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# Viscosity - Definition, Formula and Si Units of Viscosity

Viscosity is generally defined as a measure of the "thickness" of a liquid. More accurately, the viscosity of a fluid (liquid or gas) is the measure of the resistance offered by that fluid against deformation. Viscosity can be further explained as the quantification of the internal frictional force that is found between nearby layers of that fluid in motion relative to each other. The term "viscosity" is derived from the Latin word viscum, meaning mistletoe. The inverse quantity of viscosity is called fluidity, which describes the ease with which the fluid can flow.

The viscosity of a fluid must be taken into consideration if the fluid is to be used for lubrication purposes or if it is meant to be transported using pipelines. The importance of this can be seen in the case where a fluid contained in a container has to travel through a narrow tube. It can be noticed that the fluid flows more quickly near the entrance of the tube compared with other areas in the container. This is because stress, here the pressure difference between the two ends of the tube, is needed for the flow of the fluid to continue. This proves that an external force is needed to get over the internal friction between the layers of the fluid, which are in relative motion. Viscosity is the determining factor of the fluid flow in the processes such as spraying, injection, molding, and surface coating.

A desirable fluid in some cases is one that offers zero viscosity; that is, the fluid should offer zero resistance to deformation, enabling it to transfer energy without any loss in magnitude. This ideal fluid is also known as inviscid fluid. However, this property is exhibited only by certain substances called superfluids at very low temperatures. A good example of this is the helium-3, and helium-4 isotopes of helium behave as inviscid fluids at temperatures of about −180 °C (93 K; −292 °F). In fluids, the shearing stress which causes the flow of the fluid is directly proportional to the rate of deformation caused in the fluid (shear strain). Thus, the viscosity of a fluid is given by the shear stress divided by the rate of shear strain at a particular, fixed temperature. This kind of viscosity is also called dynamic or absolute viscosity.

The term kinematic viscosity or momentum diffusivity of a fluid, which is also seen in fluid mechanics, refers to the ratio of dynamic viscosity to the density of that fluid. The viscosity of a fluid is denoted using the Greek letters µ or Ƞ. The SI unit of viscosity is pascal- second (Pa. s) which is equal to newton-second per square meter (Ns/m 2 ). The force acting on the fluid that allows the fluid to flow by overcoming the internal frictional force is given by F = µA. (u/ y)

where

• F = the force acting on the fluid
• µ = the proportionality factor, called the dynamic viscosity of the fluid, or just viscosity
• A = the area over which the force is acting
• (u/ v) = the rate of shear deformation or also called shear velocity

## Units of Viscosity

• Dynamic viscosity: The SI unit of dynamic viscosity is pascal-second (Pa. s), but it is also expressed as newton-second per square meter (N·s/ m 2 ) and kilogram per meter per second (kg. m −1 . s −1 ). The CGS unit of viscosity, poise, was named after the French physicist Jean Léonard Marie Poiseuille and is denoted using P. The value of poise is given as 1 poise = 1 g. cm −1 . s −1 or 0.1 Pa. s. Poise was used in the ASTM (American Society for Testing Materials) international standard of units as centipoise (cP) and 1 cP = mPa. S (millipascal second). In the British Gravitational (BG) system, the unit of dynamic viscosity is pound- seconds per square foot (lb· s/ ft 2 ). In the English Engineering (EE) system, its unit is pound-force seconds per square foot (lbf·s/ ft 2 ).
• Kinematic viscosity: The SI unit of kinematic viscosity is square meters per second (m 2 / s). The CGS unit of kinematic viscosity, stokes, was named after Sir George Gabriel Stokes, an English physicist. It is denoted as St, and it is given as 1 St = cm 2 . s −1 = 0.0001 m 2 . s −1 . Another version of the stokes commonly used is the centistokes (cSt), the value for which is given by 1 cSt = 1 mm 2 . s −1 = 10 −6 m 2 . s −1 . In both BG and EE systems, the unit of kinematic viscosity is square feet per second (ft 2 /s).
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