Dimensional Formula of Coefficient of Viscosity

Have you ever wondered why honey is thicker than water? Or why do different liquids have different consistency? 

For example, just pour some water and honey into different tumblers simultaneously. Did you notice any difference in the time taken by each liquid to reach the respective tumblers? Did honey take more time to reach the tumbler than water or vice versa? 

This is because of an internal resistance between the molecules that prevent a liquid from moving. This thickness or friction of liquids is referred to as the viscosity of a liquid. So, we can say that honey is more viscous than water. Now, let’s see the topic in detail.

Viscosity:

As you have seen, more viscous fluid like honey tends to flow slowly, and less viscous fluid, for example, water, flows freely. Viscosity can be simply explained as the resistance caused due to friction between adjacent layers of a liquid that are in relative motion. So, the definition of viscosity would be a fluid’s resistance to flow. The SI unit of viscosity is Pascal-second(Pas), and the CGS unit is Poise(P).

They are related as 

  1 Pa.s = 10 poise

Coefficient of Viscosity Formula: 

The coefficient of viscosity in mathematical terms can be represented as: 

η = F . d / A . v

where,

F = is the amount of force required to maintain velocity gradient in between two consecutive layers of liquid per unit area.

A = area

d = distance between two consecutive layers of liquid present over each other

v = velocity

Generally, the viscosity of gas is less than that of liquid.

Units of coefficient of viscosity

• SI Unit: The Si unit of the coefficient of viscosity “η” is Ns.m-2 or Pa.s, that is, Newton-second per square metre or Pascal-seconds.

• CGS Unit: The centimetre-gram-second unit of the coefficient of viscosity “η” is Poise, or we can also say dyne-sec / cm2.

• 1 poise = 0.1 Pa.s

• MKS Unit: The metre-kilogram-second unit of the coefficient of viscosity “η” is kg m-1s-1

Dimensional Formula:

The physical quantity’s dimensions are the powers to which the basic quantities are elevated to represent that amount. The dimensional formula of any physical quantity is an equation that explains how and which of the base quantities are contained in that amount. It is written by enclosing the symbols representing base amounts in square brackets with the corresponding power, i.e. [].

E.g., the Dimension formula of Displacement is: [L]

A dimensional equation is obtained by equating a physical quantity with its dimensional formula is used to calculate the dimensional equation of any physical quantity.

Dimension of Coefficient of Viscosity:

The formula of coefficient of viscosity is written as

η = F . d / A . v

   = M L T-2. L / (L². L T-1)

after solving we get, 

η = [M1 L-1 T-1] 

which is equal to kg m-1s-1

Factors affecting viscosity:

Pressure and temperature are the major factors that affect viscosity. On increasing pressure, the viscosity of liquid molecules increases due to an increase in the resistance to the flow caused by increased interaction between the molecules, whereas the viscosity of gas molecules decreases with increasing pressure. 

The viscosity of a liquid decreases with increasing temperature, and for gases, it increases with increasing temperature because upon heating, liquids flow more freely, and gases flow slowly, but the amount of matter is the same in both liquids and gases.

Conclusion:

Viscosity can be defined as the internal resistance faced by a liquid or fluid substance, measured in terms of the shear stress of the fluid. When the viscosity of a fluid is absolutely zero, the liquid matter is considered the ideal non-viscous fluid. Due to the internal friction between the fluid layers as they slip past one another when fluid flows, the viscosity gauges resistance. When there is an increase in temperature, the viscosity of liquids decreases. In contrast, the viscosity of gases increases with the rise in temperature. There is always some confusion between the two types of viscosity measures. Sometimes it’s considered to be the same. However, the viscosity will be greater when the metal ball falls slowly. With the help of a viscometer, a more accurate measure of viscosity is provided.