Page 893 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

848 Appendix G: Dimensionless Numbers

TABLE G.1
List of 154 Dimensionless Numbers from Land Chart of Dimensionless Numbers
Dimensionless Numbers Dimensionless Numbers Dimensionless Numbers Dimensionless Numbers
Acceleration Deryagin Karman-1 Prandtl heat transfer
Aeroelastic Dulong Kirpichev heat transfer Prandtl mass transfer
Alfven Ekman Kirpichev mass transfer Prandtl velocity ratio
Archimedes Elasticity-1 Kirpitcheff Predvodetlev
Arrhenius Elasticity-2 Knudsen Radiation pressure
Bagnold Elasticity-3 Kossovich Rayleigh
Bansen Electric Reynolds Lagrange-1 Regier
Bingham Electroviscous Lagrange-2 Reynolds
Biot heat transfer Ellis Leverett Richardson
Biot mass transfer Elsasser Lewis Rossby
Blake Euler Lundquist Russell
Bodenstein Evaporation-1 Lykoudis Sachs
Boltzman Evaporation-2 Mach Schiller
Bond Evaporation elasticity Magnetic dynamic Slosh time
Bouguer Explosion Magnetic force Sommerfeld
Boussinesq Fanning Magnetic interaction Specific heat ratio
Brinkman Federov Magnetic Prandtl Specific speed
Bubble Nusselt Fliegner Magnetic pressure Squeeze
Bubble Reynolds Flow Magnetic Reynolds Stanton
Buoyancy Fourier heat transfer Marangoni Stefan
Capillarity-1 Fourier heat transfer Mass ratio Stokes
Capillarity-2 Froude McAdams Strouhal
Capillarity-3 Frueh Merkel Structural merit
Capillarity-bouyancy Galileo Momentum Suratman
Capillary Goucher Morton Surface viscosity
Carnot Graetz Nusselt heat transfer Taylor
Cavitation Grashof Nusselt mass transfer Thoma
Centrifuge Gravity Nusselt film thickness Toms
Clausius Gukhman Ocvirk Truncation
Condensation-1 Hall Ohnesorge Two-phase flow
Condensation-2 Hartmann Particle Two-phase porous flow
Crispation Heat transfer Peclet heat transfer Viscoelastic
Crocco Hedstrom-1 Peclet mass transfer Weber
Damköhler’s first Hersey Pipeline Weissenberg
Damköhler’s second Hodgson Poiseuille
Damköhler’s third J-Factor heat transfer Poisson
Damköhler’s fourth J-Factor mass transfer Pomerantsev
Darcy Jacob Porous flow
Dean Jakob Posnov
Debye Joule Power
Source: Omega Engineering, Inc., The land chart of dimensionless numbers, U.S. Patent No. 5,465,838, Omega Engineering, Inc., Stamford, CT, 1997.

The dimensionless numbers, E, R, F, W, P, are related to be used in situations that compare the two kinds of mass
the dynamics of fluid flow. On the other hand, the other transfer. As indicated in Table G.1, the world of dimension-
dimensionless numbers have to do heat transfer and=or mass less numbers is very large.
transfer and have interpretations along such lines. Some of the
numbers are simply derivatives of others that are more basic. G.3 UTILITY OF DIMENSIONLESS NUMBERS
The derivative numbers may have special uses. As an
example, the power number, P, is a derivative of the Euler In practice, dimensionless numbers are used widely to dis-
number, E. Also, some combine the effects of two kinds of play numerous kinds of empirical relationships. Examples
phenomena. For example, the Peclet number is the ratio of include friction factor versus Reynolds number in pipe
convective mass transfer to diffusion mass transfer and may flow, Euler number versus Reynolds number in fluid flow