{G} = \frac{U_e \theta}{\nu} \left( \frac{\theta}{R} \right)^{1/2}$	fluid dynamics (boundary layer flow along a concave wall)
Graetz number	Gz	$\mathrm{Gz} = {D_H \over L} \mathrm{Re}\, \mathrm{Pr}$	heat transfer, fluid mechanics (laminar flow through a conduit; also used in mass transfer)
Grashof number	Gr	$\mathrm{Gr}_L = \frac{g \beta (T_s - T_\infty ) L^3}{\nu ^2}$	heat transfer, natural convection (ratio of the buoyancy to viscous force)
Gravitational coupling constant	$\alpha _{G}$	$\alpha_G=\frac{Gm_e^2}{\hbar c}$	gravitation (attraction between two massy elementary particles; analogous to the Fine structure constant)
Hatta number	Ha	$\mathrm{Ha} = \frac{N_{\mathrm{A}0}}{N_{\mathrm{A}0}^{\mathrm{phys}}}$	chemical engineering (adsorption enhancement due to chemical reaction)
Hagen number	Hg	$\mathrm{Hg} = -\frac{1}{\rho}\frac{\mathrm{d} p}{\mathrm{d} x}\frac{L^3}{\nu^2}$	heat transfer (ratio of the buoyancy to viscous force in forced convection)
Havnes parameter	$P_{H}$	$P_{H}={\frac {Z_{d}n_{d}}{n_{i}}}$	In Dusty plasma physics, ratio of the total charge $Z_{d}$ carried by the dust particles $d$ to the charge carried by the ions $i$ , with $n$ the number density of particles
Helmholtz number	$He$	$He={\frac {wa}{c_{0}}}=k_{0}a$	The most important parameter in duct acoustics. If $\omega$ is the dimensional frequency, then $k_{0}$ is the corresponding free field wavenumber and $He$ is the corresponding dimensionless frequency ^[16]
Hydraulic gradient	i	$i = \frac{\mathrm{d}h}{\mathrm{d}l} = \frac{h_2 - h_1}{\mathrm{length}}$	fluid mechanics, groundwater flow (pressure head over distance)
Iribarren number	Ir	$\mathrm{Ir} = \frac{\tan \alpha}{\sqrt{H/L_0}}$	wave mechanics (breaking surface gravity waves on a slope)
Jakob number	Ja	$\mathrm{Ja} = \frac{c_p (T_\mathrm{s} - T_\mathrm{sat}) }{\Delta H_{\mathrm{f}} }$	chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change)^[17]
Karlovitz number	Ka	$\mathrm {Ka} ={\frac {t_{F}}{t_{\eta }}}$	turbulent combustion (characteristic chemical time scale to Kolmogorov time scale)
Keulegan–Carpenter number	K_C	$\mathrm{K_C} = \frac{V\,T}{L}$	fluid dynamics (ratio of drag force to inertia for a bluff object in oscillatory fluid flow)
Knudsen number	Kn	$\mathrm{Kn} = \frac {\lambda}{L}$	gas dynamics (ratio of the molecular mean free path length to a representative physical length scale)
Kt/V	Kt/V		medicine (hemodialysis and peritoneal dialysis treatment; dimensionless time)
Kutateladze number	Ku	$\mathrm{Ku} = \frac{U_h \rho_g^{1/2}}{\left({\sigma g (\rho_l - \rho_g)}\right)^{1/4}}$	fluid mechanics (counter-current two-phase flow)^[18]
Laplace number	La	$\mathrm{La} = \frac{\sigma \rho L}{\mu^2}$	fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentum-transport)
Lewis number	Le	$\mathrm{Le} = \frac{\alpha}{D} = \frac{\mathrm{Sc}}{\mathrm{Pr}}$	heat and mass transfer (ratio of thermal to mass diffusivity)
