Mechanical Properties of Fluids Class 11 Notes for CBSE Physics Chapter 10

Mechanical Properties of Fluids Class 11 Notes for Physics Chapter 10

Students can have a thorough understanding of all the topics and theories presented in this chapter by using the Mechanical Properties of Fluids revision notes offered by Extramarks. Class 11 Physics Chapter 10 Notes have been created by subject-matter experts in accordance with the most recent CBSE Class 11 syllabus. 

1. Fluid Mechanics:

• Fluids are often used to refer to both liquids and gases. In other words, substances that have the ability to flow are defined as fluids.
• Fluids are incompressible (i.e., the density of liquid remains constant and is not dependent on the variation in pressure).
• Fluids are not naturally viscous (i.e. the two liquid surfaces in contact do not press any tangential force on each other).

1.1. Fluid Statics:

1.1.1. Fluid Pressure:

• Fluid pressure p at each point is the normal force acting per unit area. Mathematically,  

p=dFl/dA

• Pascal (Pa) is the S.I. unit of pressure and 1 Pascal=1N/m2
• Regardless of how the surface is oriented, a fluid force acts perpendicularly to that surface. As a result, fluid pressure can be conceived as a scalar quantity because it lacks an inherent direction of its own.

Pressure:

• When the fluid is at rest or moving at a constant speed, the pressures at two positions on a horizontal plane or an equal level are the same.
• When the fluid is at rest or moving with constant velocity, the expression relates pressures at two positions that are separated at a depth of h: p2−p1=ρgh, where ρ is the density of the liquid.
• When a fluid container has constant horizontal acceleration, the pressures at two positions on a horizontal plane are related by the expression: p1−p2=lρa.
• When the liquid container is accelerating up, pressures at two positions within a liquid at a vertical distance of h are related to the expression: p2−p1=ρ (g+a) h. 

1.1.2. Atmospheric Pressure 

Atmospheric pressure is the term used to describe the pressure in the earth’s atmosphere. A manometer, often known as a U-tube manometer or simply a manometer, is used to measure gauge pressure, while a barometer is used to monitor atmospheric pressure. 

1.1.3. Pascal’s Law:

Any portions of the fluid, as well as the walls of the confining vessel, remain unaffected when a pressure change is applied to a contained fluid. The hydraulic lift is one of the several real-world uses of Pascal’s law. 

1.1.4. Archimedes Principle:

• Think of a body that is partially or completely submerged in a liquid. On this body, the fluid applies a contact force. Floatant force or upthrust is the product of all these contact forces.

•  F= weight of the fluid displaced by the body

• This force, known as the buoyant force, acts through the centre of gravity of the displaced fluid and acts vertically upward (contrary to the weight of the body). Mathematically,    F= Vσg, where σ is the density of the liquid and V is the volume of the displaced liquid.
• The apparent reduction in weight of the body = upthrust = weight of the liquid displaced by the body.

1.2. Fluid Dynamics:

Steady Flow (Streamline Flow)- The type of flow in which the velocity of fluid particles crossing a specific position is the same at all times is called a Steady Flow. Each particle, without a doubt, travels through that place on the same path as the one taken by the previous particle.

Line of flow- It is the path followed by a particle in a flowing liquid. With respect to a steady flow, it is called streamlining. Two streamlines never intersect each other.

1.2.1. Equation of Continuity:

• The volume of liquid entering the tube of flow in a steady flow at a time t is given by: A1V1Δt.
• Since the liquid is incompressible in nature, the same volume should flow out of this tube. The volume flowing is given by A2V2Δt.

1.2.2. Bernoulli’s Theorem:

Considering a streamlined flow of an ideal fluid, the potential energy per unit volume, the sum of pressure energy per unit volume and kinetic energy per unit volume are always constant at all cross-sections of the liquid. Mathematically, it is expressed as

p+ρgh+ρV2/2=const.

• Bernoulli’s equation is applicable only for a steady incompressible flow of a fluid having no viscosity.

Venturi Metre 

It is an instrument utilised for measuring the rate of flow of fluids. 

Using Bernoulli’s theorem 

PA+ρ (V12)/2=PB+ρ (V22)/2

⇒V22−V12=2ρ(PA−PB)=2ρhρg

⇒Q2/A22−Q2/A12 = 2hg (Q=AV)

1.3. Viscosity:

The characteristic of a fluid by which it opposes the relative moa viscous force dependent on its shape, velocity, and size opposes friction between its different layers is known as viscosity, and the force which comes into action is known as the viscous force. Mathematically, viscous force is expressed as follows:

F= −ηAdvdx

1.3.1. Stoke’s Law:

• When a solid materials travel through a viscous medium, a viscous force dependent on its shape, velocity and size opposes it.
• The viscous drag acting on a spherical body of radius r, travelling in a viscous medium of viscosity η with velocity v is given by: 

Fviscous = 6πηrv

This formula is called Stoke’s law.

1.3.2. Terminal Velocity:

• It refers to the maximum constant velocity of a body under free fall in a viscous medium. Mathematically, it is given below:

vr=(2r2(ρ−ρ0)g)/9η

1.3.3. Poiseuille’s Formula:

Poiseuille acquired knowledge of the liquid’s streamlined flow in capillary tubes.

