In
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
, the Graetz number (Gz) is a
dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
that characterizes
laminar flow
In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mi ...
in a conduit. The number is defined as:
:
where
: ''D
H'' is the diameter in round tubes or
hydraulic diameter The hydraulic diameter, , is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. When the cross-section is uniform along the tube or channel ...
in arbitrary cross-section ducts
: ''L'' is the length
: Re is the
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
and
: Pr is the
Prandtl number
The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as:
: \mathrm = \frac = \frac ...
.
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.
[Shah, R. K., and Sekulic, D. P. (2003) "Fundamentals of Heat Exchanger Design" (John Wiley and Sons), page 503.]
When used in connection with mass transfer the Prandtl number is replaced by the
Schmidt number
Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convect ...
, Sc, which expresses the ratio of the momentum diffusivity to the mass diffusivity.
:
The quantity is named after the physicist
Leo Graetz
Leo Graetz (26 September 1856 – 12 November 1941) was a German physicist. He was born in Breslau, Germany, and was the son of historian Heinrich Graetz.
Graetz was one of the first to investigate the propagation of electromagnetic energy. ...
.
References
{{DEFAULTSORT:Graetz Number
Dimensionless numbers of fluid mechanics
Fluid dynamics