Lift coefficient	C_L	$C_\mathrm{L} = \frac{L}{q\,S}$	aerodynamics (lift available from an airfoil at a given angle of attack)
Lockhart–Martinelli parameter	$\chi$	$\chi = \frac{m_\ell}{m_g} \sqrt{\frac{\rho_g}{\rho_\ell}}$	two-phase flow (flow of wet gases; liquid fraction)^[19]
Love numbers	h, k, l		geophysics (solidity of earth and other planets)
Lundquist number	S	$S = \frac{\mu_0LV_A}{\eta}$	plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma)
Mach number	M or Ma	$\mathrm{M} = \frac{{v}}{{v_\mathrm{sound}}}$	gas dynamics (compressible flow; dimensionless velocity)
Magnetic Reynolds number	R_m	$\mathrm{R}_\mathrm{m} = \frac{U L}{\eta}$	magnetohydrodynamics (ratio of magnetic advection to magnetic diffusion)
Manning roughness coefficient	n		open channel flow (flow driven by gravity)^[20]
Marangoni number	Mg	$\mathrm{Mg} = - {\frac{\mathrm{d}\sigma}{\mathrm{d}T}}\frac{L \Delta T}{\eta \alpha}$	fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces)
Markstein number	${\mathcal {M}}$	${\mathcal {M}}={\frac {{\mathcal {L}}_{b}}{\delta _{L}}}$	fluid dynamics, combustion (turbulent combustion flames)
Morton number	Mo	$\mathrm{Mo} = \frac{g \mu_c^4 \, \Delta \rho}{\rho_c^2 \sigma^3}$	fluid dynamics (determination of bubble/drop shape)
Nusselt number	Nu	$\mathrm{Nu} =\frac{hd}{k}$	heat transfer (forced convection; ratio of convective to conductive heat transfer)
Ohnesorge number	Oh	$\mathrm{Oh} = \frac{ \mu}{ \sqrt{\rho \sigma L }} = \frac{\sqrt{\mathrm{We}}}{\mathrm{Re}}$	fluid dynamics (atomization of liquids, Marangoni flow)
Péclet number	Pe	$\mathrm{Pe} = \frac{du\rho c_p}{k} = \mathrm{Re}\, \mathrm{Pr}$	heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer)
Peel number	N_P	$N_\mathrm{P} = \frac{\text{Restoring force}}{\text{Adhesive force}}$	coating (adhesion of microstructures with substrate)^[21]
Perveance	K	${K} = \frac{{I}}{{I_0}}\,\frac{{2}}{{\beta}^3{\gamma}^3} (1-\gamma^2f_e)$	charged particle transport (measure of the strength of space charge in a charged particle beam)
pH	$\mathrm{pH}$	$\mathrm {pH} =-\log _{10}(a_{{\textrm {H}}^{+}})$	chemistry (the measure of the acidity or basicity of an aqueous solution)
Pi	$\pi$	$\pi = \frac{C}{d} \approx 3.14159$	mathematics (ratio of a circle's circumference to its diameter)
Pierce parameter	$C$	$C^{3}={\frac {Z_{c}I_{K}}{4V_{K}}}$	Traveling wave tube
Pixel	px		digital imaging (smallest addressable unit)
Beta (plasma physics)	$\beta$	$\beta ={\frac {nk_{B}T}{B^{2}/2\mu _{0}}}$	Plasma (physics) and Fusion power. Ratio of plasma thermal pressure to magnetic pressure, controlling the level of turbulence in a magnetised plasma.
Poisson's ratio	$\nu$	$\nu = -\frac{\mathrm{d}\varepsilon_\mathrm{trans}}{\mathrm{d}\varepsilon_\mathrm{axial}}$	elasticity (strain in transverse and longitudinal direction)
