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The dilute gas viscosity contribution to the total viscosity of a fluid will only be important when predicting the viscosity of vapors at low pressures or the viscosity of dense fluids at high temperatures. The viscosity model for dilute gas, that is shown above, is widely used throughout the industry and applied science communities.
This transfer of momentum can be thought of as a frictional force between layers of flow. Since the momentum transfer is caused by free motion of gas molecules between collisions, increasing thermal agitation of the molecules results in a larger viscosity. Hence, gaseous viscosity increases with temperature.
The proportionality factor is the dynamic viscosity of the fluid, often simply referred to as the viscosity. It is denoted by the Greek letter mu ( μ ). The dynamic viscosity has the dimensions ( m a s s / l e n g t h ) / t i m e {\displaystyle \mathrm {(mass/length)/time} } , therefore resulting in the SI units and the derived units :
Consequently, if a liquid has dynamic viscosity of n centiPoise, and its density is not too different from that of water, then its kinematic viscosity is around n centiStokes. For gas, the dynamic viscosity is usually in the range of 10 to 20 microPascal-seconds, or 0.01 to 0.02 centiPoise. The density is usually on the order of 0.5 to 5 kg/m^3.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
ν is the kinematic viscosity. The L and D subscripts indicate the length scale basis for the Grashof number. The transition to turbulent flow occurs in the range 10 8 < Gr L < 10 9 for natural convection from vertical flat plates.
The first step is to calculate the Viscosity Blending Index (VBI) of each component of the blend using the following equation (known as a Refutas equation): [2] [4] (1) VBN = 14.534 × ln[ln(v + 0.8)] + 10.975. where v is the viscosity in square millimeters per second (mm²/s) or centistokes (cSt) and ln is the natural logarithm (log e). It is ...
For instance, it is 0 in a monatomic gas at low density (unless the gas is moderately relativistic [3]), whereas in an incompressible flow the volume viscosity is superfluous since it does not appear in the equation of motion. [4] Volume viscosity was introduced in 1879 by Sir Horace Lamb in his famous work Hydrodynamics. [5]