Course Content
Class 11 Physics Chapter 4 Motion In A Plane
4 Motion in a plane 4.1 Introduction 4.2 Scalars and vectors 4.3 Multiplication of vectors by real numbers 4.4 Addition and subtraction of vectors – graphical method 4.5 Resolution of vectors 4.6 Vector addition – analytical method 4.7 Motion in a plane 4.8 Motion in a plane with constant acceleration 4.9 Relative velocity in two dimensions 4.10 Projectile motion 4.11 Uniform circular motion
Class 11 Physics Chapter 5 Laws of motion
Section Name Topic Name 5 Laws of motion 5.1 Introduction 5.2 Aristotle’s fallacy 5.3 The law of inertia 5.4 Newton’s first law of motion 5.5 Newton’s second law of motion 5.6 Newton’s third law of motion 5.7 Conservation of momentum 5.8 Equilibrium of a particle 5.9 Common forces in mechanics 5.10 Circular motion 5.11 Solving problems in mechanics
Class 11 Physics Chapter 6 Work Energy and Power
Section Name Topic Name 6 Work Energy and power 6.1 Introduction 6.2 Notions of work and kinetic energy : The work-energy theorem 6.3 Work 6.4 Kinetic energy 6.5 Work done by a variable force 6.6 The work-energy theorem for a variable force 6.7 The concept of potential energy 6.8 The conservation of mechanical energy 6.9 The potential energy of a spring 6.10 Various forms of energy : the law of conservation of energy 6.11 Power 6.12 Collisions
Class 11 Physics Chapter 7 Rotation motion
Topics Introduction Centre of mass Motion of COM Linear Momentum of System of Particles Vector Product Angular velocity Torque & Angular Momentum Conservation of Angular Momentum Equilibrium of Rigid Body Centre of Gravity Moment of Inertia Theorem of perpendicular axis Theorem of parallel axis Moment of Inertia of Objects Kinematics of Rotational Motion about a Fixed Axis Dynamics of Rotational Motion about a Fixed Axis Angular Momentum In Case of Rotation about a Fixed Axis Rolling motion
Class 11 Physics Chapter 9 mechanics properties of solid
Section Name Topic Name 9 Mechanical Properties Of Solids 9.1 Introduction 9.2 Elastic behaviour of solids 9.3 Stress and strain 9.4 Hooke’s law 9.5 Stress-strain curve 9.6 Elastic moduli 9.7 Applications of elastic behaviour of materials
Class 11 Physics Chapter 11 Thermal Properties of matter
Section Name Topic Name 11 Thermal Properties of matter 11.1 Introduction 11.2 Temperature and heat 11.3 Measurement of temperature 11.4 Ideal-gas equation and absolute temperature 11.5 Thermal expansion 11.6 Specific heat capacity 11.7 Calorimetry 11.8 Change of state 11.9 Heat transfer 11.10 Newton’s law of cooling
Class 11 Physics Chapter 14 Oscillations
Section Name Topic Name 14 Oscillations 14.1 Introduction 14.2 Periodic and oscilatory motions 14.3 Simple harmonic motion 14.4 Simple harmonic motion and uniform circular motion 14.5 Velocity and acceleration in simple harmonic motion 14.6 Force law for simple harmonic motion 14.7 Energy in simple harmonic motion 14.8 Some systems executing Simple Harmonic Motion 14.9 Damped simple harmonic motion 14.10 Forced oscillations and resonance
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About Lesson

Reynolds Number

  • Reynolds number is a dimensionless number, whose value gives an idea whether the flow would be turbulent or laminar.
  • Types of flow are classified as 2 types:laminar flow and turbulent flow.
  • Reynolds number helps us to determine whether the flow is laminar or turbulent.
  • It is denoted by Re. where ‘e’ shows Reynolds.
  • Expression: Re=ρvd/ η;
    • where ρ = density of the fluid,
    • v=velocity of the fluid,
    • d=diameter of the pipe through which the fluid flows
    • η=viscosity of the fluid.

How does Reynolds number (Re) distinguish laminar flow from tubular?