Porosity	$\phi$	$\phi = \frac{V_\mathrm{V}}{V_\mathrm{T}}$	geology, porous media (void fraction of the medium)
Power factor	pf	$pf={\frac {P}{S}}$	electrical (real power to apparent power)
Power number	N_p	$N_p = {P\over \rho n^3 d^5}$	electronics (power consumption by agitators; resistance force versus inertia force)
Prandtl number	Pr	$\mathrm{Pr} = \frac{\nu}{\alpha} = \frac{c_p \mu}{k}$	heat transfer (ratio of viscous diffusion rate over thermal diffusion rate)
Prater number	β	$\beta = \frac{-\Delta H_r D_{TA}^e C_{AS}}{\lambda^e T_s}$	reaction engineering (ratio of heat evolution to heat conduction within a catalyst pellet)^[22]
Pressure coefficient	C_P	$C_p = {p - p_\infty \over \frac{1}{2} \rho_\infty V_\infty^2}$	aerodynamics, hydrodynamics (pressure experienced at a point on an airfoil; dimensionless pressure variable)
Q factor	Q	$Q = 2 \pi f_r \frac{\text{Energy Stored}}{\text{Power Loss}}$	physics, engineering (damping of oscillator or resonator; energy stored versus energy lost)
Radian measure	rad	$\text{arc length}/\text{radius}$	mathematics (measurement of planar angles, 1 radian = 180/π degrees)
Rayleigh number	Ra	$\mathrm{Ra}_{x} = \frac{g \beta} {\nu \alpha} (T_s - T_\infin) x^3$	heat transfer (buoyancy versus viscous forces in free convection)
Refractive index	n	$n=\frac{c}{v}$	electromagnetism, optics (speed of light in a vacuum over speed of light in a material)
Relative density	RD	$RD = \frac{\rho_\mathrm{substance}}{\rho_\mathrm{reference}}$	hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)
Relative permeability	$\mu _{r}$	$\mu_r = \frac{\mu}{\mu_0}$	magnetostatics (ratio of the permeability of a specific medium to free space)
Relative permittivity	$\varepsilon _{r}$	$\varepsilon_{r} = \frac{C_{x}} {C_{0}}$	electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum)
Reynolds number	Re	$\mathrm{Re} = \frac{vL\rho}{\mu}$	fluid mechanics (ratio of fluid inertial and viscous forces)^[1]
Richardson number	Ri	$\mathrm{Ri} = \frac{gh}{u^2} = \frac{1}{\mathrm{Fr}^2}$	fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)^[23]
Rockwell scale	–		mechanical hardness (indentation hardness of a material)
Rolling resistance coefficient	C_rr	$C_{rr} = \frac{F}{N_f}$	vehicle dynamics (ratio of force needed for motion of a wheel over the normal force)
Roshko number	Ro	$\mathrm{Ro} = {f L^{2}\over \nu} =\mathrm{St}\,\mathrm{Re}$	fluid dynamics (oscillating flow, vortex shedding)
Rossby number	Ro	$\mathrm{Ro}=\frac{U}{Lf}$	geophysics (ratio of inertial to Coriolis force)
Rouse number	P or Z	$\mathrm{P} = \frac{w_s}{\kappa u_*}$	sediment transport (ratio of the sediment fall velocity and the upwards velocity of grain)
Schmidt number	Sc	$\mathrm{Sc} = \frac{\nu}{D}$	mass transfer (viscous over molecular diffusion rate)^[24]
Shape factor	H	$H = \frac {\delta^*}{\theta}$	boundary layer flow (ratio of displacement thickness to momentum thickness)
