Dimensional Formula of Viscosity

Viscosity is the internal resistance to flow possessed by a liquid. Generally, it has been observed that liquids that flow slowly have a higher internal resistance. This is due to its stronger intermolecular forces. Hence, the dimension of the viscosity of those liquids is more viscous and holds a higher viscosity.

In physics, when we describe the dimensional formula of viscosity, it is conceptualised as quantifying the frictional force that arises between the adjacent layers of liquid when they are in relative motion.

Also, it is seen that liquids which have a lower internal resistance flow rapidly. This is mainly due to their lower viscosity.

Since you have understood the meaning of viscosity, let us now understand how it functions.

Functioning of Viscosity

Let us understand how viscosity actually works through an example.

Consider a liquid that flows through a narrow tube. Now all parts of the liquid would not pass from the tube with the same velocity. Now imagine that the liquid is made of various cylindrical coaxial layers that are thin. These layers, when they come into contact with the walls of tubes, are mainly stationary. As the liquid travels from the wall to the centre of the tube, the velocity of the cylindrical layer would increase and reach the maximum at the centre.

This is also known as laminar flow. This is a gradation of velocity which goes from one layer to the layer that is beside it. You would see that as the liquid travels from the centre towards the wall, the velocity of the layers keeps on decreasing. This happens because every layer majorly offers certain friction to the layer that is present immediately behind it. 

The meaning of viscosity is that it is essentially the force of friction that a part of liquid provides to another part. There is a force of friction ‘f’ that happens between two layers separated by a distance of ‘dx’ cm and having an area ‘A’ sq cm. Thus, a velocity difference of ‘dv’ cm/sec is provided as follows:

f ∝ A (dv / dx )

f = η A (dv / dx)

Here 

η- The constant which is also known as the coefficient of viscosity

(dv / dx)  is the velocity gradient.

The coefficient of viscosity can also be defined as the force of friction that needs to be maintained for a velocity difference of 1 cm/sec between the two parallel layers that are apart 1 cm and have an area of 1 sq. cm.

Derivation of Dimensional Formula of Viscosity

The dimensional formula of viscosity is M1 L-¹ T-¹

Here M= Mass

L= Length

T= Time

Now let us understand the derivation

Viscosity= Tangential Force x Distance between layers 

Area x Velocity -¹ ———(1)

Now the Tangential Force= M x a = M X [LT-²]

Now the dimensional formula of Tangential Force = M¹ L¹ T-²—– (2)

Also the dimensions of area and velocity = M0L² T0 and M0 L¹ T-¹——(3)

By substituting the equations (2), (3) in (1) we get that

Viscosity = Force Area x Velocity -¹ x Distance between layers

Or we can write as 

η = [M¹ L¹ T-²] × [M0 L² T0]-¹ × [M0 L¹ T-¹]-¹ × [M0 L¹ T0] = [M¹ L-¹ T-¹]

Hence we can say that the dimensional formula of viscosity can be represented as [M¹ L-¹ T-¹]

Now let us understand 

Fluid Viscosity: Newtonian & Non-Newtonian 

Common fluids called Newtonian fluids have constant viscosity. When the force is increased, greater resistance is seen but at a constant proportional increment. In simple words, Newtonian fluids behave like any other fluid, irrespective of the amount of force being put into it.

On the other hand, non-Newtonian fluids do not have constant viscosity. It varies based on the force applied to it. An example is Oobleck (slime – as made in science classes of elementary schools), which shows solid-like behaviour when a great amount of force is applied to it. Another example of non-Newtonian fluids is magnetorheological fluids. They become nearly solid when kept near a magnetic field but return to their fluid state when taken away from the magnetic field. 

Viscosity has significant importance in daily applications and the following areas.

Applications of Viscosity in Daily Life

One may feel that viscosity holds little importance in daily life, but it is important in quite a number of different fields:

• Vehicle Lubrication: One should be aware of their vehicle’s viscosity when putting oil. It’s important as viscosity impacts friction which in turn affects heat. Viscosity also determines the consumption of oil in your vehicle and how easily your vehicle would start in cold and hot conditions. Some oils whose viscosity is low, the oil may get thinner when it is heated. This can cause your vehicles to have problems when operating on a hot summer day.
• Cooking: Viscosity plays an essential role in preparing & serving food. Cooking oils can or cannot change their viscosity with heat. Fats can be moderately viscous when heated and may become solid when turned cold. Viscosity adds texture to different foods. For example, Honey is viscous and may change the texture of the dish. 
• Manufacturing: Manufacturing equipment needs proper lubrication for functioning smoothly. Lubricants that are highly viscous can clod the machines. On the other hand, lubricants that are too thin can provide very little protection.
• Medicines: Viscosity holds quite an importance in medicines because fluids are inserted into the human body intravenously. Blood viscosity is an important consideration – blood that is too viscous may form clots, and blood that’s very thin can lead to heavy blood loss, even death. 

Conclusion

Thus by reading the entire article, we hope you understood the meaning of viscosity, the dimensional formula of viscosity and its related derivations. We also tried to explore the different types of viscosity, specifically Newtonian and non-Newtonian. Viscosity has several applications in daily life, and some of them were discussed above. We hope that you gained a sufficient understanding of the topic through these study notes on viscosity.