Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

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

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.

Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!