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Air Viscosity

The usual idea about viscosity is that it’s a property of a fluid or semi fluid which causes its resistance to the flowing character. This resistance to flow is quite measurable as its molecular tendency make these fluids adhere to each other and based on the amount of the adherence we categorize these fluids into high and low viscous fluids. The same can be applied to air as well where the air masses of different viscosity flow above each other and cause similar high and low viscosity properties. 

These air flow of high and low density also help flying objects chart their course and that’s how birds and flying objects decide to avoid or stick to a particular route in air. Since the molecular resistance to motion is the main idea behind viscosity, regions with high temperature can make the air density lower and hence make the air flow easier. These can be quite different in case a flying object like plane or bird flies over a polar region where the air density is high due to higher volume of moisture and may be accumulated gases, making it difficult for them to fly through. The air viscosity properties help it resist the flow to some extent but not as well as fluids.

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Air Viscosity Definition

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To understand the air viscosity term better one needs to recall what exactly a plane pilot does when he or she faces cloud formation. The pilot tries to avoid such formations and looks for clearer zone where there is no dense cloud or air mass. The entire air navigation is charted exactly on the air viscosity and perhaps the significance of air viscosity lies on the single aspect of flying objects course charting. A pilot would warn the passengers about impending turbulence the moment the aircraft comes across a huge air mass or cloud formation as it flies through a denser air mass creating drag force on wings and the aircraft body on a whole. 

Technically these air mass drag force are nothing but flowing through a viscous air mass. Viscosity of air has nothing to do with its chemical characteristics as well as has nothing fear from the overall feature. It’s just a phenomenon every flying objects face and hence try avoid these viscous air mass and set clear of such zone in order to avoid delays. 

The air molecules at microscopic level causes resistance to flow and this reduction in velocity of the air flow about a particular surface is caused by skin friction or basically the drag force. When these molecules pass over a surface like in case of a rotating cylinder, the following characteristics are observed. 
  • In case of rotating cylinder the air particles near the surface which tend to resists motion have a relative velocity near zero and moreover, the rough surface of the body further impedes the motion.
  • Due to the fluid viscosity or air the molecules on the surface the body experiences a pull or drag, in the surrounding flow above the surface in the direction or rotation due to adhesion of the air mass to the body. 
There is a difference in flow around the rotating cylinder and in the flow around a non-rotating cylinder. Molecules at the surface of a rotating cylinder are not in motion relative to the cylinder as they are moving clockwise with the cylinder. Due to the viscous properties these molecules pull each other above them which results in an increase in fluid flow in a clockwise pattern. 

Viscosity of air is also very much a temperature depending phenomenon. Quite like a fluid a air mass viscosity also decrease with a rise in temperature. The air viscosity qualitatively decrease with temperature by exponential function. The atmospheric air is composed of mainly two gases, nitrogen and oxygen and to an extent trace gases but in some air zones the presence of other gases like $CO_{2}$ and $SO_{2}$ is also significant but these just air pockets where the density of air is higher than nearby regions. 

In the lower level of atmosphere the same would contain water vapor. The concentration value of this water vapor is variable as it depends mainly on the partial pressure of water vapor at a given temperature along with the relative humidity. At around 20 C and relative humidity of approximately 80%, the air would contain 0.02% of water vapour. In air layers closer to Earth surface, there are other components are also present. These rest of the gases are anthropogenic in characteristic.  

The air is liquefied at lower temperature and hence the moist air at a given atmospheric pressure begins to behave almost like an ideal gas solution. The absolute viscosity is defined by most of the physicist as the fluid coefficients of viscosity by taking the fluid as a confined matter between two parallel rigid plates with equal area. Even if all the conditions remain constant the viscosity can also change with time. For example when we consider a rheopectic fluid, the viscosity increases with time, while a thixotropic fluid is something which decrease in viscosity with time. The ones which do not change with time are called time independent fluids. 

The same goes with air mass as well. These matters also experience decrease in viscosity when the shear is increased but when this viscosity does not return to its original form we do not find any hysteresis. The relation between temperature and viscosity is paradoxical. By general rule the viscosity of fluid is inversely proportional to temperature but in case of air it’s the opposite. 

The cohesive force decrease with increasing temperature. The air viscosity is also considered to be kinetic molecular in origin and hence, the increase in temperature increases the air molecule velocity resulting in more collisions between molecules. The more these particles are agitated, the greater is the collision rate and that result in spreading out of molecules which greatly increases the viscosity. 

