# Summary

Viscosity is a measure of a fluids propensity to flow. There are two kinds of viscosity commonly reported, kinematic and dynamic. Dynamic viscosity is the relationship between the shear stress and the shear rate in a fluid. The Kinematic viscosity is the relationship between viscous and inertial forces in a fluid. Most common fluids are Newtonian fluids and their viscosity is constant with shear stress and shear rate. Non-Newtonian fluids are less common.

# Definitions

: | Shear rate | |

: | Dynamic viscosity | |

: | Kinematic viscosity | |

: | Density of the fluid | |

: | Shear stress |

# Types of Viscosity

There are two different measurements of viscosity used to describe fluids, dynamic and kinematic viscosities. These describe the flow of the fluid in different ways related to the way they are measured, however they are interchangeable if the fluid density is known.

## Dynamic Viscosity

Dynamic viscosity measures the ratio of the shear stress to the shear rate for a fluid.

## Kinematic Viscosity

Kinematic viscosity measures the ratio of the viscous force to the inertial force on the fluid. This is shown in the equation below, which may also be used to convert between dynamic and kinematic viscosity provided the density of the fluid is known. Kinematic viscosity is analogous to diffusivity of mass and heat, being the diffusivity of momentum.

## Common Units

Several common units for each type of viscosity are presented in the table below:

Viscosity | Units |
---|---|

Dynamic | cP dyn.s/cm kg/m.s P (poise) Pa.s |

Kinematic | cm^{2}/scSt ft ^{2}/sm ^{2}/sSt |

# Types of Fluids

## Newtonian Fluids

Many common fluids are practically Newtonian fluids; the viscosity of the fluid does not depend on the shear forces acting on it. The resistance to flow is directly proportional to the motion of the fluid. The viscosity of Newtonian fluids depends only on the temperature and pressure of the fluid. For incompressible liquids, such as water, the viscosity depends on temperature only.

## Non-Newtonian Fluids

Non-Newtonian fluids are different to Newtonian fluids in that the viscosity is a function of either shear stress or shear rate. There are many types of non-Newtonian fluids such as; those that vary with the duration of shear stress applied (Rheopectic and Thixotropic); those that vary with shear stress (Dilatants and Shear Thinning or Pseudoplastic); those that act as a solid up until a certain level of stress and then begin to acts as a fluid (Bingham plastic); and others. The detail of these fluid types and complex rheology is not discussed in this article.

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