Physics

Prandtl Number Calculator

Find the Prandtl number of a fluid.

Calculated Output

Prandtl number 6.977

Formula: Pr = μ·c_p ÷ k

Step-by-Step Breakdown

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

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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.