Sherwood number	Sh	$\mathrm{Sh} = \frac{K L}{D}$	mass transfer (forced convection; ratio of convective to diffusive mass transport)
Shields parameter	$\tau_*$ or $\theta$	$\tau_{\ast} = \frac{\tau}{(\rho_s - \rho) g D}$	sediment transport (threshold of sediment movement due to fluid motion; dimensionless shear stress)
Sommerfeld number	S	$\mathrm{S} = \left( \frac{r}{c} \right)^2 \frac {\mu N}{P}$	hydrodynamic lubrication (boundary lubrication)^[25]
Specific gravity	SG		(same as Relative density)
Stanton number	St	$\mathrm{St} = \frac{h}{c_p \rho V} = \frac{\mathrm{Nu}}{\mathrm{Re}\,\mathrm{Pr}}$	heat transfer and fluid dynamics (forced convection)
Stefan number	Ste	$\mathrm{Ste} = \frac{c_p \Delta T}{L}$	phase change, thermodynamics (ratio of sensible heat to latent heat)
Stokes number	Stk or S_k	$\mathrm{Stk} = \frac{\tau U_o}{d_c}$	particles suspensions (ratio of characteristic time of particle to time of flow)
Strain	$\epsilon$	$\epsilon = \cfrac{\partial{F}}{\partial{X}} - 1$	materials science, elasticity (displacement between particles in the body relative to a reference length)
Strouhal number	St or Sr	$\mathrm{St} = {\omega L\over v}$	fluid dynamics (continuous and pulsating flow; nondimensional frequency)^[26]
Stuart number	N	$\mathrm{N} = \frac {B^2 L_{c} \sigma}{\rho U} = \frac{\mathrm{Ha}^2}{\mathrm{Re}}$	magnetohydrodynamics (ratio of electromagnetic to inertial forces)
Taylor number	Ta	$\mathrm{Ta} = \frac{4\Omega^2 R^4}{\nu^2}$	fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces)
Transmittance	T	$T={\frac {I}{I_{0}}}$	optics, spectroscopy (the ratio of the intensities of radiation exiting through and incident on a sample)
Ursell number	U	$\mathrm{U} = \frac{H\, \lambda^2}{h^3}$	wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer)
Vadasz number	Va	$\mathrm{Va} = \frac{\phi\, \mathrm{Pr}}{\mathrm{Da}}$	porous media (governs the effects of porosity $\phi$ , the Prandtl number and the Darcy number on flow in a porous medium) ^[27]
van 't Hoff factor	i	$i = 1 + \alpha (n - 1)$	quantitative analysis (K_f and K_b)
Wallis parameter	j^*	$j^* = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2}$	multiphase flows (nondimensional superficial velocity)^[28]
Weaver flame speed number	Wea	$\mathrm{Wea} = \frac{w}{w_\mathrm{H}} 100$	combustion (laminar burning velocity relative to hydrogen gas)^[29]
Weber number	We	$\mathrm{We} = \frac{\rho v^2 l}{\sigma}$	multiphase flow (strongly curved surfaces; ratio of inertia to surface tension)
Weissenberg number	Wi	$\mathrm{Wi} = \dot{\gamma} \lambda$	viscoelastic flows (shear rate times the relaxation time)^[30]
Womersley number	$\alpha$	$\alpha = R \left( \frac{\omega \rho}{\mu} \right)^\frac{1}{2}$	biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)^[31]
Zel'dovich number	$\beta$	$\beta ={\frac {E}{RT_{f}}}{\frac {T_{f}-T_{o}}{T_{f}}}$	fluid dynamics, Combustion (Measure of activation energy)

