In fluid dynamics, the Graetz number (Gz) is a dimensionless number that characterizes laminar flow in a conduit. The number is defined as:[1]
\( \mathrm{Gz} = {D_H \over L} \mathrm{Re}\, \mathrm{Pr} \)
where
DH is the diameter in round tubes or hydraulic diameter in arbitrary cross-section ducts
L is the length
Re is the Reynolds number and
Pr is the Prandtl number.
This number is useful in determining the thermally developing flow entrance length in ducts. A Graetz number of approximately 1000 or less is the point at which flow would be considered thermally fully developed.[2]
When used in connection with mass transfer the Prandtl number is replaced by the Schmidt number, Sc, which expresses the ratio of the momentum diffusivity to the mass diffusivity.
\( {\mathrm {Gz}}={D_{H} \over L}{\mathrm {Re}}\,{\mathrm {Sc}} \)
The quantity is named after the physicist Leo Graetz.
References
Nellis, G., and Klein, S. (2009) "Heat Transfer" (Cambridge), page 663.
Shah, R. K., and Sekulic, D. P. (2003) "Fundamentals of Heat Exchanger Design" (John Wiley and Sons), page 503.
vte
Dimensionless numbers in fluid mechanics
Archimedes Atwood Bagnold Bejan Biot Bond Brinkman Capillary Cauchy Chandrasekhar Damköhler Darcy Dean Deborah Dukhin Eckert Ekman Eötvös Euler Froude Galilei Graetz Grashof Görtler Hagen Iribarren Kapitza Keulegan–Carpenter Knudsen Laplace Lewis Mach Marangoni Morton Nusselt Ohnesorge Péclet Prandtl
magnetic turbulent Rayleigh Reynolds
magnetic Richardson Roshko Rossby Rouse Schmidt Scruton Sherwood Shields Stanton Stokes Strouhal Stuart Suratman Taylor Ursell Weber Weissenberg Womersley
Hellenica World - Scientific Library
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