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In Chapter 10 of NCERT Class 11 Physics, we look at the fascinating field of fluid mechanics, specifically the mechanical properties that govern the behaviour of liquids and gases. Understanding fluid dynamics is important because it has applications in a variety of fields, including engineering and medicine. This chapter Mechanical Properties of Fluids class 11 notes explains fundamental concepts such as viscosity, surface tension, and pressure, giving students a strong foundation for understanding the complexities of fluid behaviour.

This Story also Contains

- Revision Notes for CBSE Class 11 Physics Chapter 10: Mechanical Properties of Fluids - Free PDF Download
- NCERT Class 11 Physics Chapter 10 Notes
- Pressure
- Pascal’s Law
- Buoyancy
- Archimedes’ Principle
- Laws of Flotation
- Density and Relative Density
- Viscosity
- Poiseuille’s Formula
- Stoke’s Law
- Flow of Liquid
- Reynold’s Number
- Equation of Continuity
- Bernoulli’s Theorem
- Torricelli’s Theorem
- Surface Tension
- Surface Energy
- NCERT Class 12 Notes Chapter-Wise

These Class 11 physics chapter 10 notes are aligned with the CBSE Class 11 syllabus and provide a structured approach to learning, covering the key topics outlined in Chapter 10. These Mechanical Properties of Fluids notes class 11, written by subject matter experts, are intended to simplify complex theories and principles, making them more accessible to students and facilitating a deeper understanding of fluid mechanical properties. By working with these ch 10 physics class 11 notes, students can improve their comprehension and prepare effectively for upcoming exams.

**Also, students can refer,**

- NCERT Solutions for Class 12 Physics Chapter 10 Mechanical Properties of Fluids
- NCERT Exemplar Solution Class 12 Physics Chapter 10 Mechanical Properties of Fluids

What are Fluids?

Fluids are substances that can flow when an external force is applied to them.

Gases and Liquids are fluids.

It does not have a finite shape rather it takes the shape of the vessel that contains it.

The normal force exerted by the liquid when it is at rest on a surface is called the thrust of liquid.

SI unit of thrust = (N) Newton.

The fluid mechanics is divided as follows

When the fluid is at rest - hydrostatics

When the fluid is in motion – hydrodynamics

The normal force applied by a liquid per unit area of the surface in contact is called the pressure of the liquid, also known as Hydrostatic pressure.

Pressure applied by a liquid column, p = hρg

here, h = height of the liquid column,

ρ= density of liquid

g =acceleration because of gravity

Mean pressure on the walls of the container containing liquid up to height h = (hρg / 2).

According to Pascal’s law at equilibrium, the pressure at any point enclosed in a container exerts the pressure and is transmitted equally in all directions and on the Walls of the container.

The working principle of hydraulic lift, hydraulic press, and hydraulic brakes is based on Pascal’s law.

Atmospheric Pressure

The pressure that is exerted by the atmosphere on Earth is known as atmospheric pressure.

It is almost 100000 N/m

^{2}.At sea level, atmospheric pressure becomes equal to 76 cm of mercury column.

Atmospheric pressure is given as "hdg" which is equal to that of 76 x 13.6 x 980 dyne cm

^{-2 }Atmospheric pressure can be measured in a torr or bar. 1 torr = 1 mm of mercury column. 1 bar = 10

^{5}PaThe aneroid barometer is the instrument that is used to measure atmospheric pressure.

When a body is partially or fully immersed in a fluid an upward force acts on it and that upward force is called buoyant force.

This whole phenomenon is known as Buoyancy.

The buoyant force acts at the centre of gravity of the liquid displaced by the immersed part of the body, that point is known as the center buoyancy.

According to Archimedes Principle, the liquid is displaced by the weight of the object when immersed fully or partially and that weight is equal to the loss in weight when immersed in the liquid.

