Name |
Standard symbol |
Definition |
Field of application
|
Abbe number |
V |
![{\displaystyle V={\frac {n_{d}-1}{n_{F}-n_{C}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/924a73f8660972554f4ec17376b57a0b9da54877) |
optics (dispersion in optical materials)
|
Activity coefficient |
![{\displaystyle \gamma }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a) |
![{\displaystyle \gamma ={\frac {a}{x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d49c86dcf47d656c4ec1ce1ed64d223278ec738) |
chemistry (Proportion of "active" molecules or atoms)
|
Albedo |
![{\displaystyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3) |
![{\displaystyle {\alpha }=(1-D){\bar {\alpha }}(\theta _{i})+D{\bar {\bar {\alpha }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f7e5cc3781ff8c355e834674c95c60a4fc67f3f) |
climatology, astronomy (reflectivity of surfaces or bodies)
|
Archimedes number |
Ar |
![{\displaystyle \mathrm {Ar} ={\frac {gL^{3}\rho _{\ell }(\rho -\rho _{\ell })}{\mu ^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8ce0359a7e01ef5462564f8356a2923460d6f5d) |
fluid mechanics (motion of fluids due to density differences)
|
Arrhenius number |
![{\displaystyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3) |
![{\displaystyle \alpha ={\frac {E_{a}}{RT}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6d277a5842817470a0b00423b11ccc278365fb4) |
chemistry (ratio of activation energy to thermal energy)[5]
|
Atomic weight |
M |
|
chemistry (mass of atom over one atomic mass unit, u, where carbon-12 is exactly 12 u)
|
Atwood number |
A |
![{\displaystyle \mathrm {A} ={\frac {\rho _{1}-\rho _{2}}{\rho _{1}+\rho _{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1af57c76470a57e552235c63c51509d18f70b4cd) |
fluid mechanics (onset of instabilities in fluid mixtures due to density differences)
|
Bagnold number |
Ba |
![{\displaystyle \mathrm {Ba} ={\frac {\rho d^{2}\lambda ^{1/2}\gamma }{\mu }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4ee59e514eb8a0a4747f9d3f8315658fdc976c3) |
fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)[6]
|
Bejan number (thermodynamics) |
Be |
![{\displaystyle \mathrm {Be} ={\frac {{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}}{{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}+{\dot {S}}'_{\mathrm {gen} ,\,\Delta p}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8d3bb418096c451f0ac3cebca57ef875f9b9d34c) |
thermodynamics (ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction)[7]
|
Bejan number (fluid mechanics) |
Be |
![{\displaystyle \mathrm {Be} ={\frac {\Delta PL^{2}}{\mu \alpha }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0328bd6105e54983bcb6d5554ecd4cb8fa08dd33) |
fluid mechanics (dimensionless pressure drop along a channel)[8]
|
Bingham number |
Bm |
![{\displaystyle \mathrm {Bm} ={\frac {\tau _{y}L}{\mu V}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/521881f326d5d86835534e6609540a86112f25ae) |
fluid mechanics, rheology (ratio of yield stress to viscous stress)[5]
|
Biot number |
Bi |
![{\displaystyle \mathrm {Bi} ={\frac {hL_{C}}{k_{b}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b333caa5e65d495ed5b8c507a5ca6905898a9ea8) |
heat transfer (surface vs. volume conductivity of solids)
|
Blake number |
Bl or B |
![{\displaystyle \mathrm {B} ={\frac {u\rho }{\mu (1-\epsilon )D}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61510bd7e01a2bec71c0266bf6ad3adc4f581f98) |
geology, fluid mechanics, porous media (inertial over viscous forces in fluid flow through porous media)
|
Bodenstein number |
Bo |
![{\displaystyle \mathrm {Bo} =vL/{\mathcal {D}}=\mathrm {Re} \,\mathrm {Sc} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3704996e24ed94a3a7c092d6dd4183c8c04585f9) |
