Dynamic Viscosity of Gases Solution

STEP 0: Pre-Calculation Summary
Formula Used
Dynamic Viscosity Fluid = (Sutherland Experimental Constant 'a'*Absolute Temperature of Fluid^(1/2))/(1+Sutherland Experimental Constant 'b'/Absolute Temperature of Fluid)
μ = (a*T^(1/2))/(1+b/T)
This formula uses 4 Variables
Variables Used
Dynamic Viscosity Fluid - (Measured in Pascal Second) - Dynamic Viscosity Fluid is the measure of fluid's resistance to flow when an external shear force is applied between the layers of fluid.
Sutherland Experimental Constant 'a' - Sutherland Experimental Constant 'a' refers to a constant value experimentally obtained by Sutherland correlation. It is a crucial parameter for determining dynamic viscosity of gases.
Absolute Temperature of Fluid - (Measured in Kelvin) - Absolute temperature of fluid is refers to the measurement of intensity of heat energy present in fluid in kelvin scale. Where 0 K, represents as the absolute zero temperature.
Sutherland Experimental Constant 'b' - Sutherland Experimental Constant 'b' refers to a constant value experimentally determined by Sutherland correlation. It is a crucial parameter for determining dynamic viscosity of gases.
STEP 1: Convert Input(s) to Base Unit
Sutherland Experimental Constant 'a': 0.008 --> No Conversion Required
Absolute Temperature of Fluid: 293 Kelvin --> 293 Kelvin No Conversion Required
Sutherland Experimental Constant 'b': 211.053 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
μ = (a*T^(1/2))/(1+b/T) --> (0.008*293^(1/2))/(1+211.053/293)
Evaluating ... ...
μ = 0.0796003933111279
STEP 3: Convert Result to Output's Unit
0.0796003933111279 Pascal Second --> No Conversion Required
FINAL ANSWER
0.0796003933111279 0.0796 Pascal Second <-- Dynamic Viscosity Fluid
(Calculation completed in 00.004 seconds)

Credits

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Osmania University (OU), Hyderabad
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Applications of Fluid Force Calculators

Dynamic Viscosity of Gases
​ Go Dynamic Viscosity Fluid = (Sutherland Experimental Constant 'a'*Absolute Temperature of Fluid^(1/2))/(1+Sutherland Experimental Constant 'b'/Absolute Temperature of Fluid)
Dynamic Viscosity of Fluids
​ Go Dynamic Viscosity of Fluid = (Shear Stress on Lower Surface*Distance Between Plates Carrying Fluid)/Velocity of Moving Plate
Dynamic Viscosity of Liquids
​ Go Dynamic Viscosity Fluid = Experimental Constant 'A'*e^((Experimental Constant 'B')/(Absolute Temperature of Fluid))
Friction Factor given Frictional Velocity
​ Go Darcy's Friction Factor = 8*(Friction Velocity/Mean Velocity)^2

Dynamic Viscosity of Gases Formula

Dynamic Viscosity Fluid = (Sutherland Experimental Constant 'a'*Absolute Temperature of Fluid^(1/2))/(1+Sutherland Experimental Constant 'b'/Absolute Temperature of Fluid)
μ = (a*T^(1/2))/(1+b/T)

What is Sutherland's Formula for Viscosity?

Sutherland's formula is a mathematical expression used to describe how the viscosity of a gas changes with temperature.The formula compares the viscosity (𝜇) of a gas at a given temperature (𝑇) to its viscosity at a reference temperature (T0). It shows that as the temperature increases, the viscosity increases. This relationship isn't linear; instead, it follows a specific curve determined by the formula. Sutherland's formula takes into account the specific behavior of each gas through a constant called the Sutherland's constant, different gases have different values for reflecting their unique molecular structures and interactions. Sutherland's formula helps engineers and scientists predict how gases will behave at high temperatures, which is crucial for designing efficient and safe systems in aerospace, combustion, and other fields

Why Viscosity Increases with Increase of Temperature in Gases?

