Learn about the effects of temperature on viscosity of liquids. In this article we will discuss about variation of viscosity of fluid. Also learn about:- 1. Concept of Dynamic Viscosity as a Modulus 2. Determination of Viscosity.

#### Variation of Viscosity with Temperature:

The viscosity of a fluid is due to two contributing factors, namely the cohesion between the fluid molecules and transfer of momentum between molecules. In the case of gases the interspace between the molecules is large and so the intermolecular cohesion is negligible.

But in the case of liquids the molecules are very close to each other and accordingly a large cohesion exists. Hence in liquids, the viscosity is mainly due to intermolecular cohesion, while in gases viscosity is mainly due to molecular momentum transfer.

The intermolecular cohesive force decreases with the rise of temperature and hence with the increase in temperature the viscosity of a liquid decreases.

The following formula given by Poiseuille shows the dependence of the viscosity of a liquid on temperature-

In the case of gases, as mentioned earlier the intermolecular cohesion being negligible the viscosity depends mainly on transfer of molecular momentum in a direction at right angles to the direction of motion. As the temperature increases the molecular agitation increases i.e., there will be large momentum transfer and hence the viscosity increases. Holman gave the following expression for the viscosity of a gas-

#### Concept of Dynamic Viscosity as a Modulus:

We know in a solid body a shear stress is produced against a shear strain. For example, let the solid body ABCD be subjected to a shear stress q. Let the body deform to the shape A ’B ’CD.

Hence, the angular deformation ɸ represents the shear strain. And, we know, that the ratio of the shear stress to the shear strain is the modulus of rigidity of the material of the solid body. It may be noted in this case that there is a definite amount of shear deformation corresponding to a shear stress.

Unless this shear is increased the shear deformation will not increase, i.e. when subjected to shear stress a solid body undergoes a shear deformation to such an extent that the shear resistance is equal to the shear stress applied, so that the solid body remains in equilibrium in the deformed shape.

On the contrary, when subject to shear stress a fluid body goes on deforming. Shear deformation continues as long as the shear stress exists. It is in this respect a fluid body differs from a solid body. The rate at which the shear deformation of a fluid body goes on increasing depends on the corresponding shear stress.

i.e. Shear stress in a fluid body α Rate of shear deformation-

Thus, the dynamic viscosity of a fluid may be defined as the shear stress needed to produce unit rate of angular deformation.

Types of Fluids:

Based on the property of viscosity, fluids may be classified into the following types:

(i) Ideal fluid – This is a fluid where shear stresses do not exist whether the fluid is at rest or in motion.

(ii) Real fluid – This is a fluid which possesses viscosity. In a real fluid shear stresses are induced when the fluid is in motion.

(iii) Newtonian fluid – This is a real fluid in which the shear stress is proportional to the velocity gradient.

(iv) Non-newtonian fluid – This is a real fluid in which the shear stress is not proportional to the velocity gradient.

(v) Ideal plastic fluid – This is a fluid in which after reaching a yield value of shear stress, the fluid begins to flow. The fluid flows such that the relationship between the shear stress and the velocity gradient is linear.

(vi) Thyxotropic fluid – This is a fluid in which after reaching a yield value of shear stress, the fluid begins to flow. The fluid flows such that the relationship between the shear stress and the velocity gradient is not linear.

#### Determination of Viscosity:

A viscometer is an instrument used to determine the viscosity of a fluid.

(i) The Capillary Tube Viscometer:

In this device, the fluid is made to pass through a horizontal capillary tube. See Fig. 1.6. Consider sections 1.1 and 2.2 of the tube l units apart.

Let P1 and P2 be the pressure intensities at sections 1.1 and 2.2. Let Q be the rate of flow of the fluid through the tube. Let d be the diameter of the tube.

The viscosity of the fluid is given by Hagen Poiseuille’s formula,

(ii) Coaxial Cylinder Viscometer or Concentric Cylinder Viscometer:

This apparatus consists of two concentric cylinders with an annular space between them. The fluid whose viscosity is to be determined is placed in this space. There will also be a very small clearance between the bottom of the inner cylinder and the outer cylinder.

The outer cylinder is rotated at a uniform rate (N rpm). The inner cylinder which is suspended by a torsion wire will remain stationary. The torque on the wire is measured by the torque dial.

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