chemistry (residence-time distribution)
|
Bond number |
Bo |
![{\displaystyle \mathrm {Bo} ={\frac {\rho aL^{2}}{\gamma }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76d542a70c5a2d893840268226c798f1f5a52c62) |
geology, fluid mechanics, porous media (buoyant versus capilary forces, similar to the Eötvös number) [9]
|
Brinkman number |
Br |
![{\displaystyle \mathrm {Br} ={\frac {\mu U^{2}}{\kappa (T_{w}-T_{0})}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d93721d4c1633ef5df77985a651f7a7f46f1b59c) |
heat transfer, fluid mechanics (conduction from a wall to a viscous fluid)
|
Brownell–Katz number |
|
|
combination of capillary number and Bond number
|
Capillary number |
Ca |
![{\displaystyle \mathrm {Ca} ={\frac {\mu V}{\gamma }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0884d41eae9f95f456939e6996c6b6ca62e3f0) |
porous media (viscous forces versus surface tension)
|
Chandrasekhar number |
Q |
![{\displaystyle \mathrm {Q} ={\frac {{B_{0}}^{2}d^{2}}{\mu _{0}\rho \nu \lambda }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f5011971813e4c029378fedcdf823b19a4ae30ea) |
magnetohydrodynamics (ratio of the Lorentz force to the viscosity in magnetic convection)
|
Coefficient of static friction |
µs |
|
mechanics (friction of solid bodies at rest)
|
Coefficient of kinetic friction |
µk |
|
mechanics (friction of solid bodies in translational motion)
|
Colburn J factors |
JM, JH, JD |
|
turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients)
|
Courant–Friedrich–Levy number |
C or 𝜈 |
![{\displaystyle C={\frac {u\,\Delta t}{\Delta x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1912e75fc60367edce694c8f5e6a2dfcfa2dd9c) |
mathematics (numerical solutions of hyperbolic PDEs)[10]
|
Damkohler number |
Da |
![{\displaystyle \mathrm {Da} =k\tau }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9720287339fa283b7a5a34a4a4eb0cc8200fc48) |
chemistry (reaction time scales vs. residence time)
|
Damping ratio |
ζ |
![{\displaystyle \zeta ={\frac {c}{2{\sqrt {km}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f17b775df1d28640a5afa39e21c040f18f088a) |
mechanics (the level of damping in a system)
|
Darcy friction factor |
Cf or fD |
|
fluid mechanics (fraction of pressure losses due to friction in a pipe; four times the Fanning friction factor)
|
Dean number |
D |
![{\displaystyle \mathrm {D} ={\frac {\rho Vd}{\mu }}\left({\frac {d}{2R}}\right)^{1/2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5a257084fd2e78547afcf04202c2fff50fbe1a5) |
turbulent flow (vortices in curved ducts)
|
Deborah number |
De |
![{\displaystyle \mathrm {De} ={\frac {t_{\mathrm {c} }}{t_{\mathrm {p} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/010666486743427ba922536ce6e81c793b30793e) |
rheology (viscoelastic fluids)
|
Decibel |
dB |
|
acoustics, electronics, control theory (ratio of two intensities or powers of a wave)
|
Drag coefficient |
cd |
![{\displaystyle c_{\mathrm {d} }={\dfrac {2F_{\mathrm {d} }}{\rho v^{2}A}}\,,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd1fe690904a5f2e81ffe36b41813a7d2c776b43) |
aeronautics, fluid dynamics (resistance to fluid motion)
|
Dukhin number |
Du |
![{\displaystyle \mathrm {Du} ={\frac {\kappa ^{\sigma }}{{\mathrm {K} _{m}}a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/10994db8d9c28d9f64fbac83206db7b5b370df63) |
colloid science (ratio of electric surface conductivity to the electric bulk conductivity in heterogeneous systems)
|
Eckert number |
Ec |
![{\displaystyle \mathrm {Ec} ={\frac {V^{2}}{c_{p}\Delta T}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4866cdac76849d839adf2f700be4d4da0a72dec2) |