Let ‘T’ be the observed weight of a body with density σ, when it is fully immersed in the liquid of density p, then the original weight of that body, w = T / (1 – p / σ)

Flotation of the object on a liquid surface requires that the mass of the object is similar to the mass of the liquid which is displaced by the immersion part of the body.

If we consider ‘W’ is the mass of a body and ‘w’ is the buoyant force acting on that body:

In the first case: W > w, the body will sink to the bottom of the liquid.

In the second case W < w, the body will float partially submerged in the liquid.

In the third case W = w, the body will float in liquid

**Conditions applicable for the stability of the body**

For stable equilibrium: The center of buoyancy of the body lies vertically above the center of gravity.

For unstable equilibrium: The center of buoyancy of the body lies vertically above the center of gravity.

For neutral equilibrium: The center of buoyancy of the body coincides with the center of gravity.

The density of a substance is defined as the ratio of its mass to that of its volume.

Density of the liquid = Mass / Volume

Density of water = 1 g/cm

^{3}or in kg 10^{3}kg/m^{3}.It is a Scalar quantity.

The dimensional formula of density is as follows: [ML

^{-3}].The relative density of a substance is defined as, the ratio of its density to the density of water which is at 4°C temperature.

Relative density = Density of a substance / Density of water at 4°C temperature

= Weight of a substance in the air / Loss of weight of the substance inwater

Relative density is also known as specific gravity, it does not have any unit and dimensions.

In the case of a solid body,

Density of body = Density of the substance

In the case of the hollow body,

The density of a hollow body is less than that of a substance.

When non-miscible liquids of different densities are in the same container, the liquid of more density will be at the bottom whereas the liquid with lesser density at the top and interfaces will be plain.

The property of a fluid by virtue of which internal frictional force acts between its different layers that oppose their relative motion is known as viscosity.

This internal frictional force of fluid is called viscous force.

Viscous force is an intermolecular force acting between the molecules of different layers of liquid moving in different velocities.

Viscos Force (F)= -η A(dv/dx)

η =-F/A(dv/dx)

here,

(dv/dx) = rate of change of the velocity with distance and velocity gradient, A = area of cross-section and coefficient of viscosity.

SI unit of η = Nsm

^{-2}or pascal-second or decapoise.Dimensional formula = [ML

^{-1}T^{-1}].The coefficient of viscosity of different oils and its variation with temperature helps us in selecting an appropriate lubricant for a given machine. Viscosity occurs due to the transmission of momentum. The value of viscosity for an ideal liquid is zero. In some organic liquids, it is used in determining the molecular weight and shape of large organic molecules like proteins and cellulose.

**Variation in Viscosity**The viscosity of liquids is indirectly proportional to temperature.

η_{t}= η_{0}/(1+αt+βt^{2} )

where η_{0} and η_{t} are coefficients of viscosities at 0°C and t°C, α and β are constants.

The viscosity of gases is directly proportional to temperatures as η is proportional to √T

The viscosity of liquids is directly proportional to pressure but the viscosity of water is indirectly proportional to pressure. The viscosity of gases remains unchanged with pressure.

In a horizontal pipe for a steady flow, the rate of flow of liquid is given by the formula as follows:

ν= π/2(pr^{4}/ηl);

Where p = pressure difference across the two ends of the tube.

r = radius of the tube,

n = coefficient of viscosity and

1 = length of the tube.

The Rate of Flow of Liquid

Inside a tube rate of flow of liquid is given as follows:

v = (P/R) where, R = (8 ηl/πr^{4} ),

“R”is called liquid resistance.

p = liquid pressure

When two tubes are connected in series

p = p_{1} + p_{2}is the Resultant pressure difference.

R = R_{1} + R_{2} is the Equivalent liquid resistance in the tube.

Both the tubes have the same rate of flow of liquid (v).

