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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 :
The poise (symbol P; / p ɔɪ z, p w ɑː z /) is the unit of dynamic viscosity (absolute viscosity) in the centimetre–gram–second system of units (CGS). [1] It is named after Jean Léonard Marie Poiseuille (see Hagen–Poiseuille equation). The centipoise (1 cP = 0.01 P) is more commonly used than the poise itself.
Dynamic viscosity is a material property which describes the resistance of a fluid to shearing flows. It corresponds roughly to the intuitive notion of a fluid's 'thickness'. For instance, honey has a much higher viscosity than water. Viscosity is measured using a viscometer. Measured values span several orders of magnitude.
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.
Volume viscosity (also called bulk viscosity, or second viscosity or, dilatational viscosity) is a material property relevant for characterizing fluid flow. Common symbols are ζ , μ ′ , μ b , κ {\displaystyle \zeta ,\mu ',\mu _{\mathrm {b} },\kappa } or ξ {\displaystyle \xi } .
is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (newtons, kg m s −2); μ (some authors use the symbol η) is the dynamic viscosity (Pascal-seconds, kg m −1 s −1); R is the radius of the spherical object (meters);
Where: , , and are material coefficients: is the viscosity at zero shear rate (Pa.s), is the viscosity at infinite shear rate (Pa.s), is the characteristic time (s) and power index. The dynamics of fluid motions is an important area of physics, with many important and commercially significant applications.
Newtonian fluids are the easiest mathematical models of fluids that account for viscosity. While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian for practical calculations under ordinary conditions.