convective heat transfer (characterizes dissipation of energy; ratio of kinetic energy to enthalpy)
|
Ekman number |
Ek |
![{\displaystyle \mathrm {Ek} ={\frac {\nu }{2D^{2}\Omega \sin \varphi }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fabed6332919818055a388859ab1c0721a2aded4) |
geophysics (viscous versus Coriolis forces)
|
Elasticity (economics) |
E |
|
economics (response of demand or supply to price changes)
|
Entropy (physics) |
σ |
|
physics, information theory (log of the number of states)[11]
|
Eötvös number |
Eo |
![{\displaystyle \mathrm {Eo} ={\frac {\Delta \rho \,g\,L^{2}}{\sigma }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/589ee1bd831d37fc53048cd5b4bef717267e8306) |
fluid mechanics (shape of bubbles or drops)
|
Ericksen number |
Er |
![{\displaystyle \mathrm {Er} ={\frac {\mu vL}{K}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/21f40de39caf67d1d7d8dbc1ec3b7a7d63d64089) |
fluid dynamics (liquid crystal flow behavior; viscous over elastic forces)
|
Euler number |
Eu |
![{\displaystyle \mathrm {Eu} ={\frac {\Delta {}p}{\rho V^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c29bc09dd2d9aa8d4e15bc54fabdb8f8b3cfbcd0) |
hydrodynamics (stream pressure versus inertia forces)
|
Euler's number |
e |
![{\displaystyle e=\sum _{k=0}^{n}{\frac {1}{k!}}\approx 2.71828}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d47fe83ddbfe5733949f4905d591cf0a36519c72) |
mathematics (base of the natural logarithm)
|
Excess temperature coefficient |
Θr |
![{\displaystyle \Theta _{r}={\frac {c_{p}(T-T_{e})}{U_{e}^{2}/2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/485154205ef7d4f8ebd13e5e4de5d97f22b62c95) |
heat transfer, fluid dynamics (change in internal energy versus kinetic energy)[12]
|
Fanning friction factor |
f |
|
fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)[13]
|
Feigenbaum constants |
, δ |
![{\displaystyle \alpha \approx 2.50290,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50caaed719ec4a6a1720c71ef4de9627d39a2781)
![{\displaystyle \ \delta \approx 4.66920}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7f6f9342f40a0ed4a857cdfb73251b2db87b26e) |
chaos theory (period doubling)[14]
|
Fine structure constant |
![{\displaystyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3) |
![{\displaystyle \alpha ={\frac {e^{2}}{2\varepsilon _{0}hc}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/129428bbe35efc671ee4a9b892d5ed273a2febc2) |
quantum electrodynamics (QED) (coupling constant characterizing the strength of the electromagnetic interaction)
|
f-number |
f |
![{\displaystyle f={\frac {\ell }{D}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4aa452f05127d80d470743224cd08073240f513b) |
optics, photography (ratio of focal length to diameter of aperture)
|
Föppl–von Kármán number |
![{\displaystyle \gamma }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a) |
![{\displaystyle \gamma ={\frac {Yr^{2}}{\kappa }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c36fdb6d9a7f81f30812d79f56529ab8a81d0c6a) |
virology, solid mechanics (thin-shell buckling)
|
Fourier number |
Fo |
![{\displaystyle \mathrm {Fo} ={\frac {\alpha t}{L^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c10ff55e67af2209948a255a007d2b2577163e4) |
heat transfer, mass transfer (ratio of diffusive rate versus storage rate)
|
Fresnel number |
F |
![{\displaystyle {\mathit {F}}={\frac {a^{2}}{L\lambda }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/57849c921d622cb7f2bf06f92b14bd24943f2703) |
optics (slit diffraction)[15]
|
Froude number |
Fr |
