# Properties of Solids and Fluids

Fluid Pressure is the force acting normally on unit area of a surface due to a fluid is called the fluid pressure.

Pressure = Force / Area

P = F/A

The unit of pressure is newton/m2. Pressure is a scalar quantity. Its dimensional formula is [ML-1T-2].

The fluid pressure is also measured in pascal.

1 pascal = 1 newton/m2

Pascal's Law

The pressure exerted anywhere in a mass of confined fluid is transmitted equally and undiminished in all directions throughout the liquid. Bramah's Hydraulic Press works on this principle.

Upthrust of a Liquid

When a solid body is immersed in a liquid, then there is some apparent loss in weight. This apparent loss in the weight of the body is due to the upward force applied by the liquid on the body. This force is called the buoyant force or the upthrust. The upthrust acts at the centre of gravity of the liquid displaced by the body, which is called the centre of buoyancy.

Principle of Archimedes

When a body is immersed in a liquid partially or completely then there is an apparent loss in its weight. This apparent loss in weight is equal to the weight of the liquid displaced by the body. This is known as Archimedes principle.

Principle of Floatation

According to this principle, a body floats in a fluid if weight of the fluid displaced by the immersed portion of the body is equal to the weight of the body. (The apparent weight of the floating body is zero).

The centre of gravity (G) and the centre of buoyancy (B) of a floating body must lie on the same straight line.

Metacentre

It is the point where the vertical line passing through new centre of buoyancy, in the displaced position of the body intersects the original line passing through the centre of gravity and original centre of buoyancy.

If the centre of gravity of the body lies below the metacentre, the body is in stable equilibrium.

Relative Density

Relative density is the ratio of weight of the body in air to the weight of the same volume of water (at 4°C).

### Atmospheric Pressure

There is air all around. This envelop of air is known as the atmosphere. The atmospheric air extends up to many kilometres above the surface of the earth. The pressure exerted by this air is known as atmospheric pressure.

Atmospheric pressure is measured by a barometer. It is equal to the pressure due to a column of 76 cm of mercury at 0°C at sea level.

### Elasticity

Elasticity is that property of the material of a body by virtue of which the body opposes any change in its shape or size when deforming forces are applied to it, and recovers its original state as soon as the deforming forces are removed.

Strain

The ratio of the change in configuration (shape, length or volume) to the original configuration of the body is called strain. There are three types of strain - longitudinal strain, volume strain and shearing strain. Strain is a pure ratio and has no unit.

Stress

Due to the external deforming force, the internal restoring force acting per unit area of cross-section of the deformed body is called stress. Its unit is newton/m2.

Limit of Elasticity

The maximum deforming force up to which a body retains its property of elasticity is called the limit of elasticity of the material of the body.

Hooke's Law

Within the limit of elasticity, the strain produced in a body is directly proportional to the stress applied to it. This is called the Hooke's law. Thus,

Stress / Strain = E (modulus of elasticity)

The constant E is known as modulus of elasticity. The value of modulus of elasticity of a material depends upon the type of stress and strain produced. If strain is longitudinal, then the modulus of elasticity is called Young's modulus. If strain is in volume then it is called bulk modulus and if strain is shearing, then it is called 'modulus of rigidity.

### Surface Tension

Every liquid has a property that its free surface behaves like a stretched elastic membrane and has a natural tendency to contract, i.e., the free surface of a liquid tends to occupy a minimum surface area. This property of liquid is called the surface tension.

Definition of Surface Tension

The surface tension of a liquid is defined as the force per unit length in the plane of the liquid surface, acting at right angles on either side of an imaginary line drawn in that surface. Its unit is newton/metre and dimensions are [MT-2].

Factors Affecting Surface Tension

Following three factors affect the surface tension of a liquid:

1. Temperature - The surface tension of a liquid decreases with the rise in temperature.
2. Soluble impurities - If the impurity is less soluble the surface tension of the liquid decreases. If the impurity is more soluble, the surface tension of liquid increases.
3. Insoluble impurities - The surface tension of liquid decreases due to contamination.

Relation Between Surface Tension and Work Done in Increasing the Surface Area

If the work done in increasing the surface area of liquid by ΔA is W, then surface tension of the liquid T is

T = W/ΔA

Hence, the surface tension of a liquid is equal to the work required to increase the surface area of the liquid film by unity at a constant temperature.

The force of attraction between the molecules of the same substance (like water) is called cohesive force and that between the molecules of different substances (like paper and gum) is called adhesive force.

The maximum distance up to which two molecules attract each other is called molecular range.

Rise of Liquid in the Capillary

When a glass capillary tube open at both ends is dipped vertically in water (or in some other liquid which sticks with glass), the water rises in the tube due to surface tension to a height h above the water level outside the tube.

### Flow of Liquids and Viscosity

Principle of Continuity

When an ideal fluid (non-viscous and non-compressible) flows in a stream line condition through a tube of nonuniform cross-section, at each section of the tube, the product of area of cross-section (a) and velocity (v) of fluid is constant. It is called principle of continuity.

Bernoulli's Theorem

When a non-viscous and non-compressible fluid flows from one point to the other in a stream line condition without any frictional or resistive force, the total energy of fluid = (kinetic energy + potential energy + pressure energy) remains constant at each point of its flow.

Venturimeter

It is a device based on Bernoulli's theorem. It is used to find the rate of flow of liquid in a tube.

Viscosity

The property of fluids by virtue of which there is a tendency to oppose the relative motion between its different layers, is called viscosity.

Coefficient of viscosity is the viscous force acting between the two layers of a liquid.

The viscosity of liquids decreases with rise in temperature. On the other hand the viscosity of gases increases with rise in temperature.