Prandtl Number


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Prandtl number

[′pränt·əl ‚nəm·bər]
(fluid mechanics)
A dimensionless number used in the study of diffusion in flowing systems, equal to the kinematic viscosity divided by the molecular diffusivity. Symbolized Prm . Also known as Schmidt number 1 (NSc ).
(thermodynamics)
A dimensionless number used in the study of forced and free convection, equal to the dynamic viscosity times the specific heat at constant pressure divided by the thermal conductivity. Symbolized NPr .

Prandtl Number

 

one of the similarity criteria of thermal processes in liquids and gases; Pr = v/a = μcp/λ, where v = μ /p is the coefficient of kinematic viscosity, μ is the coefficient of dynamic viscosity, p is the density, λ is the thermal conductivity, a - λ /pcp is the thermal diffusivity, and cp is the specific heat of the medium at constant pressure. Named after L. Prandtl, the Pr number is a physical characteristic of a medium and depends only on the thermodynamic state. For gases, it hardly varies with change in temperature; for diatomic gases, Pr ≈ 0,72, and for triatomic and polyatomic gases, Pr varies from about 0.75 to 1.0. In nonmetallic liquids, Pr varies more markedly with temperature for liquids of higher viscosity. For example, for water, Pr - 13.5 at 0°C, and Pr = 1.74 at 100°C; for transformer oil, Pr = 866 at 0°C and Pr - 43.9 at 100°C. For liquid metals, Pr ≪ 1 and changes little with temperature. For example, for sodium Pr - 0.0115 at 100°C and Pr = 0.0039 at 700°C.

The Prandtl number is related to the other similarity criteria —the Peclet number Pe and the Reynolds number Re —by the formula Pr = Pe/Re,

S. L. VISHNEVETSKII

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