![{\displaystyle \mathrm {Fr} ={\frac {v}{\sqrt {g\ell }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ac0d3b7a290182449f186f5a90e9a902e6dee47) |
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)[16]
|
Galilei number |
Ga |
![{\displaystyle \mathrm {Ga} ={\frac {g\,L^{3}}{\nu ^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2a6ac87fffb10123f18130f79bc7438f2714ab6) |
fluid mechanics (gravitational over viscous forces)
|
Golden ratio |
![{\displaystyle \varphi }](https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e) |
![{\displaystyle \varphi ={\frac {1+{\sqrt {5}}}{2}}\approx 1.61803}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a4f25824810e77ee275698ed5f6c4413d680532) |
mathematics, aesthetics (long side length of self-similar rectangle)
|
Görtler number |
G |
![{\displaystyle \mathrm {G} ={\frac {U_{e}\theta }{\nu }}\left({\frac {\theta }{R}}\right)^{1/2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af90e4013884eb3bcfc969d5e7a45708d4b61140) |
fluid dynamics (boundary layer flow along a concave wall)
|
Graetz number |
Gz |
![{\displaystyle \mathrm {Gz} ={D_{H} \over L}\mathrm {Re} \,\mathrm {Pr} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7965dfd36d7cd162fe713b79c25d32fb9ab989a1) |
heat transfer, fluid mechanics (laminar flow through a conduit; also used in mass transfer)
|
Grashof number |
Gr |
![{\displaystyle \mathrm {Gr} _{L}={\frac {g\beta (T_{s}-T_{\infty })L^{3}}{\nu ^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/62b757370465e792fd08d7f0305587ddff868564) |
heat transfer, natural convection (ratio of the buoyancy to viscous force)
|
Gravitational coupling constant |
![{\displaystyle \alpha _{G}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/781e76139e38347149164fbece70efa7ac3eb5ab) |
![{\displaystyle \alpha _{G}={\frac {Gm_{e}^{2}}{\hbar c}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/99dca6acf33a6d29c9dd3cbd3e09bf0a947d2abb) |
gravitation (attraction between two massy elementary particles; analogous to the Fine structure constant)
|
Hatta number |
Ha |
![{\displaystyle \mathrm {Ha} ={\frac {N_{\mathrm {A} 0}}{N_{\mathrm {A} 0}^{\mathrm {phys} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a27f90bf16b72e080b242ccc5afcb98fe00b21bf) |
chemical engineering (adsorption enhancement due to chemical reaction)
|
Hagen number |
Hg |
![{\displaystyle \mathrm {Hg} =-{\frac {1}{\rho }}{\frac {\mathrm {d} p}{\mathrm {d} x}}{\frac {L^{3}}{\nu ^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c627f63a4b1e865823059f7c512e052ed30a1b49) |
heat transfer (ratio of the buoyancy to viscous force in forced convection)
|
Hydraulic gradient |
i |
![{\displaystyle i={\frac {\mathrm {d} h}{\mathrm {d} l}}={\frac {h_{2}-h_{1}}{\mathrm {length} }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2427427c02bab7e19f328e90f93de1a9c62e400) |
fluid mechanics, groundwater flow (pressure head over distance)
|
Iribarren number |
Ir |
![{\displaystyle \mathrm {Ir} ={\frac {\tan \alpha }{\sqrt {H/L_{0}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc00dbc8ff39f6c50c268a73981cc379b2f80bbd) |
wave mechanics (breaking surface gravity waves on a slope)
|
Jakob Number |
Ja |
![{\displaystyle \mathrm {Ja} ={\frac {c_{p}(T_{\mathrm {s} }-T_{\mathrm {sat} })}{\Delta H_{\mathrm {f} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/945adc71d43dd0901b41670e5cd14d595721542d) |
chemistry (ratio of sensible to latent energy absorbed during liquid-vapor phase change)[17]
|
Karlovitz number |
Ka |
![{\displaystyle \mathrm {Ka} =kt_{c}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/935378923fbcc09c1e87c4ead7e83c540b389f25) |
turbulent combustion (characteristic flow time times flame stretch rate)
|
Keulegan–Carpenter number |
