Graetz number
In fluid dynamics, the Graetz number, \(\mathrm{Gz}\) is a dimensionless number that characterises laminar flow in a conduit. The number is defined as:[1]
\[\mathrm{Gz}={D_H \over L} \mathrm{Re} \mathrm{Pr}\]
where
\[D_H\] is the diameter in round tubes or hydraulic diameter in arbitrary cross-section ducts \[L\] is the length \[\mathrm{Re}\] is the Reynolds number and \[\mathrm{Pr}\] 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 \(\mathrm{Sc}\) 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.
fa:عدد گراتز fr:Nombre de Graetz nl:Getal van Graetz ru:Число Гретца
