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One of the characteristics of similarity of heat processes in fluids and gasses. The Prandtl number depends only on the thermodynamical state of the medium, and is defined by

$$ 
 \mathop{\rm Pr}  =  
\frac \nu {a}
  = \ 

\frac{\mu c _ {p} } \lambda 
 ,
$$

where  $  \nu = \mu / \rho $
is the kinematic coefficient of viscosity,  $  \mu $
is the dynamic coefficient of viscosity,  $  \rho $
is the density,  $  \lambda $
is the coefficient of heat conductivity,  $  a = \lambda / \rho c _ {p} $
is the coefficient of thermal diffusion, and  $  c _ {p} $
is the specific heat capacity of the medium at constant pressure.

The Prandtl number is connected with other characteristics of similarity, the [[Péclet number|Péclet number]] and the [[Reynolds number|Reynolds number]], by the relation  $   \mathop{\rm Pr} =  \mathop{\rm Pe} /  \mathop{\rm Re} $.

The Prandtl number is named after L. Prandtl.

====Comments====
The Prandtl number is sometimes also called the Darcy–Prandtl number.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  N. Curle,   H.J. Davies,   "Modern fluid dynamics" , '''II''' , v. Nostrand-Reinhold  (1971)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  S. Chandrasekhar,   "Hydrodynamics and hydrodynamic stability" , Dover, reprint  (1981)  pp. Chapt. VII</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  C.-S. Yih,   "Stratified flows" , Acad. Press  (1980)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  L.D. Landau,   E.M. Lifshitz,   "Fluid mechanics" , Pergamon  (1959)  pp. 203, 208  (Translated from Russian)</TD></TR></table>