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The SI unit of kinematic viscosity is square meter per second (m 2 /s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm 2 ·s −1 = 0.0001 m 2 ·s −1), named after Sir George Gabriel Stokes. [29] In U.S. usage, stoke is sometimes used as the singular form.
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.
Here dynamic viscosity is denoted by and kinematic viscosity by . The formulas given are valid only for an absolute temperature scale; therefore, unless stated otherwise temperatures are in kelvins .
β is the thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute temperature). is the kinematic viscosity; α is the thermal diffusivity; T s is the surface temperature; T ∞ is the quiescent temperature (fluid temperature far from the surface of the object) Gr x is the Grashof number for characteristic length x
This will result in another viscosity value if the fluid is a non-Newtonian fluid such as paint, but it will give the same viscosity value for a Newtonian fluid such as water, petroleum oil or gas. If another parameter like temperature, T {\displaystyle T} , is changed, and the experiment is repeated with the same force, a new value for ...
The difference between them and the closely related Euler equations is that Navier–Stokes equations take viscosity into account while the Euler equations model only inviscid flow. As a result, the Navier–Stokes are an elliptic equation and therefore have better analytic properties, at the expense of having less mathematical structure (e.g ...
μ is the dynamic viscosity of the fluid (Pa·s or N·s/m 2 or kg/(m·s)) ν is the kinematic viscosity of the fluid (m 2 /s). The Brezina equation. The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface.
where U is the oil's kinematic viscosity at 40 °C (104 °F), Y is the oil's kinematic viscosity at 100 °C (212 °F), and L and H are the viscosities at 40 °C for two hypothetical oils of VI 0 and 100 respectively, having the same viscosity at 100 °C as the oil whose VI we are trying to determine.