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# Graetz number

In fluid dynamics, the Graetz number (Gz) is a dimensionless number that characterises laminar flow in a conduit. The number is defined as:

$Gz={d_i\over L}RePr$

where

di is the internal 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.

When used in connection with mass transfer the Prandtl number is replaced by the Schmidt number which expresses the ratio of the momentum diffusivity to the mass diffusivity.

$Gz={d_i\over L}ReSc$

The quantity is named after the physicist Leo Graetz.