Name
|
Standard symbol
|
Definition
|
Field of application
|
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)
|
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)
|
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)[4]
|
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)
|
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 capillary forces, similar to the Eötvös number)[6]
|
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)
|
Burger number
|
Bu
|
|
meteorology, oceanography (density stratification versus Earth's rotation)
|
Brownell–Katz number |
NBK |
![{\displaystyle \mathrm {N} _{\mathrm {BK} }={\frac {u\mu }{k_{\mathrm {rw} }\sigma }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd18d44d302fab05e8a69195b4f936490ad2520d) |
fluid mechanics (combination of capillary number and Bond number)[7]
|
Capillary number |
Ca |
![{\displaystyle \mathrm {Ca} ={\frac {\mu V}{\gamma }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0884d41eae9f95f456939e6996c6b6ca62e3f0) |
porous media, fluid mechanics (viscous forces versus surface tension)
|
Cauchy number |
Ca |
![{\displaystyle \mathrm {Ca} ={\frac {\rho u^{2}}{K}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1915378bdaa55113792189a45facedbb1fc2fbe4) |
compressible flows (inertia forces versus compressibility force)
|
Cavitation number |
Ca |
![{\displaystyle \mathrm {Ca} ={\frac {p-p_{\mathrm {v} }}{{\frac {1}{2}}\rho v^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b6934c6714d597fc0704dd5fa99c7e52f00a6a8) |
multiphase flow (hydrodynamic cavitation, pressure over dynamic pressure)
|
Chandrasekhar number |
C |
![{\displaystyle \mathrm {C} ={\frac {B^{2}L^{2}}{\mu _{o}\mu D_{M}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/566c73247fe7b4915c72495e0526eebf5322d834) |
hydromagnetics (Lorentz force versus viscosity)
|
Colburn J factors |
JM, JH, JD |
|
turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients)
|
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)
|
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)
|
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)
|
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)
|
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)
|
Excess temperature coefficient |
![{\displaystyle \Theta _{r}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/517aaf0ab8477050855bad98d6186b1246a43caa) |
![{\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)[8]
|
Fanning friction factor |
f |
|
fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)[9]
|
Froude number |
Fr |
![{\displaystyle \mathrm {Fr} ={\frac {U}{\sqrt {g\ell }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f68cd1ef04c96406902999041270d13b3286189d) |
fluid mechanics (wave and surface behaviour; ratio of a body's inertia to gravitational forces)
|
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)
|
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)
|
Garcia-Atance number |
GA |
![{\displaystyle \mathrm {G_{A}} ={\frac {p-p_{v}}{\rho aL}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c9bdd5af8ce17bef2b5eae81040b4e4ebf54d94b) |
phase change (ultrasonic cavitation onset, ratio of pressures over pressure due to acceleration)
|
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)
|
Hartmann number |
Ha |
![{\displaystyle \mathrm {Ha} =BL\left({\frac {\sigma }{\rho \nu }}\right)^{\frac {1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2494bc3701cd1590f652660baa29462a78135566) |
magnetohydrodynamics (ratio of Lorentz to viscous forces)
|
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)
|
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,f}(T_{w}-T_{sat})}{h_{fg}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/218e93e316dc04a28ee46d7c7ab756bfa0cab6f0) |
heat transfer (ratio of sensible heat to latent heat during phase changes)
|
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)
|
Kapitza number |
Ka |
![{\displaystyle \mathrm {Ka} ={\frac {\sigma }{\rho (g\sin \beta )^{1/3}\nu ^{4/3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f617ab7218668ac33118feca86c30b8c3ef5ca18) |
fluid mechanics (thin film of liquid flows down inclined surfaces)
|
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)
|
Kutateladze number |
Ku |
![{\displaystyle \mathrm {Ku} ={\frac {U_{h}\rho _{g}^{1/2}}{\left({\sigma g(\rho _{l}-\rho _{g})}\right)^{1/4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/65ef076d453485a397443cd11872b95aec03c671) |
fluid mechanics (counter-current two-phase flow)[10]
|
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)[11]
|
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)
|
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)
|
Markstein number |
Ma |
![{\displaystyle \mathrm {Ma} ={\frac {L_{b}}{l_{f}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca46ece9c7a3b16ea2f4c219579eed0d595efe0c) |
turbulence, combustion (Markstein length to laminar flame thickness)
|
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 |
or ![{\displaystyle \mathrm {Pe} ={\frac {Lu}{\alpha }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/35a328a23534bcfbd0a4f951df0227b0d0a43300) |
fluid mechanics (ratio of advective transport rate over molecular diffusive transport rate), heat transfer (ratio of advective transport rate over thermal diffusive transport rate)
|
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)
|
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)
|
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)
|
Reynolds number |
Re |
![{\displaystyle \mathrm {Re} ={\frac {UL\rho }{\mu }}={\frac {UL}{\nu }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ba72985d5d9d25bac4d25319640e3ffa57a3515) |
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/a6b7b2cd7bf07c6b7ea434010486fed18f10114e) |
fluid dynamics (effect of buoyancy on flow stability; ratio of potential over kinetic energy)[12]
|
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 {\text{Ro}}={\frac {U}{Lf}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/20fd3aa3aa970115d66c899afe3a54684eed2edb) |
fluid flow (geophysics, ratio of inertial force to Coriolis force)
|
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)[13]
|
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)
|
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)[14]
|
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)
|
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)
|
Strouhal number |
St |
![{\displaystyle \mathrm {St} ={\frac {fL}{U}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1d1aad0d71cc41b22503684d9cfebe2426a6cd65) |
Vortex shedding (ratio of characteristic oscillatory velocity to ambient flow velocity)
|
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)
|
Wallis parameter |
j∗ |
![{\displaystyle j^{*}=R\left({\frac {\omega \rho }{\mu }}\right)^{\frac {1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2dc1efa4377898e665e821afc8a6bc0758789ca) |
multiphase flows (nondimensional superficial velocity)[15]
|
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)[16]
|
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)[17]
|
Zel'dovich number |
![{\displaystyle \beta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8) |
![{\displaystyle \beta ={\frac {E}{RT_{f}}}{\frac {T_{f}-T_{o}}{T_{f}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e90e2169d35f79fbea43cae3b93a2504db8130f) |
fluid dynamics, Combustion (Measure of activation energy)
|