KC |
![{\displaystyle \mathrm {K_{C}} ={\frac {V\,T}{L}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b6f334de66e04fefc2c183813ed321ac3029e9e) |
fluid dynamics (ratio of drag force to inertia for a bluff object in oscillatory fluid flow)
|
Knudsen number |
Kn |
![{\displaystyle \mathrm {Kn} ={\frac {\lambda }{L}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38b0497925dbb4bb7c4b2017366a881d32ed7556) |
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 |
|
counter-current two-phase flow
|
Laplace number |
La |
![{\displaystyle \mathrm {La} ={\frac {\sigma \rho L}{\mu ^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f81c04132aa6d486e6e2ea0eba3887602aebdee5) |
fluid dynamics (free convection within immiscible fluids; ratio of surface tension to momentum-transport)
|
Lewis number |
Le |
![{\displaystyle \mathrm {Le} ={\frac {\alpha }{D}}={\frac {\mathrm {Sc} }{\mathrm {Pr} }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2b573ef86861138988a9614457ea820e37b6e856) |
heat and mass transfer (ratio of thermal to mass diffusivity)
|
Lift coefficient |
CL |
![{\displaystyle C_{\mathrm {L} }={\frac {L}{q\,S}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a29b76cfc15aedad2f606809f59d5b76dba2fce6) |
aerodynamics (lift available from an airfoil at a given angle of attack)
|
Lockhart–Martinelli parameter |
![{\displaystyle \chi }](https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437) |
![{\displaystyle \chi ={\frac {m_{\ell }}{m_{g}}}{\sqrt {\frac {\rho _{g}}{\rho _{\ell }}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/515cde027e80a99e6056b777fde59160aa9adeb0) |
two-phase flow (flow of wet gases; liquid fraction)[18]
|
Love numbers |
h, k, l |
|
geophysics (solidity of earth and other planets)
|
Lundquist number |
S |
![{\displaystyle S={\frac {\mu _{0}LV_{A}}{\eta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/07380dd8d89973e50689282bc09429d0593bb2b3) |
plasma physics (ratio of a resistive time to an Alfvén wave crossing time in a plasma)
|
Mach number |
M or Ma |
![{\displaystyle \mathrm {M} ={\frac {v}{v_{\mathrm {sound} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6492816fe198d2b069fffb547356d28e380d23cd) |
gas dynamics (compressible flow; dimensionless velocity)
|
Magnetic Reynolds number |
Rm |
![{\displaystyle \mathrm {R} _{\mathrm {m} }={\frac {UL}{\eta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/96dc7d0f50e574127ffaf4e061dbe9005861ea65) |
magnetohydrodynamics (ratio of magnetic advection to magnetic diffusion)
|
Manning roughness coefficient |
n |
|
open channel flow (flow driven by gravity)[19]
|
Marangoni number |
Mg |
![{\displaystyle \mathrm {Mg} =-{\frac {\mathrm {d} \sigma }{\mathrm {d} T}}{\frac {L\Delta T}{\eta \alpha }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a174f8e720c05f5fa7a85ac840d2a6ca15bb4941) |
fluid mechanics (Marangoni flow; thermal surface tension forces over viscous forces)
|
Morton number |
Mo |
![{\displaystyle \mathrm {Mo} ={\frac {g\mu _{c}^{4}\,\Delta \rho }{\rho _{c}^{2}\sigma ^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76e3d3e1019a391ca31d0a3e34c16a2c31ba3ed2) |
fluid dynamics (determination of bubble/drop shape)
|
Nusselt number |
Nu |
![{\displaystyle \mathrm {Nu} ={\frac {hd}{k}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/457a3c7593ee4c6d7c4e94eee6cdf1d40688708e) |
heat transfer (forced convection; ratio of convective to conductive heat transfer)
|
Ohnesorge number |
Oh |
![{\displaystyle \mathrm {Oh} ={\frac {\mu }{\sqrt {\rho \sigma L}}}={\frac {\sqrt {\mathrm {We} }}{\mathrm {Re} }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/873d76124ef4f557e0d198569861cb1c7e01cd08) |
