9. Mechanical Properties of Fluids 5 Viscosity And Fluid Flow.pptx

chapter-9 of class 11th physics

1. Properties of bulk matters

2. 1– 1 ■ INTRODUCTION Mechanics: The oldest physical science that deals with both stationary and moving bodies under the influence of forces. Fluid mechanics: The science that deals with the behavior of fluids at rest ( fluid statics ) or in motion ( fluid dynamics ), and the interaction of fluids with solids or other fluids at the boundaries. Fluid dynamics: Fluid mechanics is also referred to as fluid dynamics by considering fluids at rest as a special case of motion with zero velocity. Fluid mechanics deals with liquids and gases in motion or at res 2 t.

3. Fluid Fluid is a substance that flows under the action of an applied force and does not have a shape of its own. Examples: Liquids and Gases

4. Fluid Statics Fluid either at rest or moving in a manner that there is no relative motion between adjacent particles. No shearing stress in the fluid Only pressure (force that develop on the surfaces of the particles)

5. Pressure Pressure is defined as a normal force exerted by a fluid per unit area . Units of pressure are N/m 2 , which is called a pascal (Pa). Since the unit Pa is too small for pressures encountered in practice, kilopascal (1 kPa = 10 3 Pa) and megapascal (1 MPa = 10 6 Pa) are commonly used. Other units include bar , atm, kgf/cm 2 , lbf/in 2 =psi .

6. Absolute, ga u ge , and vacuum pressures Actual pressure at a give point is called the absolute pressure . Most pressure-measuring devices are calibrated to read zero in the atmosphere, and therefore indicate ga u ge pressure , P gage =P abs - P atm . Pressure below atmospheric pressure are called vacuum pressure , P vac =P atm - P abs .

7. Pressure at a Point Pressure at any point in a fluid is the same in all directions. Pressure has a magnitude, but not a specific direction, and thus it is a scalar quantity.

8. Pressure Exerted by a Liquid Column F = mass of liquid in the column of depth h x g = V olum e x Densit y x g = A h x ρ x g or F=Ahρg Pressure of the liquid at a depth h is given by: P=F/A = Ahρg/A or P=hρg Thus Pressure α height of fluid column & Density of fluid

9. Variation of pressure with depth F BOTTOM - F TOP = mg = (density x Vol) x g F BOT T O M - F T O P = ρ A H g Since pressure is Force / area, Force = P x A P Bottom A – P Top A = ρ A H g, or P Bottom – P Top = ρ H g The pressure below is greater than the pressure above. Here, P Bottom = Pressure at depth & P Top =P a (Atmospheric Pressure) Hence P = Pa + hρg

10. Variation of pressure with depth Variation of pressure with depth: P = Pa + hρg where Pa =atmospheric pressure, h= depth of liquid, ρ=density , g=acceleration due to gravity In the presence of a gravitational field, pressure increases with depth because more fluid rests on deeper layers.

11. Blood Pressure The blood pressure in your feet can be greater than the blood pressure in your head depending on whether a person is standing or reclining

12. How much does P increase At the surface of a body of water the pressure is 1 atm = 100,000 Pa As we go down into the water, at what depth does the pressure double, from 1 atm to 2 atm or 200,000 Pa W an t ρ g h = 100,00 Pa 1000 kg/m 3 x 10 x h = 100,000 So h = 10 meters or about 30 feet 100,000 Pa h

13. Ans. Pressure increases with depth, so the speed of water leaking from the bottom hole is larger than that from the higher ones. Why speed of water leaking from the bottom hole is Larger?

14. Pascal’s Law According to this Law the Pressure applied to an enclosed liquid is transmitted undiminished to every point of the liquid and walls of the containing vessel . The normal forces F a , F b and F c as shown in Fig on the faces BEFC, ADFC and ADEB denoted by A a , A b and A c respectively. Thus

15. Hydrostatic Paradox Pressure in a fluid at rest is independent of the shape of the container. Pressur e i s th e same a t al l point s o n a horizontal plane in a given fluid.

16. A hydraulic lift Pressure is F / A At the same depth the pressures are the same so F 1 /A 1 = F 2 /A 2 , or with a little force you can lift a heavy object! the jack

17. Measuring atmospheric pressure - Barometers Inverted closed tube filled with liquid The column of liquid is held up by the pressure of the liquid in the tank. Near the surface this pressure is atmospheric pressure, so the atmosphere holds the liquid up. P ATM P ATM P liquid

18. Barometric pressure Atmospheric pressure can support a column of water 10.3 m high, or a column of mercury (which is 13.6 times as dense as water) 30 inches high 🡪 the mercury barometer

19. Buoyant Force W P Top A P Bottom A h submerged object that has a mass density ρ O F = P ⋅ A The density of the water is ρ W

20. Buoyant force The water pushes down on the top of the object, and pushes up on the bottom of the object The difference between the upward force and the downward force is the buoyant force F B since the pressure is larger on the bottom the buoyant force is UP

21. Archimedes principle buoyant force is F B = P x A = ρ W g h A • = ρ W g (volum e o f object) • = ρ W (volum e o f object ) g • = mass of displaced water x g th e pressur e di f ferenc e i s ρ W g h , so the F = weight of displaced water B This is Archimedes principle A h object

22. Will it float? The object will float if the buoyant force is enough to support the object’s weight The object will displace just enough water so that the buoyant force = its weight If it displaces as much water as possible and this does not match its weight, it will sink. Objects that have a density less than water will always float.