(ii) When two tubes are connected in parallel

The difference in pressure(p) is always the same across both tubes.

v = v_{1} + v_{2} is the rate of flow of the liquid

(1/R) = (1/R_{1}) + (1/R_{2})is the Equivalent liquid resistance in the tube

Stoke’s Law says that when a small spherical body drops in a liquid column sometimes it reaches a constant velocity. This velocity is called terminal velocity. When a small spherical object drops in the liquid column with terminal velocity, then the viscous force acting on it is given by

F = 6πηrv

where, r = radius of the body, V = terminal velocity, and η = coefficient of viscosity.

This is called Stokes law; where,

∙ ρ = density of the body

∙ σ = density of the liquid,

∙ η = coefficient of viscosity of liquid and,

∙ g = acceleration due to gravity 1. If ρ > ρ0, the body falls downwards.

If ρ < p0, the body moves upwards with the constant velocity.

If p0 << ρ, then v = (2r^{2 }ρg/9η)

** Importance of Stokes Law**

1. It helps to find the electric charge by Millikan’s oil drop experiment.

2. It helps during parachuting..

3. This is the phenomenon behind the formation of clouds.

We can define the flow in three types as follows:

1. Streamline Flow -In this type of flow of liquid, each particle of liquid follows the same path of its proceeding particles.

2. Laminar Flow- This type of flow is seen in the steady flow of liquid, where on a horizontal surface liquid is present in the form of layers of different velocities.

3. Turbulent Flow- This type of flow is seen where the flow of liquids having velocity greater than its critical velocity

Critical Velocity

Critical velocity is defined as the velocity of the liquid, below which the flow is streamlined and above which flow is turbulent.

Critical velocity is expressed as follows:

vc = (kη/rρ) ;

where, K = Reynold’s number

η = coefficient of viscosity of liquid

r = radius of capillary tube and;

ρ = density of the liquid.

Reynold’s number is defined for flowing fluid is the number that is equal to the ratio of inertial force per unit area to the viscous force per unit area.

Reynold’s Number (K)= v_{c} pr/η

No unit and dimension

Where; p = density of the liquid and vc = critical velocity.

K is about 1000, for pure water flowing in a cylindrical pipe

0< K< 2000-: Streamline Flow

2000 < K < 3000-:Flow variation between streamlined and turbulent.

K > 3000-: Turbulent Flow.

In a pipe of nonuniform cross-sectional area, the liquid is flowing in a streamlined flow, and the rate of liquid across the pipe is found to be constant at every cross-section of the area of the pipe

The equation of continuity is given as follows:

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

We observe that two types of velocities are seen inside the pipe the velocity is found to be slower where the cross-section area is larger on the other hand it is faster in the case of a smaller cross-section area.

The narrower the cross-section area the velocity of the falling stream will increase and on the broader side it will decrease.

**The energy of a Liquid**

A liquid in motion has three types of energy

Pressure energy per unit density = p/ρ

where p= pressure of the liquid and p = density of the liquid.

Pressure energy per unit volume = p

Kinetic Energy

Kinetic energy per unit mass = 0.5v^{2}

Kinetic energy per unit volume = 0.5ρv^{2 }

Potential Energy

Potential energy per unit mass = gh

Potential energy per unit volume = ρgh

According to Bernoulli’s theorem, the sum of all the energies such as pressure energy, kinetic energy, and potential energy per unit volume of the liquid remains constant at every cross-section of the tube in an ideal liquid when flowing in streamlined flow

P/ρ + v^{2}/2 + gh = constant

Applications of Bernoulli’s Theorem

1. The action of the carburetor, paint gun, scent sprayer, insect sprayer is based on Bernoulli’s theorem.

2. The Magnus effect is based on the Bernoulli theorem.

3. By the action of wind storms the roofs are blown away from the house.

4. The attraction in between two close parallel moving boats.

5. Fluttering of a flag

All the above mentioned are based on Bernoulli’s theorem.

According to this theorem, explains the relation between fluid leaving a hole and the liquid’s height in that container.