fluid dynamics (atomization of liquids, Marangoni flow)
|
Péclet number |
Pe |
![{\displaystyle \mathrm {Pe} ={\frac {du\rho c_{p}}{k}}=\mathrm {Re} \,\mathrm {Pr} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7176382f7a5d4db8a5be9910fd112f3821118eef) |
heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer)
|
Peel number |
|
|
adhesion of microstructures with substrate[20]
|
Perveance |
K |
![{\displaystyle {K}={\frac {I}{I_{0}}}\,{\frac {2}{{\beta }^{3}{\gamma }^{3}}}(1-\gamma ^{2}f_{e})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ceedb358859edf83114fcfb855e4cb42b623393) |
charged particle transport (measure of the strength of space charge in a charged particle beam)
|
Pi |
π |
![{\displaystyle \pi ={\frac {C}{d}}\approx 3.14159}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41f498d411d95bd63e57a33815c7cf46297dccb5) |
mathematics (ratio of a circle's circumference to its diameter)
|
Poisson's ratio |
ν |
![{\displaystyle \nu =-{\frac {\mathrm {d} \varepsilon _{\mathrm {trans} }}{\mathrm {d} \varepsilon _{\mathrm {axial} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60116247b19bcd5a871bc5f46289f766a2942cca) |
elasticity (load in transverse and longitudinal direction)
|
Porosity |
ϕ |
![{\displaystyle \phi ={\frac {V_{\mathrm {V} }}{V_{\mathrm {T} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43be9f48ff5af36c9b4c0eb2e1757a0b7424f811) |
geology, porous media (void fraction of the medium)
|
Power factor |
P/S |
|
electronics (real power to apparent power)
|
Power number |
Np |
![{\displaystyle N_{p}={P \over \rho n^{3}d^{5}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b25a8aaea338f137247cb66c605eee64f140ffc) |
electronics (power consumption by agitators; resistance force versus inertia force)
|
Prandtl number |
Pr |
![{\displaystyle \mathrm {Pr} ={\frac {\nu }{\alpha }}={\frac {c_{p}\mu }{k}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c789ae3617f8f489280fc2e6c0ac4b551324efd4) |
heat transfer (ratio of viscous diffusion rate over thermal diffusion rate)
|
Prater number |
|
|
ratio of heat evolution to heat conduction within a catalyst pellet
|
Pressure coefficient |
CP |
![{\displaystyle C_{p}={p-p_{\infty } \over {\frac {1}{2}}\rho _{\infty }V_{\infty }^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18a52469764e17ef751a9ea91e321ac4cd755c82) |
aerodynamics, hydrodynamics (pressure experienced at a point on an airfoil; dimensionless pressure variable)
|
Q factor |
Q |
|
physics, engineering (damping of oscillator or resonator; energy stored versus energy lost)
|
Radian measure |
rad |
![{\displaystyle {\text{arc length}}/{\text{radius}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/09249fe6c61b924f0993682be8c099582f9a40a7) |
mathematics (measurement of planar angles, 1 radian = 180/π degrees)
|
Rayleigh number |
Ra |
![{\displaystyle \mathrm {Ra} _{x}={\frac {g\beta }{\nu \alpha }}(T_{s}-T_{\infty })x^{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c76e1bf07351d253bace5831d0fb9707bf465aab) |
heat transfer (buoyancy versus viscous forces in free convection)
|
Refractive index |
n |
![{\displaystyle n={\frac {c}{v}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33da8c421d52a437e59e6726572ed6d09cb6f3e3) |
electromagnetism, optics (speed of light in a vacuum over speed of light in a material)
|
Relative density |
RD |
![{\displaystyle RD={\frac {\rho _{\mathrm {substance} }}{\rho _{\mathrm {reference} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf5c023440c35ab04cab4a1e37b90890fdca04a) |
hydrometers, material comparisons (ratio of density of a material to a reference material—usually water)
|
Relative permeability |
