Turbulent Prandtl Number Calculator

✖Turbulent Eddy Viscosity is defined as the turbulent transfer of momentum by eddies giving rise to internal fluid friction, in a manner analogous to the action of molecular viscosity in laminar flow.ⓘ Turbulent Eddy Viscosity [ε_M]			+10% -10%
✖Eddy Diffusivity of heat is defined as the turbulent exchange coefficient for temperature.ⓘ Eddy Diffusivity [ε_H]			+10% -10%

✖Turbulent Prandtl Number is a non-dimensional term defined as the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity.ⓘ Turbulent Prandtl Number [Pr_t]

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Formula

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Turbulent Prandtl Number

Formula

Pr t = \frac{ε M}{ε H}

Example

5 = \frac{100.0000 m²/s}{20 m²/s}

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Turbulent Prandtl Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Turbulent Prandtl Number = Turbulent Eddy Viscosity/Eddy Diffusivity
Pr_t = ε_M/ε_H
This formula uses 3 Variables

Variables Used

Turbulent Prandtl Number - Turbulent Prandtl Number is a non-dimensional term defined as the ratio between the momentum eddy diffusivity and the heat transfer eddy diffusivity.
Turbulent Eddy Viscosity - (Measured in Square Meter per Second) - Turbulent Eddy Viscosity is defined as the turbulent transfer of momentum by eddies giving rise to internal fluid friction, in a manner analogous to the action of molecular viscosity in laminar flow.
Eddy Diffusivity - (Measured in Square Meter Per Second) - Eddy Diffusivity of heat is defined as the turbulent exchange coefficient for temperature.

STEP 1: Convert Input(s) to Base Unit

Turbulent Eddy Viscosity: 100 Square Meter per Second --> 100 Square Meter per Second No Conversion Required
Eddy Diffusivity: 20 Square Meter Per Second --> 20 Square Meter Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Pr_t = ε_M/ε_H --> 100/20

Evaluating ... ...

Pr_t = 5

STEP 3: Convert Result to Output's Unit

5 --> No Conversion Required

FINAL ANSWER

5 <-- Turbulent Prandtl Number

(Calculation completed in 00.004 seconds)

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Created by Ravi Khiyani

Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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< Prandtl and Peclet Number Calculators

Prandtl number given Stanton number and other dimensionless groups

Go Prandtl Number = Nusselt Number/(Stanton Number*Reynolds Number)

Prandtl number in convection

Go Prandtl Number = Molecular Diffusivity of Momentum/Molecular Diffusivity of Heat

Prandtl number given Rayleigh number

Go Prandtl Number = Rayleigh Number/Grashof Number

Peclet number given Reynolds number

Go Peclet Number = Reynolds Number*Prandtl Number

Turbulent Prandtl Number Formula

Turbulent Prandtl Number = Turbulent Eddy Viscosity/Eddy Diffusivity
Pr_t = ε_M/ε_H

Where the Turbulent Prandtl number is used?

The Turbulent Prandtl number is useful for solving the heat transfer problem of turbulent boundary layer flows. The simplest model for turbulent Prandtl number is the Reynolds analogy, which yields a turbulent Prandtl number of 1. From experimental data, turbulent Prandtl number has an average value of 0.85 but ranges from 0.7 to 0.9 depending on the Prandtl number of the fluid.

How to Calculate Turbulent Prandtl Number?

Turbulent Prandtl Number calculator uses Turbulent Prandtl Number = Turbulent Eddy Viscosity/Eddy Diffusivity to calculate the Turbulent Prandtl Number, Turbulent Prandtl Number is a dimensionless number used in fluid dynamics to describe the ratio of momentum diffusivity to thermal diffusivity in turbulent flow. It plays a crucial role in modeling the transfer of heat and momentum in turbulent boundary layers, affecting heat exchanger design, climate models, and aerodynamics. Turbulent Prandtl Number is denoted by Pr_t symbol.

How to calculate Turbulent Prandtl Number using this online calculator? To use this online calculator for Turbulent Prandtl Number, enter Turbulent Eddy Viscosity (ε_M) & Eddy Diffusivity (ε_H) and hit the calculate button. Here is how the Turbulent Prandtl Number calculation can be explained with given input values -> 5 = 100/20.

FAQ

What is Turbulent Prandtl Number?

Turbulent Prandtl Number is a dimensionless number used in fluid dynamics to describe the ratio of momentum diffusivity to thermal diffusivity in turbulent flow. It plays a crucial role in modeling the transfer of heat and momentum in turbulent boundary layers, affecting heat exchanger design, climate models, and aerodynamics and is represented as Pr_t = ε_M/ε_H or Turbulent Prandtl Number = Turbulent Eddy Viscosity/Eddy Diffusivity. Turbulent Eddy Viscosity is defined as the turbulent transfer of momentum by eddies giving rise to internal fluid friction, in a manner analogous to the action of molecular viscosity in laminar flow & Eddy Diffusivity of heat is defined as the turbulent exchange coefficient for temperature.

How to calculate Turbulent Prandtl Number?

Turbulent Prandtl Number is a dimensionless number used in fluid dynamics to describe the ratio of momentum diffusivity to thermal diffusivity in turbulent flow. It plays a crucial role in modeling the transfer of heat and momentum in turbulent boundary layers, affecting heat exchanger design, climate models, and aerodynamics is calculated using Turbulent Prandtl Number = Turbulent Eddy Viscosity/Eddy Diffusivity. To calculate Turbulent Prandtl Number, you need Turbulent Eddy Viscosity (ε_M) & Eddy Diffusivity (ε_H). With our tool, you need to enter the respective value for Turbulent Eddy Viscosity & Eddy Diffusivity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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