References

1 2 3 "Table of Dimensionless Numbers" (PDF). Retrieved 2009-11-05.
↑ Bagnold number Archived 2005-05-10 at the Wayback Machine.
↑ Bhattacharjee S.; Grosshandler W.L. (1988). "The formation of wall jet near a high temperature wall under microgravity environment". ASME MTD. 96: 711–6.
↑ Paoletti S.; Rispoli F.; Sciubba E. (1989). "Calculation of exergetic losses in compact heat exchanger passager". ASME AES. 10 (2): 21–9.
↑ Becker, A.; Hüttinger, K. J. (1998). "Chemistry and kinetics of chemical vapor deposition of pyrocarbon—II pyrocarbon deposition from ethylene, acetylene and 1,3-butadiene in the low temperature regime". Carbon. 36 (3): 177. doi:10.1016/S0008-6223(97)00175-9.
↑ Bond number Archived 2012-03-05 at the Wayback Machine.
↑ "Home". OnePetro. 2015-05-04. Retrieved 2015-05-08.
↑ Behjani, Mohammadreza Alizadeh; Rahmanian, Nejat; Ghani, Nur Fardina bt Abdul; Hassanpour, Ali. "An investigation on process of seeded granulation in a continuous drum granulator using DEM". Advanced Powder Technology. 28 (10): 2456–2464. doi:10.1016/j.apt.2017.02.011.
↑ Alizadeh Behjani, Mohammadreza; Hassanpour, Ali; Ghadiri, Mojtaba; Bayly, Andrew (2017). "Numerical Analysis of the Effect of Particle Shape and Adhesion on the Segregation of Powder Mixtures". EPJ Web of Conferences. 140. doi:10.1051/epjconf/201714006024. ISSN 2100-014X.
↑ Courant–Friedrich–Levy number Archived 2008-06-05 at the Wayback Machine.
↑ Schetz, Joseph A. (1993). Boundary Layer Analysis. Englewood Cliffs, NJ: Prentice-Hall, Inc. pp. 132–134. ISBN 0-13-086885-X.
↑ Fanning friction factor
↑ Feigenbaum constants
↑ Fresnel number Archived 2011-10-01 at the Wayback Machine.
↑ Gain Ratio – Sheldon Brown
↑ S.W. RIENSTRA, 2015, Fundamentals of Duct Acoustics, Von Karman Institute Lecture Notes
↑ Incropera, Frank P. (2007). Fundamentals of heat and mass transfer. John Wiley & Sons, Inc. p. 376.
↑ Tan, R. B. H.; Sundar, R. (2001). "On the froth–spray transition at multiple orifices". Chemical Engineering Science. 56 (21–22): 6337. doi:10.1016/S0009-2509(01)00247-0.
↑ Lockhart–Martinelli parameter
↑ "Manning coefficient" (PDF). (109 KB)
↑ Van Spengen, W. M.; Puers, R.; De Wolf, I. (2003). "The prediction of stiction failures in MEMS". IEEE Transactions on Device and Materials Reliability. 3 (4): 167. doi:10.1109/TDMR.2003.820295.
↑ Davis, Mark E.; Davis, Robert J. (2012). Fundamentals of Chemical Reaction Engineering. Dover. p. 215. ISBN 978-0-486-48855-4.
↑ Richardson number Archived 2015-03-02 at the Wayback Machine.
↑ Schmidt number Archived 2010-01-24 at the Wayback Machine.
↑ Sommerfeld number
↑ Strouhal number, Engineering Toolbox
↑ Straughan, B. (2001). "A sharp nonlinear stability threshold in rotating porous convection". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 457 (2005): 87–88. Bibcode:2001RSPSA.457...87S. doi:10.1098/rspa.2000.0657.
↑ Petritsch, G.; Mewes, D. (1999). "Experimental investigations of the flow patterns in the hot leg of a pressurized water reactor". Nuclear Engineering and Design. 188: 75. doi:10.1016/S0029-5493(99)00005-9.
↑ Kuneš, J. (2012). "Technology and Mechanical Engineering". Dimensionless Physical Quantities in Science and Engineering. pp. 353–390. doi:10.1016/B978-0-12-416013-2.00008-7. ISBN 978-0-12-416013-2.
↑ Weissenberg number Archived 2006-11-01 at the Wayback Machine.
↑ Womersley number Archived 2009-03-25 at the Wayback Machine.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[berkley-1] 1 2 3 "Table of Dimensionless Numbers" (PDF). Retrieved 2009-11-05.

[2] Bagnold number Archived 2005-05-10 at the Wayback Machine.

[3] Bhattacharjee S.; Grosshandler W.L. (1988). "The formation of wall jet near a high temperature wall under microgravity environment". ASME MTD. 96: 711–6.

[4] Paoletti S.; Rispoli F.; Sciubba E. (1989). "Calculation of exergetic losses in compact heat exchanger passager". ASME AES. 10 (2): 21–9.