  • If the value of Reynold’s number (Re) reaches 1000 then the flow is laminar.
  • When the value of Reynold’s number(Re)is greater than 2000 then the flow is turbulent.
  • If the value of (Re)is between 1000 and 2000 then the flow is unstable.The flow is in intermediate stage.
    • At this state it has some characteristics of laminar flow and some of turbulent flow.
Mechanical Properties of Fluids
Mechanical Properties of Fluids

Alternative expression of Re: Inertial force/force of viscosity

  • By using Re= ρvd/ η
  • Multiplying both numerator and den by v:- Re= ρv2d/ ηv
  • By rearranging, ρv2/( ηv/d)
  • Multiplying both numerator and den by A:- Re= ρv2A/(ηv/d)A
    • Where
      • ρv2A = Inertial force
      • (ηv/d)A = Force of viscosity

(a)Calculating inertial force

  • Inertial force = ma
    • =ρV xv/t = (ρVxAxdisplacement)/t
    • =ρvAv =ρv2A

(b)Calculating Force of viscosity:-

  • Coefficient of viscosity η =stress/shearing strain
    • F/A/(x/lt)
    • F/A/v/l =Fl/Av
    • η=Fl/Av
    • F = ηAv/l
    • =(ηv/l)A (Expression is same as   )

Turbulence:boon or bane

  • Turbulence has both advantages and disadvantages.
  • Advantages:-
    • Promotes mixing and increases the rates of transfer of mass,momentum and energy. For example: – Mixer and Grinder or a juice mixer.
Mechanical Properties of Fluids
Mechanical Properties of Fluids

Grinding of flour

  • Disadvantages:-
    • Dissipates Kinetic energy in the form of heat.

Problem:- The flow rate of water froma tap of diameter 1.25 cm is 0.48 L/min.The coefficient of viscosity of water is10-3 Pa s. After sometime the flow rate isincreased to 3 L/min. characterise the flowfor both the flow rates.

Answer:- Let the speed of the flow be v and thediameter of the tap be d = 1.25 cm. Thevolume of the water flowing out per second isQ = v × π d2 / 4

v = 4 Q / d2

We then estimate the Reynolds number to be

Re = 4 ρ Q / π d η

= 4 ×103 kg m–3 × Q/(3.14 ×1.25 ×10-2 m ×10-3 Pa s)

= 1.019 × 108 m–3 s Q

Since initially

Q = 0.48 L / min = 8 cm3 / s = 8 × 10-6 m3 s-1,

We obtain,

Re = 815

Since this is below 1000, the flow is steady.After some time when

Q = 3 L / min = 50 cm3 / s = 5 × 10-5 m3 s-1,

We obtain,

Re = 5095

Liquid Surfaces

  • Certain properties of free surfaces:-
  • Whenever liquids are poured in any container they take the shape of that container in which they are poured and they acquire a free surface.
    • Consider a case if we pour water inside the glass it takes the shape of the glass with a free surface at the top.
    • Top surface of the glass is a free surface. Water is not in contact with anything else,it is in contact with the air only.
    • This is known as free surfaces.
  • Liquids have free surfaces. As liquids don’t have fixed shape they have only fixed volume.
  • Free surfaces have additional energy as compared to inner surfaces of the liquid.
Mechanical Properties of Fluids
Mechanical Properties of Fluids

Surface Energy

  • Surface energy is the excess energy exhibited by the liquid molecules on the surface compared to those inside the liquid.
  • This means liquid molecules at the surface have greater energy as compared to molecules inside it.
    • Suppose there is a tumbler and when we pour water in the tumbler,it takes the shape of the tumbler.
    • It acquires free surface.
  • Case 1: When molecules are inside the liquid:-
    • Suppose there is a molecule inside the water,there will be several other molecules that will attract that molecule in all the directions.
    • As a result this attraction will bind all the molecules together.
    • This results in negative potential energy of the molecule as it binds the molecule.
    • To separate this molecule huge amount of energy is required to overcome potential energy.
    • Some external energy is required to move this molecule and it should be greater than the potential energy.
    • Therefore in order to separate this molecule a huge amount of energy is required.
  • Therefore a large amount of energy is required by the molecules which are inside the liquid.
  • Case2: When the molecules are at the surface:-
    • When the molecule is at the surface, half of it will be inside and half of it is exposed to the atmosphere.
    • For the lower half of the molecule it will be attracted by the other molecules inside the liquid.
    • But the upper half is free. The negative potential energy is only because of lower half.
    • But the magnitude is half as compared to the potential energy of the molecule which is fully inside the liquid.
    • So the molecule has some excess energy, because of this additional energy which the molecules have at the surface different phenomenon happen like surface energy, surface tension.
  • Liquids always tend to have least surface are when left to itself.
  • As more surface area will require more energy as a result liquids tend to have least surface area.
Mechanical Properties of Fluids
Mechanical Properties of Fluids

Surface energy for two fluids in contact

  • Whenever there are two fluids,in contact, surface energy depends on materials of the surfaces in contact.
  • Surface energy decreases if the molecules of the two fluids attract.
  • Surface energy increases if molecules of the two fluids repel.


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