Prandtl Number Calculator

✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [c]			+10% -10%
✖Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ_viscosity]			+10% -10%
✖Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.ⓘ Thermal Conductivity [k]			+10% -10%

✖Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.ⓘ Prandtl Number [Pr]

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Formula

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Prandtl Number

Formula

`"Pr" = "c"*"μ"_{"viscosity"}/"k"`

Example

`"0.71128"="4.184kJ/kg*K"*"1.02Pa*s"/"6000W/(m*K)"`

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Prandtl Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity
Pr = c*μ_viscosity/k
This formula uses 4 Variables

Variables Used

Prandtl Number - Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
Dynamic Viscosity - (Measured in Pascal Second) - Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
Dynamic Viscosity: 1.02 Pascal Second --> 1.02 Pascal Second No Conversion Required
Thermal Conductivity: 6000 Watt per Meter per K --> 6000 Watt per Meter per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Pr = c*μ_viscosity/k --> 4184*1.02/6000

Evaluating ... ...

Pr = 0.71128

STEP 3: Convert Result to Output's Unit

0.71128 --> No Conversion Required

FINAL ANSWER

0.71128 <-- Prandtl Number

(Calculation completed in 00.004 seconds)

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Created by Ishan Gupta

Birla Institute of Technology & Science (BITS), Pilani

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< 11 Co-Relation of Dimensionless Numbers Calculators

Nusselt Number for Transitional and Rough Flow in Circular Tube

Go Nusselt Number = (Darcy Friction Factor/8)*(Reynolds Number-1000)*Prandtl Number/(1+12.7*((Darcy Friction Factor/8)^(0.5))*((Prandtl Number)^(2/3)-1))

Stanton Number using Basic Fluid Properties

Go Stanton Number = External Convection Heat Transfer Coefficient/(Specific Heat Capacity*Fluid Velocity*Density)

Reynolds Number for Non-Circular Tubes

Go Reynolds Number = Density*Fluid Velocity*Characteristic Length/Dynamic Viscosity

Reynolds Number for Circular Tubes

Go Reynolds Number = Density*Fluid Velocity*Diameter of Tube/Dynamic Viscosity

Fourier Number

Go Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)

Prandtl Number

Go Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity

Stanton Number using Dimensionless Numbers

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

Stanton Number given Fanning Friction Factor

Go Stanton Number = (Fanning Friction Factor/2)/(Prandtl Number)^(2/3)

Nusselt Number using Dittus Boelter Equation for Cooling

Go Nusselt Number = 0.023*(Reynolds Number)^0.8*(Prandtl Number)^0.3

Nusselt Number using Dittus Boelter Equation for Heating

Go Nusselt Number = 0.023*(Reynolds Number)^0.8*(Prandtl Number)^0.4

Prandtl Number using Diffusivities

Go Prandtl Number = Momentum Diffusivity/Thermal Diffusivity

Prandtl Number Formula

Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity
Pr = c*μ_viscosity/k

What is Prandtl number?

How to Calculate Prandtl Number?

Prandtl Number calculator uses Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity to calculate the Prandtl Number, The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. For most gases over a wide range of temperature and pressure, Pr is approximately constant. Therefore, it can be used to determine the thermal conductivity of gases at high temperatures, where it is difficult to measure experimentally due to the formation of convection currents. Prandtl Number is denoted by Pr symbol.

How to calculate Prandtl Number using this online calculator? To use this online calculator for Prandtl Number, enter Specific Heat Capacity (c), Dynamic Viscosity (μ_viscosity) & Thermal Conductivity (k) and hit the calculate button. Here is how the Prandtl Number calculation can be explained with given input values -> 142.256 = 4184*1.02/6000.

FAQ

What is Prandtl Number?

The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. For most gases over a wide range of temperature and pressure, Pr is approximately constant. Therefore, it can be used to determine the thermal conductivity of gases at high temperatures, where it is difficult to measure experimentally due to the formation of convection currents and is represented as Pr = c*μ_viscosity/k or Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity. Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied & Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.

How to calculate Prandtl Number?

The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is often found in property tables alongside other properties such as viscosity and thermal conductivity. For most gases over a wide range of temperature and pressure, Pr is approximately constant. Therefore, it can be used to determine the thermal conductivity of gases at high temperatures, where it is difficult to measure experimentally due to the formation of convection currents is calculated using Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity. To calculate Prandtl Number, you need Specific Heat Capacity (c), Dynamic Viscosity (μ_viscosity) & Thermal Conductivity (k). With our tool, you need to enter the respective value for Specific Heat Capacity, Dynamic Viscosity & Thermal Conductivity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Prandtl Number?

In this formula, Prandtl Number uses Specific Heat Capacity, Dynamic Viscosity & Thermal Conductivity. We can use 1 other way(s) to calculate the same, which is/are as follows -

Prandtl Number = Momentum Diffusivity/Thermal Diffusivity

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