- 2. 1.REYNOLDS NUMBER It is the ratio of inertia force to the viscous force. Where, Re VL is density is velocity L is linear dimension is viscosity Significance-It is used to identify the nature of flow (Laminar or Turbulent) V
- 3. 2.FROUDE NUMBER It is the ratio of inertia force to the gravity force Where , V is the velocity g is the acceleration due to gravity L is the characteristics length Significance-It is used to analyze nature of flow where free surface is present. e.g. weirs ,channels ,spillways V Fr gL
- 4. 3.WEBERS NUMBER It is the ratio of inertia force to surface tension force. Where V is the velocity L is the characteristics length Significance-It is used in analyzing formation of droplet and in capillary studies. / V We L is the surface tension is the density
- 5. 4.EULER NUMBER It is the ratio of inertia force to pressure force. Where P is the pressure V is the velocity Significance-It is used to characterize energy losses in a flow. V Eu P is the density
- 6. 5.MACH NUMBER It is the ratio of inertia force to elastic force. Where V is the velocity of object C is the speed of sound Significance-It is used to analyze fluid flow where compressibility is a important factor. V M C
- 7. 6.BIOT NUMBER It is the ratio of conductive resistance to convective resistance. Where h is the heat transfer coefficient K is the thermal conductivity Significance-It is used in the heat transfer calculation (lumped heat analysis). chL Bi K cL is the characteristics length(volume of the body/surface area of contact)
- 8. 7.FOURIER NUMBER It is the ratio of heat conducted through a body to the heat stored. Where, t is the characteristics time Significance-It is used in transient heat analysis. 2 c t L is the thermal diffusivity cL is the length
- 9. 8.NUSSELT NUMBER It is the ratio of convective heat transfer to conductive heat transfer. Where h is the convective heat transfer coefficient L is the characteristics length K is the thermal conductivity Significance-It describe the enhancement of heat transfer because of convection in comparison to conduction hL Nu K
- 10. 9.PRANDTL NUMBER It is the ratio of momentum diffusivity to heat diffusivity Where K is the thermal conductivity Significance-Prandtl number is used to describe thermal boundary layer. Pr PC K is the dynamic viscosity PC is the specific heat
- 11. 10.GRASHOF NUMBER It is the ratio of buoyancy force to viscous force. Where g is acceleration due to gravity Significance-It is used in flow analysis in natural convection. is the coefficient of thermal expansion sT is the surface temperature T is the fluid temperature far from the surface is the kinematic viscosity of fluid 3 2 ( )s cg T T L Gr
- 12. 11.RAYLEIGH NUMBER Rayleigh number is the product of Grashof number and Prandtl number. Ra= Gr . Pr Significance-It is associated with buoyancy driven flow . Its value is used to characterize laminar to turbulent transition.
- 13. 12.STANTON NUMBER It is defined as the ratio of heat transferred by convection to the heat capacity of fluid. Where h is the heat transfer coefficient u is the speed of fluid Significance-It is used in heat transfer for forced convection flows. Re.Pr p Nu h St uC is the density of fluid pC is the Specific heat capacity of the fluid
- 14. 13.PECLET NUMBER It is defined as the product of Reynold number and Prandtl number. Where L is the characteristics length u is the velocity Significance-It is used in calculations including convective heat transfer rate. Re.Pr Lu Pe is the thermal diffusivity
- 15. 14.JAKOB NUMBER It is the ratio of sensible energy absorbed to latent energy absorbed during liquid- vapor phase change. Where Significance-It is used in analyzing flow pattern in process of boiling. ( )P s sat fg C T T Ja h PC s satT T fgh is the specific heat capacity is the temperature difference Latent heat of vaporization
- 16. 15.BOND NUMBER It is the ratio of buoyancy force to the surface tension force. Where g is the acceleration due to gravity Significance-It is used in analyzing the behavior of bubbles. 1 2( )g Bo 1 2( ) is the difference in density is the surface tension
- 17. 16.SCHIMDT NUMBER It is the ratio of momentum diffusivity to mass diffusivity. Where D is the mass diffusivity Significance-It is used in fluid flows where simultaneous mass and momentum diffusion occurs. Sc D is the kinematic viscosity
- 18. 17.LEWIS NUMBER It is the ratio of thermal diffusivity to the mass diffusivity. Where D is the mass diffusivity K is the thermal conductivity Significance-It is used to analyze fluid flow with simultaneous heat and mass transfer by convection. p K Le D C D is the thermal diffusivity pC is the specific heat capacity
- 19. 18.SOMMERFELD NUMBER Sommerfeld number is defined by the following equation Where r is the radius of the journal c is the radial clearance P is the bearing pressure Significance-It is used in hydrodynamic lubrication analysis. 2 . snr S c P is the dynamic viscosity sn is the journal speed in r.p.s
- 20. 19.KNUDSEN NUMBER It is the ratio of molecular mean free path to the characteristics length. Where L is the characteristics length Significance-It is useful in determining whether continuum mechanics formulation can be applied or not in a system. Kn L is the mean free path
- 21. 20.SHERWOOD NUMBER It is the ratio of convection mass transfer to the diffusion mass transfer Where K is the mass transfer coefficient l is the characteristics length D is the mass diffusivity Significance-It is used in mass transfer problems. Kl Sh D