µr |
![{\displaystyle \mu _{r}={\frac {\mu }{\mu _{0}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d667bdb0fb40dac1dd065932d515fc68f7288a57) |
magnetostatics (ratio of the permeability of a specific medium to free space)
|
Relative permittivity |
εr |
![{\displaystyle \varepsilon _{r}={\frac {C_{x}}{C_{0}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/06bbbf7a441c9fc4c2b968d8cd3fa54d86e951e6) |
electrostatics (ratio of capacitance of test capacitor with dielectric material versus vacuum)
|
Reynolds number |
Re |
![{\displaystyle \mathrm {Re} ={\frac {vL\rho }{\mu }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c48482707cd0310416df48078fc2db3e9a31ab92) |
fluid mechanics (ratio of fluid inertial and viscous forces)[5]
|
Richardson number |
Ri |
![{\displaystyle \mathrm {Ri} ={\frac {gh}{u^{2}}}={\frac {1}{\mathrm {Fr} ^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84b21127296564f221dd263117e48c651ead84e8) |
fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)[21]
|
Rockwell scale |
– |
|
mechanical hardness (indentation hardness of a material)
|
Rolling resistance coefficient |
Crr |
![{\displaystyle C_{rr}={\frac {F}{N_{f}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1139e8c4bc9bc5b130ad3c9fa83600a8ca35c2d) |
vehicle dynamics (ratio of force needed for motion of a wheel over the normal force)
|
Roshko number |
Ro |
![{\displaystyle \mathrm {Ro} ={fL^{2} \over \nu }=\mathrm {St} \,\mathrm {Re} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b9c0e275b8aa232d9f6658fc780d6b26ce7f475) |
fluid dynamics (oscillating flow, vortex shedding)
|
Rossby number |
Ro |
![{\displaystyle \mathrm {Ro} ={\frac {U}{Lf}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/674aef3885100a0b8d46446e97b7873714e80ce9) |
geophysics (ratio of inertial to Coriolis force)
|
Rouse number |
P or Z |
![{\displaystyle \mathrm {P} ={\frac {w_{s}}{\kappa u_{*}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0aaedde614d17d3076200ed600b9957629a7549d) |
sediment transport (ratio of the sediment fall velocity and the upwards velocity of grain)
|
Schmidt number |
Sc |
![{\displaystyle \mathrm {Sc} ={\frac {\nu }{D}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adeb9a6634a836c01b8be68406e75556972e3fa3) |
mass transfer (viscous over molecular diffusion rate)[22]
|
Shape factor |
H |
![{\displaystyle H={\frac {\delta ^{*}}{\theta }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b77f62ed3e5d956cc14e28a4bc579e80b411705) |
boundary layer flow (ratio of displacement thickness to momentum thickness)
|
Sherwood number |
Sh |
![{\displaystyle \mathrm {Sh} ={\frac {KL}{D}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a3a410b2c29b4aca568ce2ed0b12b524ee5cad63) |
mass transfer (forced convection; ratio of convective to diffusive mass transport)
|
Shields parameter |
τ∗ or θ |
![{\displaystyle \tau _{\ast }={\frac {\tau }{(\rho _{s}-\rho )gD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf31523d447b4ee797f864f44241fe94ce3e8cb) |
sediment transport (threshold of sediment movement due to fluid motion; dimensionless shear stress)
|
Sommerfeld number |
S |
![{\displaystyle \mathrm {S} =\left({\frac {r}{c}}\right)^{2}{\frac {\mu N}{P}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d32912c1f4b573b71400aeca707eddf3b8c0c987) |
hydrodynamic lubrication (boundary lubrication)[23]
|
Specific gravity |
SG |
|
(same as Relative density)
|
Stanton number |
St |
![{\displaystyle \mathrm {St} ={\frac {h}{c_{p}\rho V}}={\frac {\mathrm {Nu} }{\mathrm {Re} \,\mathrm {Pr} }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7415b71e5fe566ed75ed77cb081f654fd32665c) |
