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# 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 ft2 oF/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 ft2 oF/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 ft2 oF/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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