Prandtl Number
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 (m 2 /s)
α = thermal diffusivity (m 2 /s)
The Prandtl number can alternatively be expressed as
Pr = μ c p / k (2)
where
μ = absolute or dynamic viscosity (kg/m s, lb m /(ft h) )
c p = specific heat (J/kg K, Btu/(lb m o F))
k = thermal conductivity (W/m K, Btu/(h ft 2 o F/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)
c p = 0.50 Btu/(lb m o F)
k = 0.06 (Btu/(h ft 2 o F/ft)
Dynamic viscosity can be converted from cP to lb m /(ft h) as
μ = 15 (cP) ( 2.4191 (lb m /(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/(lb m o F) / 0.06 (Btu/(h ft 2 o F/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
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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.
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Properties of saturated liquid Carbon Dioxide - CO2 - density, specific heat, kinematic viscosity, thermal conductivity and Prandtl number.
Dimensionless Numbers
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Figures and table showing changes in Prandtl number for methane with changes in temperature and pressure.
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Figures and tables showing Prandtl number of nitrogen at varying temperarure and pressure, SI and Imperial units.
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Figures and tables with Prandtl Number of liquid and gaseous propane at varying temperarure and pressure, SI and Imperial units.
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