heat transfer and fluid dynamics (forced convection)
|
Stefan number |
Ste |
![{\displaystyle \mathrm {Ste} ={\frac {c_{p}\Delta T}{L}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/01f5e94ef7974a674d45de8edb888b7330b30032) |
phase change, thermodynamics (ratio of sensible heat to latent heat)
|
Stokes number |
Stk or Sk |
![{\displaystyle \mathrm {Stk} ={\frac {\tau U_{o}}{d_{c}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/083df09cde8dfe1eeb4652e8c490624849296cb3) |
particles suspensions (ratio of characteristic time of particle to time of flow)
|
Strain |
ϵ |
![{\displaystyle \epsilon ={\cfrac {\partial {F}}{\partial {X}}}-1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7b728d1a5f08ae0ecf6e30fc69f275e3dcc4b0e2) |
materials science, elasticity (displacement between particles in the body relative to a reference length)
|
Strouhal number |
St or Sr |
![{\displaystyle \mathrm {St} ={\omega L \over v}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32b6a366f8610d53bd8d1ff7f94c6476f9e0e84b) |
fluid dynamics (continuous and pulsating flow; nondimensional frequency)[24]
|
Stuart number |
N |
![{\displaystyle \mathrm {N} ={\frac {B^{2}L_{c}\sigma }{\rho U}}={\frac {\mathrm {Ha} ^{2}}{\mathrm {Re} }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81937cdaf00119980da4afbf5a71fe7c93236c90) |
magnetohydrodynamics (ratio of electromagnetic to inertial forces)
|
Taylor number |
Ta |
![{\displaystyle \mathrm {Ta} ={\frac {4\Omega ^{2}R^{4}}{\nu ^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f097fff0636027e240b5963985a77c5fdbfeb0a) |
fluid dynamics (rotating fluid flows; inertial forces due to rotation of a fluid versus viscous forces)
|
Ursell number |
U |
![{\displaystyle \mathrm {U} ={\frac {H\,\lambda ^{2}}{h^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/747b64f6dcf9bb35f837f0d67542d430f4c988d5) |
wave mechanics (nonlinearity of surface gravity waves on a shallow fluid layer)
|
Vadasz number |
Va |
![{\displaystyle \mathrm {Va} ={\frac {\phi \,\mathrm {Pr} }{\mathrm {Da} }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1aab10de3591c4196db3380538e0360fd77cf7f3) |
porous media (governs the effects of porosity , the Prandtl number and the Darcy number on flow in a porous medium)
|
van 't Hoff factor |
i |
![{\displaystyle i=1+\alpha (n-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6727544fcf66acc52fb8c0d7a05379f9c75656c4) |
quantitative analysis (Kf and Kb)
|
Wallis parameter |
J* |
![{\displaystyle \alpha =R\left({\frac {\omega \rho }{\mu }}\right)^{\frac {1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c707dfd9e4ceacf3d3e64f36dcbd77bab5923c4) |
multiphase flows (nondimensional superficial velocity)
|
Weaver flame speed number |
|
|
combustion (laminar burning velocity relative to hydrogen gas)[25]
|
Weber number |
We |
![{\displaystyle \mathrm {We} ={\frac {\rho v^{2}l}{\sigma }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af88baa80544c927dfa26c08f471599a0fbd8e11) |
multiphase flow (strongly curved surfaces; ratio of inertia to surface tension)
|
Weissenberg number |
Wi |
![{\displaystyle \mathrm {Wi} ={\dot {\gamma }}\lambda }](https://wikimedia.org/api/rest_v1/media/math/render/svg/305734fece08e48422d34c81a0c723e0c681f026) |
viscoelastic flows (shear rate times the relaxation time)[26]
|
Womersley number |
![{\displaystyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3) |
![{\displaystyle \alpha =R\left({\frac {\omega \rho }{\mu }}\right)^{\frac {1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c707dfd9e4ceacf3d3e64f36dcbd77bab5923c4) |
biofluid mechanics (continuous and pulsating flows; ratio of pulsatile flow frequency to viscous effects)[27]
|