Viscosity

Summary

Viscosity (also known as dynamic viscosity, absolute viscosity, or simple viscosity) is …

represented by the Greek letter η (eta).
defined informally as the quantity that describes a fluid's resistance to flow.

defined mathematically as the ratio of the shearing stress to the velocity gradient in a fluid.

η =

⎛
⎝

F

⎞
⎠

÷

⎛
⎝

Δv_x

⎞
⎠

or

η =

⎛
⎝

F

⎞
⎠

÷

⎛
⎝

dv_x

⎞
⎠

A

Δz

A

dz

often expressed using Newton's equation for fluids (which is similar to Newton's second law of motion).


F	=	η	Δv_x	or	F	=	η	dv_x
A	=	η	Δz	or	A	=	η	dz

Units
- The SI unit of viscosity is the pascal second [Pa s].
- The Gaussian unit of viscosity is the poise [P = dyne s/cm²].
- Ten poise equal one pascal second [10 P = 1 Pa s].

Kinematic viscosity is …

represented by the Greek letter ν (nu).
defined informally as a measure of the resistive flow of a fluid under the influence of gravity.

defined mathematically as the ratio of the viscosity of a fluid to its density.


ν =	η
ν =	ρ

Units
- The SI unit of kinematic viscosity is the square meter per second [m²/s].
- The Gaussian unit of kinematic viscosity is the stokes [St = cm²/s].
- Ten thousand stokes equal one square meter per second [10,000 stoke = 1 m²/s].

Factors Affecting Viscosity
- Viscosity varies with material. (Viscosity is a property of materials.)
- The viscosity of simple liquids …
  - decreases with increasing temperature
  - increases under very high pressures.
- The viscosity of gases …
  - increases with increasing temperature
  - is independent of pressure and density.

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