Prandtl Number Calculator

Understanding Prandtl Number Calculator

The Prandtl number compares the rate of momentum diffusion to thermal diffusion. For water Pr ≈ 7, for air Pr ≈ 0.71, for liquid metals Pr << 1.

How to use this calculator

1. Enter the dynamic viscosity \(\mu\) of the fluid.
2. Enter the specific heat capacity \(c_p\).
3. Enter the thermal conductivity \(k\).
4. Click calculate to get \(Pr = \frac{\mu c_p}{k}\).

The formula explained

The formula \(Pr = \frac{\mu c_p}{k}\) computes the Prandtl number from a fluid's viscosity, specific heat capacity, and thermal conductivity. It is a dimensionless ratio, so the units cancel.

• Pr = Prandtl number, a dimensionless ratio
• \(\mu\) = dynamic viscosity
• \(c_p\) = specific heat capacity at constant pressure
• k = thermal conductivity

Step by step method

1. Multiply the dynamic viscosity \(\mu\) by the specific heat capacity \(c_p\).
2. Divide that product by the thermal conductivity \(k\).
3. Check that the result has no units, because the Prandtl number is dimensionless.

Worked example

Problem. A fluid has \(\mu = 0.001\,\text{Pa}\cdot\text{s}\), \(c_p = 4180\,\text{J}/(\text{kg}\cdot\text{K})\), and \(k = 0.60\,\text{W}/(\text{m}\cdot\text{K})\). Find the Prandtl number.

1. Substitute into the formula, \(Pr = \frac{\mu c_p}{k} = \frac{(0.001)(4180)}{0.60}\).
2. Compute the numerator, \((0.001)(4180) = 4.18\).
3. Divide, \(\frac{4.18}{0.60} \approx 6.97\), so \(Pr \approx 6.97\).

Tips and common mistakes

• Make sure \(\mu\), \(c_p\), and \(k\) are in consistent units, because mismatched units can give the wrong result.
• Remember that \(Pr\) is dimensionless, so a unit label on the final answer usually means something was entered incorrectly.

Frequently asked questions