Prandtl Number Calculator

Enter value and click on calculate. Result will be displayed. P = ( η × Cp ) / λ
P = Prandtl Number
Cp = Specific Heat Capacity
η= dynamic viscosity
λ = thermal conductivity

Dynamic Viscosity (η):
kgm-1s-1
Specific Heat Capacity (Cp):
Jkg-1K-1
Thermal Conductivity (λ):
Wm-1K-1
Prandtl Number (P):

The Prandtl number (Pr) is a dimensionless quantity used in fluid mechanics and heat transfer to compare the relative thickness of the velocity and thermal boundary layers. It is given by the formula:

Where:

  • is the kinematic viscosity (in m2/s),
  • is the thermal diffusivity (in m2/s).

Alternatively, the Prandtl number can be expressed as:

Where:

  • is the dynamic viscosity (in Pa⋅s or kg/(m⋅s)),
  • is the specific heat capacity (in J/(kg⋅K)),
  • is the thermal conductivity (in W/(m⋅K)).

Prandtl number values:

  • Low Prandtl number (Pr < 1): Thermal diffusivity is higher than momentum diffusivity. This is typical for liquids like liquid metals.
  • High Prandtl number (Pr > 1): Momentum diffusivity dominates over thermal diffusivity. This is common for oils, glycerin, and most gases.
  • Prandtl number around 1: The diffusion of momentum and heat are comparable. This is typical for air and water.