# Mechanical Properties Of Fluids Class 11 Notes Physics Chapter 10 - CBSE

## Chapter : 10

## What Are Mechanical Properties Of Fluids ?

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## Pressure

The thrust exerted by a liquid per unit area of the surface in contact with it is known as pressure.

$$\text{Pressure =}\frac{\text{Thrust}}{\text{Area}}\\\text{or,}\space \rho =\frac{\text{F}}{\text{A}}$$

## Density

The density of any material is defined as its mass per unit volume.

$$\text{Density} =\frac{\text{Mass}}{\text{volume}}\\\text{or}\rho =\frac{\text{M}}{\text{V}}$$

## Pascal‘s Law

It states that a change in pressure applied to an enclosed in compressible fluid is transmitted undiminished to every point of the fluid and the walls of the containing vessel.

**Hydraulic Lift**

It is an application of Pascal‘s law. It is used to lift heavy objects.

**Hydraulic brakes**

The hydraulic brakes used in automobiles are based on Pascal‘s law of transmission of pressure in a liquid.

## Pressure Exerted By A Liquid

A liquid column of height h and density ρ exerts a pressure given by, P = hρg

## Viscosity

It is the property of a fluid due to which an opposing force comes into play whenever there is relative motion between its different layers.

## Newton‘s Formula For Viscous Force

$$\text{F} =η\text{A}\frac{dv}{dx}$$

where η is the coefficient of viscosity of the liquid. dv/dx is velocity gradient. A is area of parallel layers of fluid.

Units of η : SI unot if η is decapoises.

## Poissuill‘s Formula

The volume of a liquid flowing per second through a horizontal capillary tube of length l, radius r under a pressure difference p across its two ends is given by

$$\text{Q} =\frac{\text{V}}{\text{t}}=\frac{\pi pr^{4}}{8ηl}$$

## Stokes‘ Law

It states that the backward dragging force of viscosity acting an a spherical body of radius r moving with velocity v through a fluid of viscosity

η is F = 6*πη*rv.

## Terminal Velocity

It is the maximum constant velocity attained by a spherical body while falling through a viscous medium. The terminal velocity of a spherical body of density ρ and radius r maing through a fluid of density ρ’ and viscosity η is given by

$$v =\frac{2}{9}\frac{r^{2}}{η}(\rho - \rho')g$$

## Critical Velocity

The critical velocity of a liquid is that limiting value of its velocity of flow above which the flow become turbulent. It is given by

$$v_{c}=\frac{kη}{\rho r}$$

## Equation Of Continuity

If there is no source or sink of the fluid along the length of the pipe, the mass of the fluid crossing any section of the pipe per second is always constant

m = a_{2} v_{1} ρ_{1} = a_{2} v_{2} ρ_{2}

It is called equation of continuity. For an incompressible liquid ρ_{1} = ρ_{2} , then

a_{2} v_{1} = av_{2} or av = constant

## Bernoulli‘s Principle

It states that the sum of pressure energy, kinetic energy and potential energy per unit volume of an incompressible, non-viscous fluid in a streamlined, irrotatinal flow remains constant along a streamline.

$$\text{Thus}\space\text{P} + \frac{1}{2}\rho v^{2} + \rho\text{gh = constant}$$

## Torricelli‘s Law

Velocity of efflux of a liquid through an orifice at depth h from the liquid surface will be

$$\text{v} =\sqrt{2gh}$$

## Surface Tension

It is measured as the force per unit length on an imaginary line drawn on the surface of the liquid.

$$\text{S.I} =\frac{\text{Force}}{\text{length}}$$

Its SI unit is Nm^{–1}.

## Surface Energy

The additional potential energy per unit area of the surface film as compared to the molecules in the interior is called the surface energy. Surface energy of a liquid is numerically equal to surface tension of the liquid.

## Excess Pressure Inside A Drop And Bubble

$$\text{Excess pressure inside a liquid drop }\\=\frac{2\text{T}}{\text{R}}\\\text{Excess pressure inside a liquid dubble }\\=\frac{4\text{T}}{\text{R}}\\\text{Excess pressure inside a air bubble }\\=\frac{2\text{T}}{\text{R}}$$

## Ascent Formula

When a capillary tube of radius r is dipped in α liquid of density ρ and surface tension T, the liquid rises or falls through a distance,

$$h =\frac{\text{2T cos}\space\theta}{\text{rpg}}$$