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) |
Asakuma number | As | ![{\displaystyle \mathrm {As} ={\frac {W}{\alpha \rho d_{p}H}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42056b15b7bd0551fcf5afd982cb4745da1d4ffe) | heat transfer (ratio of heat generation of microwave dielectric heating to thermal diffusion[6] |
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}{\dot {\gamma }}}{\mu }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb9af380cc551b8964aa634afc8697bfc9582f42) | fluid mechanics, geology (ratio of grain collision stresses to viscous fluid stresses in flow of a granular material such as grain and sand)[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] |
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)[9] |
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)[1] |
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) [10] |
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 | 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) [11] |
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) |
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) |
Colburn J factors | JM, JH, JD | | turbulence; heat, mass, and momentum transfer (dimensionless transfer coefficients) |
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) |
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) |
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)[12] |
Fanning friction factor | f | | fluid mechanics (fraction of pressure losses due to friction in a pipe; 1/4th the Darcy friction factor)[13] |
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) |
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) |
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) |
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) |
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) |
Karlovitz number | Ka | ![{\displaystyle \mathrm {Ka} ={\frac {t_{F}}{t_{\eta }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4456135f27ebd63460a098585b49d5d720233220) | turbulent combustion (characteristic chemical time scale to Kolmogorov time scale) |
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)[14] |
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)[15] |
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)[16] |
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 | ![{\displaystyle {\mathcal {M}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc2abebd45ec020509a0ec548b67c9a2cb7cecd) | ![{\displaystyle {\mathcal {M}}={\frac {{\mathcal {L}}_{b}}{\delta _{L}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec794e105f28c445400b3e074964e64a31d7ef88) | fluid dynamics, combustion (turbulent combustion flames) |
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} _{d}={\frac {hd}{k}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f427850cddfcdcdc43faccc62b1ec7893f2ace5e) | 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} _{d}={\frac {du\rho c_{p}}{k}}=\mathrm {Re} _{d}\,\mathrm {Pr} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/5ac17ec326248da13b4aa5fedb44a21dfe3d4f9a) | heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer) |
Péclet number | Pe | ![{\displaystyle \mathrm {Pe} _{d}={\frac {du}{D}}=\mathrm {Re} _{d}\,\mathrm {Sc} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef3caa30b99eaa3055f53211982cbb8eb25169b5) | mass transfer (advection–diffusion problems; total momentum transfer to diffusive mass transfer) |
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} _{L}={\frac {vL\rho }{\mu }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c02e970db7521beca3ee428900de6a323d059f2) | fluid mechanics (ratio of fluid inertial and viscous forces)[1] |
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)[17] |
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) |
Schmidt number | Sc | ![{\displaystyle \mathrm {Sc} _{D}={\frac {\nu }{D}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/289240ffab4c9e228d8fbe7ec05c202d06cdedfa) | mass transfer (viscous over molecular diffusion rate)[18] |
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} _{D}={\frac {KL}{D}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8d7815368abada05bd248323b54695201588ed) | 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)[19] |
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 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)[20] |
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) [21] |
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)[22] |
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)[23] |
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)[24] |
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) |