Prandtl, Reynolds and Nusselt Number Calculator

Find the Reynolds number, the Prandtl number, the Nusselt number and the film coefficient for a fluid flowing in a pipe.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

The Reynolds number tells you whether the flow is laminar or turbulent. The Prandtl number compares how well the fluid carries momentum with how well it carries heat. The Nusselt number is the ratio of convective to conductive heat transfer and depends on both: Nu = f(Re, Pr).

For turbulent flow in a pipe the Gnielinski equation is used, with the Dittus-Boelter equation as a check. For laminar flow in a long pipe the Nusselt number is 3.66 for a constant wall temperature. The film coefficient is the Nusselt number times the conductivity over the diameter.

Formulas used

  • Re = \dfrac{\rho V D}{\mu}
  • Pr = \dfrac{\mu c_p}{k} = \dfrac{\nu}{\alpha}
  • Nu = 0.023\,Re^{0.8}Pr^{0.4}
  • h = \dfrac{Nu\,k}{D}

Worked example

With the default numbers in the calculator above:

  1. Kinematic viscosity and thermal diffusivity: 1.0040e-6 and 1.4328e-7 m²/s
  2. Reynolds number: 74700.60
  3. Prandtl number: 7.01
  4. Flow regime: turbulent
  5. Nusselt number (Gnielinski): 465.94
  6. Nusselt number (Dittus-Boelter, a check): 396.83
  7. Film heat transfer coefficient: 5572.64 W/(m²·K)
  8. Thickness of the velocity layer compared to the thermal layer (flat-surface laminar estimate): 1.91

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What does a high Prandtl number mean?

The fluid is thick compared with how well it conducts heat. Oils have a high Prandtl number, gases are about 0.7 and water at room temperature is about 7.

Where do the properties come from?

The listed fluids use typical handbook values at one temperature. Use your own properties at the average temperature for a real design.

Related calculators

Further reading: Standard heat transfer texts (forced convection in tubes: Dittus-Boelter and Gnielinski correlations).

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