[5] Becker, A.; Hüttinger, K. J. (1998). "Chemistry and kinetics of chemical vapor deposition of pyrocarbon—II pyrocarbon deposition from ethylene, acetylene and 1,3-butadiene in the low temperature regime". Carbon. 36 (3): 177. doi:10.1016/S0008-6223(97)00175-9.

[6] Bond number Archived 2012-03-05 at the Wayback Machine.

[7] "Home". OnePetro. 2015-05-04. Retrieved 2015-05-08.

[8] Behjani, Mohammadreza Alizadeh; Rahmanian, Nejat; Ghani, Nur Fardina bt Abdul; Hassanpour, Ali. "An investigation on process of seeded granulation in a continuous drum granulator using DEM". Advanced Powder Technology. 28 (10): 2456–2464. doi:10.1016/j.apt.2017.02.011.

[9] Alizadeh Behjani, Mohammadreza; Hassanpour, Ali; Ghadiri, Mojtaba; Bayly, Andrew (2017). "Numerical Analysis of the Effect of Particle Shape and Adhesion on the Segregation of Powder Mixtures". EPJ Web of Conferences. 140. doi:10.1051/epjconf/201714006024. ISSN 2100-014X.

[10] Courant–Friedrich–Levy number Archived 2008-06-05 at the Wayback Machine.

[11] Schetz, Joseph A. (1993). Boundary Layer Analysis. Englewood Cliffs, NJ: Prentice-Hall, Inc. pp. 132–134. ISBN 0-13-086885-X.

[12] Fanning friction factor

[13] Feigenbaum constants

[14] Fresnel number Archived 2011-10-01 at the Wayback Machine.

[15] Gain Ratio – Sheldon Brown

[16] S.W. RIENSTRA, 2015, Fundamentals of Duct Acoustics, Von Karman Institute Lecture Notes

[17] Incropera, Frank P. (2007). Fundamentals of heat and mass transfer. John Wiley & Sons, Inc. p. 376.

[18] Tan, R. B. H.; Sundar, R. (2001). "On the froth–spray transition at multiple orifices". Chemical Engineering Science. 56 (21–22): 6337. doi:10.1016/S0009-2509(01)00247-0.

[19] Lockhart–Martinelli parameter

[20] "Manning coefficient" (PDF). (109 KB)

[21] Van Spengen, W. M.; Puers, R.; De Wolf, I. (2003). "The prediction of stiction failures in MEMS". IEEE Transactions on Device and Materials Reliability. 3 (4): 167. doi:10.1109/TDMR.2003.820295.

[22] Davis, Mark E.; Davis, Robert J. (2012). Fundamentals of Chemical Reaction Engineering. Dover. p. 215. ISBN 978-0-486-48855-4.

[23] Richardson number Archived 2015-03-02 at the Wayback Machine.

[24] Schmidt number Archived 2010-01-24 at the Wayback Machine.

[25] Sommerfeld number

[26] Strouhal number, Engineering Toolbox

[27] Straughan, B. (2001). "A sharp nonlinear stability threshold in rotating porous convection". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 457 (2005): 87–88. Bibcode:2001RSPSA.457...87S. doi:10.1098/rspa.2000.0657.

[28] Petritsch, G.; Mewes, D. (1999). "Experimental investigations of the flow patterns in the hot leg of a pressurized water reactor". Nuclear Engineering and Design. 188: 75. doi:10.1016/S0029-5493(99)00005-9.

[29] Kuneš, J. (2012). "Technology and Mechanical Engineering". Dimensionless Physical Quantities in Science and Engineering. pp. 353–390. doi:10.1016/B978-0-12-416013-2.00008-7. ISBN 978-0-12-416013-2.

[30] Weissenberg number Archived 2006-11-01 at the Wayback Machine.

[31] Womersley number Archived 2009-03-25 at the Wayback Machine.