In fluid dynamics, the Graetz number (Gz) is a dimensionless number that characterizes laminar flow in a conduit. The number is defined as:^[1]

${\displaystyle \mathrm {Gz} ={D_{H} \over L}\mathrm {Re} \,\mathrm {Pr} }$

where

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

L is the length

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.

${\displaystyle \mathrm {Gz} ={D_{H} \over L}\mathrm {Re} \,\mathrm {Sc} }$

The quantity is named after the physicist Leo Graetz.