# Graetz number

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

1. ^ Nellis, G., and Klein, S. (2009) "Heat Transfer" (Cambridge), page 663.
2. ^ Shah, R. K., and Sekulic, D. P. (2003) "Fundamentals of Heat Exchanger Design" (John Wiley and Sons), page 503.