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Fluid Mechanics - Fluid Viscosity

Viscosity is a measure of a fluid’s internal friction. The more “viscous” a fluid is, the “thicker” it is when stirred. Clean water is an example of a low-viscosity liquid, while honey at room temperature is an example of a high-viscosity liquid.

There are two different ways to quantify the viscosity of a fluid: absolute viscosity and kinematic viscosity. Absolute viscosity (symbolized by the Greek symbol “eta” η, or sometimes by the Greek symbol “mu” μ), also known as dynamic viscosity, is a direct relation between stress placed on a fluid and its rate of deformation (or shear). The textbook definition of absolute viscosity is based on a model of two flat plates moving past each other with a film of fluid separating them. The relationship between the shear stress applied to this fluid film (force divided by area) and the velocity/film thickness ratio is viscosity:




  η = Absolute viscosity (pascal-seconds)

  F = Force (newtons)

  L = Film thickness (meters) – typically much less than 1 meter for any realistic demonstration!

  A = Plate area (square meters)

  v = Relative velocity (meters per second)


Another common unit of measurement for absolute viscosity is the poise, with 1 poise being equal to 0.1 pascal-seconds. Both units are too large for common use, and so absolute viscosity is often expressed in centipoise. Water has an absolute viscosity of very nearly 1.000 centipoise.

Kinematic viscosity (symbolized by the Greek letter “nu” ν) includes an assessment of the fluid’s density in addition to all the above factors. It is calculated as the quotient of absolute viscosity and mass density:



  ν = Kinematic viscosity (stokes)

  η = Absolute viscosity (poises)

  ρ = Mass density (grams per cubic centimeter)


As with the unit of poise, the unit of stokes is too large for convenient use, so kinematic viscosities are often expressed in units of centistokes. Water has an absolute viscosity of very nearly 1.000 centistokes.

The mechanism of viscosity in liquids is inter-molecular cohesion. Since this cohesive force is overcome with increasing temperature, most liquids tend to become “thinner” (less viscous) as they heat up. The mechanism of viscosity in gases, however, is inter-molecular collisions. Since these collisions increase in frequency and intensity with increasing temperature, gases tend to become “thicker” (more viscous) as they heat up.

As a ratio of stress to strain (applied force to yielding velocity), viscosity is often constant for a given fluid at a given temperature. Interesting exceptions exist, though. Fluids whose viscosities change with applied stress, and/or over time with all other factors constant, are referred to as non-Newtonian fluids. A simple example of a non-Newtonian fluid is cornstarch mixed with water, which “solidifies” under increasing stress then returns to a liquid state when the stress is removed.

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