Air Viscosity Density

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Viscosity of air refers to the magnitude of internal friction between different layers of specific air mass. As these layers of air matter molecules are set into motion the molecular attractions creates the resistive moments and is detected as friction. Energy is essential to create movement and as per first law of thermodynamics the energy is never lost but is transformed into heat or kinetic energy. The rest are stored as potential energy by increasing the force in between the layers of air masses. 

The measure of air’s resistance to flow is refered as viscosity. Air results in formation of a thin layer of air close to the surface of the Earth that interacts with air and this thin air layer is better known as boundary layer. This interaction causes disturbance in the flow pattern of air causing the pressure difference between the air mass layers. 

All of these are directly linked to the density of the matter and in this case the density of air is foremost. More air molecules in a given space and lower temperature makes it ideal for the density of the air mass greater than the surrounding air zones. With lesser kinetic energy in air molecules the movement of these particles is limited and hence more molecules in a given space. Moreover, when these air mass layers move at a very low velocity the bulk air material move in discreet layers parallel to one another and makes it serve as viscous medium. 

The fluidity factors that help in influencing the size of force exerted on an object moving through it involves density and viscosity. Since, density is defined as mass distribution over a given volume of space, hence greater the number of molecules in a given space, greater the mass of air molecules and denser the medium. With more density the resistance to the flow of air mass increase as well and that increases the viscosity. The more dense or more viscous a air matter is the more it gets disturbed when a object passess through the matter. Denser and more viscous air matter provides more resistance against the moving objects. 

Air Viscosity Coefficient

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The measure of adhesive quality of air is better known as coefficient of viscosity. Greater the viscosity of the air mass, the greater is the surface friction drag. The viscosity of air is affected by the temperature and also increase with a rise in temperature. 

The airflow in terms of laminar part of an airplane is turbulent at a point. The rate at which the speed of airflow changes is found to highest at the contact surface of the airplane. This is true for turbulent flow but not laminar. The magnitude of the amount of surface friction is found to be highest where rate of change of speed is greatest. 

Flow transition is directly related to the proximity of transition point. The location of transition point from laminar flow to turbulent flow is dependent on four factors.
  • Surface tension between the layers 
  • Speed of flow of air 
  • Size of the object on which the air flow is acting
  • Adverse pressure gradient
The absolute coefficient is also a direct measure of the viscosity. And these are direct impact of the stationary phase interaction with mobile phase. Hence, the absolute coefficient viscosity is also called the dynamic viscosity coefficient. 

Air Viscosity Equation

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Air viscosity, air density and mean free path of air completely depend upon the temperature and the relative humidity. The dimensionless functions for variations in particle density, air velocity, air viscosity, air density and mean free path in air is taken into account to find the relation in between. Air viscosity, air density and mean free path in air depend on temperature and relative humidity. The values for each of these are taken as ‎η, ρa and λa when the relative density are taken as 50% and 100%. 

At standard temperature the values of each of the component are measured as:
  • $\frac{\lambda a}{\lambda ao}$ = $\frac{T}{To}$ 
  • $\frac{\rho a}{\rho ao}$ = $\frac{To}{T}$
  • $\frac{\eta}{\eta o}$ = √T / √To $\frac{\sqrt{T}}{\sqrt{To}}$
To, λao, ηo and ρao are the standard and the rest are corresponding values at various temperature.  
  • These various parameters which when increased do not change dpi by more than 1 µm, which are relative humidity, mean free path and air temperature. 
  • The parameters which when increased decrease dpi like air velocity, particle density, and air density. 
  • Parameters which when increased, increase the dpi is air viscosity. 

Air Viscosity at Different Temperature

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Viscosity is a property associated with a fluid’s resistance to flow and this accounts for air as well. But unlike fluid where the increase in temperature directly affects the density of the fluid matter and increases the resistance to the flow and the viscosity as well, the absolute viscosity for air depends primarily on temperature and to some extent on pressure as well. 

The relative humidity of air water mixture can also be calculated in case we know the actual air temperature T along with the dew point temperature. The viscosity of air increases with the increase in temperature. The viscosity of air at atmospheric pressure and various temperatures are given in the table below.  

 Temperature oC    Dynamic viscosity (N. s/m^2) 
 -10   $1.667 x 10^{-5} N. s/m^{2}$
 0   $1.705 x 10^{-5} N. s/m^{2}$
 10  $1.761 x 10^{-5} N. s/m^{2}$
 20  $1.785 x 10^{-5} N. s/m^{2}$
 30  $1.864 x 10^{-5} N. s/m^{2}$

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