Viscosity in gases tends to increase with temperature due to several factors. Firstly, as temperature rises, gas molecules gain kinetic energy, resulting in faster and more frequent collisions. These collisions disrupt the weak intermolecular forces present in gases, making it more difficult for molecules to move past each other smoothly. Additionally, the increased kinetic energy leads to a more tangled and chaotic motion within the gas, further increasing resistance to flow. Moreover, the higher temperature reduces the mean free path—the average distance a gas molecule travels between collisions—resulting in more frequent collisions and hence higher viscosity. Overall, the combined effect of increased collision frequency, disruption of intermolecular forces, and reduced mean free path contributes to the observed increase in viscosity with temperature in gases.

How to Calculate Dynamic Viscosity of Gases?

Dynamic Viscosity of Gases calculator uses Dynamic Viscosity Fluid = (Sutherland Experimental Constant 'a'*Absolute Temperature of Fluid^(1/2))/(1+Sutherland Experimental Constant 'b'/Absolute Temperature of Fluid) to calculate the Dynamic Viscosity Fluid, Dynamic viscosity of gases, also known as absolute viscosity, is a measure of a fluid's internal resistance to flow. Dynamic Viscosity of gases is a function of gas composition and static temperature. Sutherland's formula can be used to derive the dynamic viscosity of an ideal gas as a function of temperature. Dynamic Viscosity Fluid is denoted by μ symbol.

How to calculate Dynamic Viscosity of Gases using this online calculator? To use this online calculator for Dynamic Viscosity of Gases, enter Sutherland Experimental Constant 'a' (a), Absolute Temperature of Fluid (T) & Sutherland Experimental Constant 'b' (b) and hit the calculate button. Here is how the Dynamic Viscosity of Gases calculation can be explained with given input values -> 0.13444 = (0.008*293^(1/2))/(1+211.053/293).

FAQ

What is Dynamic Viscosity of Gases?
Dynamic viscosity of gases, also known as absolute viscosity, is a measure of a fluid's internal resistance to flow. Dynamic Viscosity of gases is a function of gas composition and static temperature. Sutherland's formula can be used to derive the dynamic viscosity of an ideal gas as a function of temperature and is represented as μ = (a*T^(1/2))/(1+b/T) or Dynamic Viscosity Fluid = (Sutherland Experimental Constant 'a'*Absolute Temperature of Fluid^(1/2))/(1+Sutherland Experimental Constant 'b'/Absolute Temperature of Fluid). Sutherland Experimental Constant 'a' refers to a constant value experimentally obtained by Sutherland correlation. It is a crucial parameter for determining dynamic viscosity of gases, Absolute temperature of fluid is refers to the measurement of intensity of heat energy present in fluid in kelvin scale. Where 0 K, represents as the absolute zero temperature & Sutherland Experimental Constant 'b' refers to a constant value experimentally determined by Sutherland correlation. It is a crucial parameter for determining dynamic viscosity of gases.
How to calculate Dynamic Viscosity of Gases?
Dynamic viscosity of gases, also known as absolute viscosity, is a measure of a fluid's internal resistance to flow. Dynamic Viscosity of gases is a function of gas composition and static temperature. Sutherland's formula can be used to derive the dynamic viscosity of an ideal gas as a function of temperature is calculated using Dynamic Viscosity Fluid = (Sutherland Experimental Constant 'a'*Absolute Temperature of Fluid^(1/2))/(1+Sutherland Experimental Constant 'b'/Absolute Temperature of Fluid). To calculate Dynamic Viscosity of Gases, you need Sutherland Experimental Constant 'a' (a), Absolute Temperature of Fluid (T) & Sutherland Experimental Constant 'b' (b). With our tool, you need to enter the respective value for Sutherland Experimental Constant 'a', Absolute Temperature of Fluid & Sutherland Experimental Constant 'b' 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 Dynamic Viscosity Fluid?
In this formula, Dynamic Viscosity Fluid uses Sutherland Experimental Constant 'a', Absolute Temperature of Fluid & Sutherland Experimental Constant 'b'. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Dynamic Viscosity Fluid = Experimental Constant 'A'*e^((Experimental Constant 'B')/(Absolute Temperature of Fluid))
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