Influid dynamics, theGraetz number (Gz) is adimensionless number that characterizeslaminar flow in a conduit. The number is defined as:^[1]

${\displaystyle \mathrm{G}\mathrm{z}=\frac{D_H}{L}\mathrm{R}\mathrm{e}\mathrm{P}\mathrm{r}}$

where

D_H is the diameter in round tubes orhydraulic diameter in arbitrary cross-section ducts

L is the length

Re is theReynolds number and

Pr is thePrandtl 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 theSchmidt number, Sc, which expresses the ratio of the momentum diffusivity to the mass diffusivity.

${\displaystyle \mathrm{G}\mathrm{z}=\frac{D_H}{L}\mathrm{R}\mathrm{e}\mathrm{S}\mathrm{c}}$

The quantity is named after the physicistLeo Graetz.

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