# 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.

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