Prandtl Number
A dimensionless number approximating the ratio of momentum diffusivity to thermal diffusivity.
The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity - and can be expressed as
Pr = v / α (1)
where
Pr = Prandtl's number
v = momentum diffusivity (m2/s)
α = thermal diffusivity (m2/s)
The Prandtl number can alternatively be expressed as
Pr = μ cp / k (2)
where
μ = absolute or dynamic viscosity (kg/m s, lbm /(ft h) )
cp = specific heat (J/kg K, Btu/(lbm oF))
k = thermal conductivity (W/m K, Btu/(h ft2oF/ft))
The Prandtl Number is often used in heat transfer and free and forced convection calculations. It depends on the fluid properties.
- gases - Pr ranges 0.7 - 1.0
- dry air
- water - Pr ranges 1 - 10
- liquid metals - Pr ranges 0.001 - 0.03
- oils - Pr ranges 50 - 2000
Example - Calculation of a Prandtl Number
μ = 15 (cP)
cp = 0.50 Btu/(lbm oF)
k = 0.06 (Btu/(h ft2oF/ft)
Dynamic viscosity can be converted from cP to lbm /(ft h) as
μ = 15 (cP) ( 2.4191 (lbm /(ft hr)) / (1 cP))
= 36.3 lb/(ft hr)
The Prandtl Number can be calculated as
Pr = 36.3 ( lb/(ft hr)) 0.50 Btu/(lbm oF) / 0.06 (Btu/(h ft2oF/ft)
= 302
Related Topics
-
Fluid Mechanics
The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.
Related Documents
-
Air Properties - Imperial Units
Thermodynamic properties of air at low pressures - imperial units. -
Air Properties - SI Units
Ideal gas properties of air at low pressure - SI units. -
Ammonia - Prandtl Number vs. Temperature and Pressure
Figures and table with changes in Prandtl number for ammonia with changes in temperature and pressure. -
Carbon Dioxide - Liquid Properties
Properties of saturated liquid Carbon Dioxide - CO2 - density, specific heat, kinematic viscosity, thermal conductivity and Prandtl number. -
Dimensionless Numbers
Physical and chemical dimensionless quantities - Reynolds number, Euler, Nusselt, and Prandtl number - and many more. -
Dry Air - Thermodynamic and Physical Properties
Thermodynamic properties of dry air - specific heat, ratio of specific heats, dynamic viscosity, thermal conductivity, Prandtl number, density and kinematic viscosity at temperatures ranging 175 - 1900 K. -
Methane - Prandtl number vs. Temperature
Figures and table showing changes in Prandtl number for methane with changes in temperature and pressure. -
Nitrogen - Prandtl number vs. Temperature and Pressure
Figures and tables showing Prandtl number of nitrogen at varying temperarure and pressure, SI and Imperial units. -
Propane - Prandtl Number vs. Temperature and Pressure
Figures and tables with Prandtl Number of liquid and gaseous propane at varying temperarure and pressure, SI and Imperial units. -
Reynolds Number
Introduction and definition of the dimensionless Reynolds Number - online calculators. -
Water - Thermophysical Properties
Thermal properties of water at different temperatures like density, freezing temperature, boiling temperature, latent heat of melting, latent heat of evaporation, critical temperature and more.
