Prandtl Number Calculator

Find the Prandtl number of a fluid.

Prandtl number 6.977

Formula: Pr = μ·c_p ÷ k

Step-by-step with your numbers:

1. Values used:

2. Dynamic viscosity = 0.001 Pa·s

3. Specific heat = 4,186 J/(kg·K)

4. Thermal conductivity = 0.6 W/(m·K)

6. Dynamic viscosity x Specific heat = 0.001 x 4,186 = 4.186

7. Prandtl number = (Dynamic viscosity x Specific heat) / Thermal conductivity = 4.186 / 0.6 = 6.977

Did we solve your problem today?

The Prandtl number compares momentum diffusivity to thermal diffusivity.

The math behind it

Pr = μ·c_p ÷ k. Water is about 7; air about 0.7; liquid metals far below 1.

Water (μ 0.001, c_p 4186, k 0.6) → Pr ≈ 6.98.

Why does it matter?

It governs how heat and momentum boundary layers compare in convection.