The relationship can be given according to the following manner.

If a container is filled with fluid and a small hole is present at the bottom of the container, the fluid leaves through the hole.

The liquid would experience the same velocity if dropped from the same height to the hole level.

Let’s suppose the liquid is dropped from a height h, then it would have a velocity v

The velocity ‘v’ is the same velocity at which the liquid leaves the hole and this case the height of fluid is taken as ‘hand is also as same as liquid dropped in the container.

The velocity of efflux, v = √2gh where h is the depth of the orifice below the free surface of the liquid.

The Horizontal range, S = √4h(H — h) ; where H is the height of the liquid column.

The horizontal range is maximum, equal to the height of the liquid column H when the orifice is at half of the height of the liquid column.

The property of the liquid by virtue of which the free surface of the liquid starts minimizing due to force of attraction in between the layers of the liquid at rest.

The surface tension is the physical property of the liquid in which molecules of liquids draw each and every side.

SI unit of surface tension = Nm

^{-1 }Dimensional formula = [MT

^{-2}]

The liquid does not have any shape and when placed in any container possesses some additional energy, and this energy is different from the molecules that are present in the bulk amount inside the liquid. This energy is present at the surface of the molecules.

The product of surface tension and change in surface area is termed as a change in surface energy and all are under constant temperature conditions.

**Significance of NCERT Class 11 Physics Chapter 11 Notes**

Concise Overview: The Mechanical Properties of Fluids class 11 notes provide a brief summary of the chapter, allowing for quick recognition and comprehension of key concepts.

Comprehensive Coverage: These class 11 physics chapter 10 notes include all of the chapter's highlights, ensuring that students fully understand important topics.

Exam Preparation: By guiding students in the right direction and covering essential content, these CBSE class 11 physics ch 10 notes make an effective preparation for CBSE board exams easier, increasing the likelihood of a good score.

Accessibility: Students can easily access these notes whether offline or online, allowing for flexible study sessions at any time and from any location.

Enhanced Efficiency: The notes' streamlined format improves learning efficiency, allowing students to focus on comprehension rather than searching for information.

Flexibility: With these CBSE class 11 physics ch 10 notes, students can study at their own pace, reinforcing learning and increasing confidence.

In essence, NCERT Class 11 Physics Chapter 11 notes are invaluable resources for improving learning, comprehension, and exam preparation.

- NCERT Exemplar Class 11 Solutions
- NCERT Exemplar Class 11 Maths
- NCERT Exemplar Class 11 Physics
- NCERT Exemplar Class 11 Chemistry
- NCERT Exemplar Class 11 Biology

1. According to Class 11, Mechanical Properties of Fluids notes, write the appropriate Bernoulli equation.

P/ρ + v^{2}/2 + gh = constant

2. Explain the concept that the blood pressure in humans is found to be greater at the feet in comparison to the brain.

In Class 11 Physics chapter 10 notes we studied the concept that the height of the blood column inside the feet is more as compared to that for the brain, therefore, the blood exerts more pressure on the feet than on the brain.

3. State the reason: Hydrostatic pressure is a scalar quantity. Why?

According to Pascal’s law, the pressure exerted by the liquid is transmitted equally in all directions inside the liquid container. Hence, there is no fixed direction for the pressure to be applied in a particular direction. Thus, hydro static pressure is a scalar quantity.

4. Why is the Surface tension of a liquid independent of the area of the surface?

Surface tension of the liquid is defined as the force acting per unit length.

Since the force which is in action, is independent of the area of the liquid surface, thus the surface tension is also independent of the area of the liquid surface. You can understand this by reading Mechanical Properties of Fluids Class 11 notes PDF download.

5. Write the formula to calculate the variation in viscosity

Variation in viscosity is given as follows:

η_{t}= η_{0}/(1+αt+βt^{2} )

where η_{0} and η_{t} are coefficients of viscosity at 0°C and t°C, α and β are constants.

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