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Prandtl Number Formula

GoPrandtl Number using Diffusivities Formula

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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. Check FAQs

Pr = c \cdot \frac{μ viscosity}{k}

Pr - Prandtl Number?c - Specific Heat Capacity?μ_viscosity - Dynamic Viscosity?k - Thermal Conductivity?

Prandtl Number Example

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Here is how the Prandtl Number equation looks like with Values.

Here is how the Prandtl Number equation looks like with Units.

Here is how the Prandtl Number equation looks like.

0.7113 = 4.184 \cdot \frac{1.02}{6000}

0.7113 = 4.184kJ/kg*K \cdot \frac{1.02Pa*s}{6000W/(m*K)}

0.7113 = 4.184 \cdot \frac{1.02}{6000}

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Prandtl Number Solution

Follow our step by step solution on how to calculate Prandtl Number?

FIRST Step Consider the formula

Pr = c \cdot \frac{μ viscosity}{k}

Next Step Substitute values of Variables

∴

Pr = 4.184kJ/kg*K \cdot \frac{1.02Pa*s}{6000W/(m*K)}

Next Step Convert Units

∴

Pr = 4184J/(kg*K) \cdot \frac{1.02Pa*s}{6000W/(m*K)}

Next Step Prepare to Evaluate

∴

Pr = 4184 \cdot \frac{1.02}{6000}

Next Step Evaluate

∴

Pr = 0.71128

LAST Step Rounding Answer

∴

Pr = 0.7113

Prandtl Number Formula Elements

Variables

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.

Symbol: Pr

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Prandtl Number

Specific Heat Capacity

Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: c

Measurement: Specific Heat CapacityUnit: kJ/kg*K

Note: Value can be positive or negative.

Formulas to find Specific Heat Capacity

Dynamic Viscosity

Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.

Symbol: μ_viscosity

Measurement: Dynamic ViscosityUnit: Pa*s

Note: Value should be greater than 0.

Formulas to find Dynamic Viscosity

Thermal Conductivity

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.

Symbol: k

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value should be greater than 0.

Formulas to find Thermal Conductivity

Other Formulas to find Prandtl Number

Go Prandtl Number using Diffusivities

Pr = \frac{𝜈}{α}

Other formulas in Co Relation of Dimensionless Numbers category

Go Reynolds Number for Circular Tubes

Re = ρ \cdot u Fluid \cdot \frac{D Tube}{μ viscosity}

Go Reynolds Number for Non-Circular Tubes

Re = ρ \cdot u Fluid \cdot \frac{L c}{μ viscosity}

Go Nusselt Number for Transitional and Rough Flow in Circular Tube

Nu = (\frac{f Darcy}{8}) \cdot (Re - 1000) \cdot \frac{Pr}{1 + 12.7 \cdot ({(\frac{f Darcy}{8})}^{0.5}) \cdot ({(Pr)}^{\frac{2}{3}} - 1)}

Go Stanton Number using Dimensionless Numbers

St = \frac{Nu}{Re \cdot Pr}

How to Evaluate Prandtl Number?

Prandtl Number evaluator uses Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity to evaluate 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 evaluate Prandtl Number using this online evaluator? To use this online evaluator for Prandtl Number, enter Specific Heat Capacity (c), Dynamic Viscosity (μ_viscosity) & Thermal Conductivity (k) and hit the calculate button.

FAQs on Prandtl Number

What is the formula to find Prandtl Number?

The formula of Prandtl Number is expressed as Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity. Here is an example- 142.256 = 4184*1.02/6000.

How to calculate Prandtl Number?

With Specific Heat Capacity (c), Dynamic Viscosity (μ_viscosity) & Thermal Conductivity (k) we can find Prandtl Number using the formula - Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity.

What are the other ways to Calculate Prandtl Number?

Here are the different ways to Calculate Prandtl Number-

Prandtl Number=Momentum Diffusivity/Thermal Diffusivity

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Prandtl Number Formula

​GoPrandtl Number using Diffusivities Formula

Prandtl Number Example

Prandtl Number Solution

Prandtl Number Formula Elements

Other Formulas to find Prandtl Number

Other formulas in Co Relation of Dimensionless Numbers category

How to Evaluate Prandtl Number?

FAQs on Prandtl Number

Variable Name

GoPrandtl Number using Diffusivities Formula