The following formula is used to determine how much liquid is released from the tube per second:

πPr4/8ηl

1.3.4. Reynold Number:

It is a dimensionless number whose value provides an approximate idea about the flow rate and whether it would be turbulent or not. Mathematically, it is as given below:

Re=(ρvD)/η

1.4. Surface Tension:

Surface tension can be defined as the force per unit length in the plane of a liquid surface that is perpendicular to either side of an imaginary line drawn on that surface. Mathematically, it is: S= F/l

1.4.1. Surface Energy:

For increasing the surface area, work needs to be done over the surface of the liquid. This work is stored on the surface of the liquid as its potential energy. Thus, the surface energy of a liquid is the excess potential energy per unit area of the liquid surface. Mathematically, it is given by the following formula: 

W=SΔA, where ΔA= increase in surface area.

1.4.2. Excess Pressure:

Excess pressure in a liquid drop or liquid bubble is given by: P=2TR.

As a soap bubble has two surfaces, excess pressure in it is given by: P=4TR.

1.4.3 Angle of Contact:

The angle between the solid surface inside the liquid and the tangent to the liquid surface at the point of contact is known as the angle of contact ().

When a glass plate is immersed in mercury, the surface of the glass bends and the mercury is forced downward. It turns out that Mercury’s angle of contact is obtuse.

When a plate is submerged in water with one of its sides upright, the water takes on a curved shape. A sharp angle of contact can be seen in the water.

1.4.4 Capillary Tube and Capillary Action:

A very narrow glass tube that opens at both ends and with a fine borehole is called a capillary tube. Capillarity is the reaction that occurs when a capillary tube is dipped in a liquid, causing the liquid to rise or sink within the tube. Mathematically, capillary rise or fall (h) is as given below: 

h=(2Scosθ)/(rρg)=(2S)/(Rρg)

Where,

The surface tension is denoted by ‘S’

The angle of contact is denoted by ‘’

‘r’ denotes the radius of the capillary tube

‘R’ denotes the radius of the meniscus

The density of the liquid is denoted by ρ

Mechanical Properties of Fluids Class 11 Notes 

Fluids and Their Properties 

Fluids are substances that may easily flow from higher to lower levels and have no distinct structure. For instance, gases and liquids.

They take on the shape of the container and have no distinct shape. 

Properties of Fluid 

• Hydrostatic – Fluids at rest
• Hydro-dynamic – Fluids in motion 

Thrust 

It is a force exerted on the walls of the container by the fluid. Its S.I. unit is Newton, and its CGS unit is Dyne. 

Pascal’s Law 

Pascal’s law states that ignoring gravity’s effect, if pressure is applied to any point in an enclosed incompressible fluid, it is transmitted equally in all directions throughout the fluid. 

It is known that P1 – P2 = hρg 

At g = 0,  P1 – P2 = 0  

⇒ P1 = P2 

This means that at g = 0, the pressure at every two points inside the liquid is the same.

Archimedes’ Principle 

At rest, the body loses some of its weight when a body or object is completely or partially immersed in a liquid. This apparent loss in the weight of the body is equivalent to the weight of the liquid displaced when such a body is completely or partially immersed. 

Specific Gravity of the body 

The specific gravity of the body is equal to the relative density of the body. Mathematically, it is given by:

Weight of body in air/Loss of weight of the body in the water at 4°C

The Density of the Mixture of a Substance 

• When two liquids of different masses m1 and m2, and densities ρ1 and ρ2 are mixed, then the density of a mixture is given by the following formula: 

ρMixture=[ ρ1ρ2(m1+m2)] / [m1ρ2+m2ρ1]

•  If the mass of the two liquids mixed is the same, but their densities are different, i.e.,  ρ1 and ρ2, then ρMixture  is:  (ρ1+ρ2)/2 
• If the number of substances of volume V1, V2 and densities ρ1 and ρ2 are mixed, then the density of the resulting mixture is as follows: 

ρMixture=(ρ1V1+ρ2V2)/(V1+V2)

Law of Floatation 

When a body with density and volume V is fully submerged in a liquid, two forces are at play. Three scenarios are possible. In this scenario, if w is the buoyant force and W is the body’s weight, Then these are the cases:

Case 1: W > w. In this scenario, the body will entirely submerge in the liquid.

Case 2: W < w. In this scenario, the body will float somewhat and submerge partially.

Three: W = w. In this scenario, the body will float in the liquid in a balanced position.

Viscosity

• Stoke’s Law
• Terminal Velocity
• Poiseuille’s Formula
• Reynold Number

There are numerous observations made by eminent scientists in the field of fluid mechanics. All the fundamental rules and principles are included in this section of

Class 11 Physics Chapter 10 Notes

The explanations, SI and CGI units,  equations and other information are all well laid out so that students don’t miss anything while revising. 

Surface Tension 

• Surface Energy
• Excess Pressure
• Angle of Contact
• Capillary Tube and Capillary Action

The final section of the CBSE Class 11 Physics Chapter 10 Notes goes into great length about surface tension. The calculation of the angle of contact, the excess pressure in a liquid bubble, and the increase in surface area are also covered. A capillary tube experiment is also offered in order to rule out the effects of capillarity and radius of curvature.

Solved Sample Numerical Problem

Q1. A vessel of 6m in height is half-filled with water and then filled with the oil of density 0.96 g/c.c at the top. Find out the pressure at the bottom of the vessel due to these liquids. 

Given: h = 6 m, ρ0 = 0.96 g/c.c. = 0.96 x 103kgm-3, ρW = 103kgm-3 

To find:  P

Let’s find out the mean density first. The formula for this is:          ρMean=(ρw+ρ0)/2 

=(103+0.96×103)/2

=0.98×103kgm−3

The pressure at the bottom will then be calculated by: 

 P = hρg 

⇒P=6×0.98×103×9.8=5.7624×104Nm-2