23. VISCOSITY The property of a liquid by virtue of which an opposing force(internal friction) comes into play between different layers of a liquid whenever there is a relative motion between these layers of the liquid is called viscosity.

24. Coefficient of Viscosity 8 The coefficient of viscosity (pronounced ‘eta’) for a fluid is defined as the ratio of shearing stress(F/A) to the strain rate(v/l). The SI unit of viscosity is poiseiulle (Pl). Its other units are N s m -2 or Pa s. The dimensions are [ML -1 T -1 ]

25. Effect of Temperature on Viscosity 25 The Viscosity of liquids decreases with increase in temperature and increases with decrease in temperature i.e. η α The viscosity of Gases increases with increase in temperature and vice versa i.e. η α

26. Stoke’s Law 26 According to Stoke’s Law the viscous drag(F) acting on a spherical body of radius r moving with terminal velocity v in a fluid of coefficient of viscosity η is given by , F=6ᴨηrv F mg

27. Terminal Velocity 27 When a body is dropped in a viscosity fluid, it is first accelerated and then its acceleration becomes zero and it attains a constant velocity called terminal velocity. where r = radius of spherical body η= coefficient of viscosity σ = density of fluid ρ = density of material of body

28. 12 Laminar versus Turbulent Flow Laminar flow: The highly ordered fluid motion characterized by smooth layers of fluid. The flow of high-viscosity fluids such as oils at low velocities is typically laminar. Turbulent flow: The highly disordered fluid motion that typically occurs at high velocities and is characterized by velocity fluctuations. The flow of low-viscosity fluids such as air at high velocities is typically turbulent. T ransitiona l flow: A flow that alternates between being laminar and turbulent. Laminar, transitional, and turbulent flows over a flat plate.

29. Poiseuille’s Equation 29 According to Poiseuille volume of liquid coming out the tube per second is directly proportional to the Pressure difference(P) directly proportional to fourth power of radius(r) of capillary tube inversely proportional to coefficient of viscosity( η) of liquid inversely proportional to length (l) of capillary tube i.e. where K= ᴨ/8

30. Reynold’s Number 30 Where v c = Critical velocity of liquid ρ = density of liquid η = coefficient of viscosity D= Diameter of the tube If R< 1000 , the flow of liquid is streamline or laminar If R> 2000 , The flow is turbulent If R lies between 1000 and 2000 , the flow is unstable and may change from streamline to turbulent flow

31. For incompressible liquid ρ 1 =ρ 2 = ρ Then A 1 v 1 =A 2 v 2 =A v Thus Av=Constant , This is known as equation of continuity 31

32. Steady versus Unsteady Flow The term steady implies no change at a point with time . The opposite of steady is unsteady . The term uniform implies no change with location over a specified region. The term periodic refers to the kind of unsteady flow in which the flow oscillates about a steady mean. 32 .

33. Compressible versus Incompressible Flow 33 Incompressible flow: If the density of flowing fluid remains nearly constant throughout (e.g., liquid flow). Compressible flow: If the density of fluid changes during flow (e.g., high-speed gas flow) When analyzing rockets, spacecraft, and other systems that involve high-speed gas flows, the flow speed is often expressed by Mach number Ma = 1 Sonic flow Ma < 1 Subsonic flow Ma > 1 Supersonic flow Ma >> 1 Hypersonic flow

34. Bernauli’s Theorem 34

35. Applications of Bernoulli's Theorem 35

36. Limitations of Bernoulli's Theorem 36 [1] The viscous drag has been neglected as we assume the flow to be non-viscous. [2] We also used that there is no loss of energy as the liquid moves, but some of its kinetic energy is always converted into heat due to viscous forces. [3] If liquid moves along a curved path then the centrifugal forces should also be considered. [4] We assume all the liquid particles moving with the same velocity but liquid particles near the center of tube moves faster than outer particles.

37. Cohesive & Adhesive Forces

38. Surface Tension (T) It is the property of a liquid by virtue of which, it behaves like an elastic stretched membrane with a tendency to contract so as to occupy a minimum surface area Mathematically T = F/l S.I Unit is : Nm -1 Dimensional formula : M 1 L T -2

39. Do you Like Hot soup or Cold Soup? Q. Why hot soup is tastier than cold soup? Ans: When soup is hot its surface tension get reduced so it will spread on all taste buds so is more tastier than cold soup.

40. Surface Energy The potential energy per unit area of the surface film is called the surface energy. Surface energy = “Surface tension is numerically equal to surface energy”

41. Pressure inside a Drop or Bubble Excess of pressure inside a drop and double:- There is excess of pressure on concave side of a curved surface 1. Excess of pressure inside a liquid drop = 2T/R 2. Excess of pressure inside a liquid bubble = 4T/R 3. Excess of pressure inside an air bubble = 2T/R, Where T is the surface tension , R = radius of liquid drop

42. Angle of Contact The angle which the tangent to the free surface of the liquid at the point of contact makes with the wall of the containing vessel, is called the angle of contact. For liquid having convex meniscus, the angle of contact is obtuse and for having concave meniscus, the angle of contact is acute.

43. Capillarity Capillary tube:- A tube of very fine bore is called capillary tube Capillarity:-The rise or fall of liquid inside a capillary tube when it is dipped in it is called capillarity

44. Ascent formula When a capillary tube of radius ‘r’ is dipped in a liquid of density s and surface tension T, the liquid rises or depresses through a height, H = 2 T c o s θ / r ρ g There will be rise in a liquid whe n angl e of c o n t ac t θ is acu t e . Ther e wil l be f al l i n liquid whe n angl e of c o n t ac t θ is obtuse.