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The Relationship Between the Kinematic Viscosity of Air and Temperature

Key Takeaways

  • Two different fluids can have the same absolute or dynamic viscosity, but never the same kinematic viscosity.

  • The SI unit of kinematic viscosity is m2/s. The commonly used unit is Stoke. 

  • The kinematic viscosity of air at 15℃ is 1.48 x 10-5 m2/s or 14.8 cSt.

 Fluids in motion

Viscosity is an important property of fluids

Imagine a slow-motion video of a bullet passing through the air. We see the air near the bullet become disturbed and move around the bullet, and there are aerodynamic forces generated between the air and the bullet. The magnitude of the aerodynamic forces generated depends on the properties of the air and the bullet. The shape and speed of the bullet, the mass of gas displaced by the bullet, the compressibility of air, and the viscosity of air are all factors that influence the aerodynamic forces generated.

Viscosity is an important property of fluids. The viscosity can be described using dynamic viscosity or kinematic viscosity. Both viscosity terms are interconnected. For example, the kinematic viscosity of air can be determined if the dynamic viscosity and density are known.  In this article, we will explore viscosity, with a focus on the kinematic viscosity of fluids, gases, and air.  

The Viscosity of Fluids 

In daily life, we encounter several applications where fluid is involved. In these applications, the fluid may be in motion or at rest. To analyze the behavior of the fluid and how it interacts with solid boundaries, viscosity is utilized. Viscosity gives the measure of the fluid’s resistance to gradual deformation by tensile stress or shear stress.

When fluid layers attempt to move over each other, intermolecular friction is exerted, producing shear resistance in the fluid to initiate a motion or deformation. Highly viscous fluids show high resistance to flow, such as molasses. As the viscosity decreases, the fluid has less shear resistance.

The viscosity of fluids can be expressed in two ways.

  1. Dynamic Viscosity

The dynamic or absolute viscosity, otherwise called the coefficient of absolute viscosity, is the measure of internal resistance exerted by the fluids. Dynamic viscosity can be defined as the tangential force per unit area required to slide a horizontal plane, which is at a unit distance from the neighboring plane at unit velocity.

Dynamic viscosity can be given by the equation:

 Equation of dynamic viscosity

Note that is the dynamic viscosity, is the shearing stress in the fluid, y is the shear rate, and the SI units of dynamic viscosity are N s/m2, Pa s, and kg/m s.

  1. Kinematic Viscosity

The relationship between the absolute viscosity and the fluid’s mass density can be given by the kinematic viscosity. Kinematic viscosity is also called the diffusivity of momentum.  The kinematic viscosity (v) is determined by the ratio of absolute viscosity to density (). 

Equation of kinematic viscosity

In certain cases, you may analyze two different fluids with the same absolute viscosity. In such cases, the determination of kinematic viscosity helps in distinguishing between the fluids. Since there is a difference in density, the kinematic viscosity of the fluids will be different. Two different fluids can have the same dynamic viscosity, but never the same kinematic viscosity. The SI unit of kinematic viscosity is m2/s. The commonly used unit is Stoke. 

Kinematic Viscosity of Liquids and Gases 

Kinematic viscosity variations seen in liquids and gases are entirely different. Fluids, such as water and mercury, exhibit a drop in kinematic viscosity with an increase in temperature. Gas is an example of a fluid with low viscosity. Gases such as helium, hydrogen, and air share a direct relationship between kinematic viscosity and temperature. In these gases, the kinematic viscosity increases with an increase in temperature. 

Kinematic Viscosity of Air

The absolute or dynamic viscosity shares a direct relationship with the square root of temperature. 

Absolute viscosity-temperature relationship

From the equation:

PV = pRT

The relationship between density and temperature can be given as:

Relationship between density and temperature

Substituting the above two proportionalities in the kinematic viscosity equation, we can derive the relationship governing kinematic viscosity and temperature as:

Relationship between kinematic viscosity and temperature

According to the above-mentioned equation, the kinematic viscosity of air is highly dependent on temperature. The kinematic viscosity of air at 15℃ is 1.48 x 10-5 m2/s or 14.8 cSt. As the temperature increases, the kinematic viscosity of air increases. At 25 ℃, the kinematic viscosity of air is 15.7 cSt. The table below shows the kinematic viscosity variations of air with temperature. 

Table showing variations in the kinematic viscosity of air with rise in temperature

The kinematic viscosity of air is an important parameter to consider when designing aerodynamic systems. While solving complex fluid flow problems, a clear understanding of the viscosity of the fluid is necessary. You can solve fluid flow problems using Cadence’s suite of CFD software. With these tools, it is easier to run CFD simulations in complex fluid-dependent systems that facilitate fluid flow modeling.

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About the Author

With an industry-leading meshing approach and a robust host of solver and post-processing capabilities, Cadence Fidelity provides a comprehensive Computational Fluid Dynamics (CFD) workflow for applications including propulsion, aerodynamics, hydrodynamics, and combustion.

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