Coefficient of Viscosity - Definition, Formula & Example

Coefficient of Viscosity

What is Viscosity?

Viscosity is an empirical quantity that describes the resistance a fluid offers to induced flow under the action of an external force. Simply put, viscosity refers to the “fluid’s resistance to flow.” Viscosity also describes the internal friction of a moving liquid. In any fluid when the viscosity is large the flow of the fluid will be slower because of the larger amount of resistance put forth by the fluid to the flow. Examples of this would be syrup, tar, honey, etc all of which have higher viscosity. Water on the other hand has a low viscosity and therefore offers much less resistance to flow. 

A simple example of this would be if you pour down a stream of water and honey side by side on an inclined plane, it’s would be evident that the water would flow down much faster down the incline plane then the honey. This difference is a function of their respective viscosities. All fluids including gasses have viscosity. However, as the viscosities of gasses are extremely low, it is imperceptible in everyday life. 

Viscosity measurement

Viscosity, as discussed above is the resistance that a fluid offers to flow. Conversely, it can be thought of as the amount of force required to get the fluid moving. It can therefore be measured as the force per unit area required to induce motion. The coefficient of viscosity is used to categorically determine the degree of viscosity of any given fluid. For any fluid, this coefficient remains constant and is an intrinsic property of that liquid. In an ideal Newtonian fluid, the viscosity of the fluid is directly proportional to the shear rate of the fluid and the constant of proportionality is called the coefficient of viscosity. The coefficient of viscosity of liquids decreases with the increase in temperature as the molecules get more excited and expand thereby reducing the resistance that they offer to movement. On the other hand, the coefficient of viscosity increases as the temperature increases in gasses as the already spaced out molecules of the gasses interact and collide with each other more as the temperature increases thereby increasing their coefficient of viscosity.

The coefficient of Viscosity Formula

Viscosity is a measure of resistance to flow which arises due to the internal friction between layers of fluid as they slip past one another while liquid flows. These layers are joined by strong intramolecular forces which resist the movement of layers on one another. The velocity of the upper layer increases as the distance of it increases from the fixed layer. If we choose any layer from the flowing liquid, the layer above it accelerate its flow while the layer below it resists its flow. 


If the velocity of the layer at a distance dz is changed by a value du then velocity gradient is given by the amount dudz . A force is required to maintain the flow of layers. This force is proportional to the area of contact of layers and velocity gradient i.e. –

f A, where A is the area of contact

f   dudz, where  dudz is the change in velocity with distance or velocity gradient 

f   Adudz

f = Adudz

  • is the proportionality constant which is called coefficient of viscosity. 

If value of  dudz is unity and A is also unit area, then –

f =

SI unit of is – N s m-2 (Newton second per square metre) = Pa s (Pascal second)

Therefore, the coefficient of viscosity can also be defined as the force required per unit area to maintain a unit relative velocity between two layers of fluid which are a unit distance apart. 

Viscosity Examples

There are a lot of uses that requires the knowledge of the viscosity or the coefficient of viscosity of a fluid. Especially in industrial use cases where products with specific properties need to be designed to fulfil their desired use cases.

A lot of pharmaceutical companies that develop syrups and the like take into consideration the viscosity of the fluid that they develop. For example, a cough syrup must have a coefficient of viscosity such that it is easily drinkable but still coats the lining of the throat effectively.

In developing paints, the viscosity comes into play even more. The viscosity of the fluid thus designed will have to be such that they can be effectively applied using a brush or a paint roller and also stick to the surface of vertical surfaces with ease. This requires careful calibration of the viscosity of the eventual paint fluid.

There are several other use cases where the viscosity or the coefficient of viscosity can be used. It is one of the most fundamental properties of any fluid.

In Summary

  • Viscosity refers to the “fluid’s resistance to flow.”

  • All fluids including gasses have viscosity. However, as the viscosities of gasses are extremely low, it is imperceptible in everyday life. 

  • The coefficient of viscosity is used to categorically determine the degree of viscosity of any given fluid.

  • The coefficient of viscosity of liquids decreases with the increase in temperature.

  • In gasses, the coefficient of viscosity increases as the temperature increases.

The coefficient of viscosity is given as, η= fAdudx