1. Pertemuan 01 - 02 Introduction

2. Bina Nusantara INTRODUCTION TO FLUID MECHANICS

3. Bina Nusantara Definition of a Fluid A fluid is a substance that flows under the action of shearing forces. If a fluid is at rest, we know that the forces on it are in balance. A gas is a fluid that is easily compressed. It fills any vessel in which it is contained. A liquid is a fluid which is hard to compress. A given mass of liquid will occupy a fixed volume, irrespective of the size of the container. A free surface is formed as a boundary between a liquid and a gas above it.

4. Bina Nusantara Density Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space

5. Bina Nusantara Pressure A measure of the amount of force exerted on a surface area

6. Bina Nusantara Pressure in a Fluid The pressure is just the weight of all the fluid above you Atmospheric pressure is just the weight of all the air above on area on the surface of the earth In a swimming pool the pressure on your body surface is just the weight of the water above you (plus the air pressure above the water)

7. Bina Nusantara Pressure in a Fluid So, the only thing that counts in fluid pressure is the gravitational force acting on the mass ABOVE you The deeper you go, the more weight above you and the more pressure Go to a mountaintop and the air pressure is lower

8. Bina Nusantara Pressure in a Fluid Pressure acts perpendicular to the surface and increases at greater depth.

9. Bina Nusantara Pressure in a Fluid

10. Bina Nusantara Buoyancy Net upward force is called the buoyant force!!! Easier to lift a rock in water!!

11. Bina Nusantara Displacement of Water The amount of water displaced is equal to the volume of the rock.

12. Bina Nusantara Archimedes’ Principle An immersed body is buoyed up by a force equal to the weight of the fluid it displaces. If the buoyant force on an object is greater than the force of gravity acting on the object, the object will float The apparent weight of an object in a liquid is gravitational force (weight) minus the buoyant force

13. Bina Nusantara Flotation A floating object displaces a weight of fluid equal to its own weight.

14. Bina Nusantara Flotation

15. Bina Nusantara Fluids: Statics vs Dynamics

16. Bina Nusantara Density The density of a fluid is defined as its mass per unit volume. It is denoted by the Greek symbol, .  = V m3m3 kgm -3 If the density is constant (most liquids), the flow is incompressible. If the density varies significantly (eg some gas flows), the flow is compressible. (Although gases are easy to compress, the flow may be treated as incompressible if there are no large pressure fluctuations)  water = 998 kgm -3  air =1.2kgm -3 kg m

17. Bina Nusantara Density Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space

18. Bina Nusantara Pressure Pressure is the force per unit area, where the force is perpendicular to the area. p= A m2m2 Nm -2 (Pa) N F This is the Absolute pressure, the pressure compared to a vacuum. p a = 10 5 Nm -2 1psi =6895Pa The pressure measured in your tyres is the gauge pressure, p-p a.

19. Bina Nusantara Pressure A measure of the amount of force exerted on a surface area

20. Bina Nusantara Pressure Pressure in a fluid acts equally in all directions Pressure in a static liquid increases linearly with depth  p= increase in depth (m) pressure increase  g  h The pressure at a given depth in a continuous, static body of liquid is constant. p1p1 p2p2 p3p3 p 1 = p 2 = p 3

21. Bina Nusantara Measuring pressure (1) Manometers h p1p1 p 2 =p a liquid density  x y z p 1 = p x p x = p y p z = p 2 = p a (negligible pressure change in a gas) (since they are at the same height) p y - p z =  gh p 1 - p a =  gh So a manometer measures gauge pressure.

22. Bina Nusantara Measuring Pressure (2) Barometers A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid. p 1 = 0vacuum h p 2 = p a p 2 - p 1 =  gh p a =  gh examples water: h = p a /  g =10 5 /(10 3 *9.8) ~10m mercury: h = p a /  g =10 5 /(13.4*10 3 *9.8) ~800mm

23. Bina Nusantara Atmospheric Pressure Pressure = Force per Unit Area Atmospheric Pressure is the weight of the column of air above a unit area. For example, the atmospheric pressure felt by a man is the weight of the column of air above his body divided by the area the air is resting on P = (Weight of column)/(Area of base) Standard Atmospheric Pressure : 1 atmosphere (atm) 14.7 lbs/in 2 (psi) 760 Torr (mm Hg) 1013.25 millibars = 101.3 kPascals 1kPa = 1Nt/m 2

24. Bina Nusantara Fluid Statics Basic Principles:  Fluid is at rest : no shear forces  Pressure is the only force acting What are the forces acting on the block?  Air pressure on the surface - neglect  Weight of the water above the block  Pressure only a function of depth

25. Bina Nusantara Units SI - International System LengthMeter TimeSec Mass Kg Temp 0 K = 0 C + 273.15 ForceNewton = Nt = 1 kg m / s 2 Gravity9.81 m/s 2 Work = Fxd Joule = Nt-m Power = F/t Watt = Joule/sec

26. Bina Nusantara Units English Length in Ft Time in Sec lbm (slug) - 1 slug = 32.2 lbm Force - lb Gravity - 32.2 ft/sec 2 Work = slug-ft/s 2

27. Bina Nusantara Properties of Fluids Density =  (decreases with rise in T)  mass per unit volume ( lbs/ft 3 or kg/m 3 ) for water density = 1.94 slugs/ft 3 or 1000 kg/m 3 Specific Weight =  (Heaviness of fluid)  weight per unit volume  =  g for water spec wt = 62.4 lbs/ft 3 or 9.81 kN/m 3 Specific Gravity = SG  Ratio of the density of a fluid to the density of water SG =  f /  w SG of Hg = 13.55

28. Bina Nusantara Ideal Gas Law relates pressure to Temp for a gas P =  RT T in 0 K units R = 287 Joule / Kg- 0 K Pressure Force per unit area: lbs/in 2 (psi), N/m 2, mm Hg, mbar or atm 1 Nt/m2 = Pascal = Pa Std Atm P = 14.7 psi = 101.33 kPa = 1013 mb Viscosity fluid deforms when acted on by shear stress  = 1.12 x 10 -3 N-s/m 2 Surface tension - forces between 2 liquids or gas and liquid - droplets on a windshield.

29. Bina Nusantara Section 1: Pressure Pressure at any point in a static fluid not fcn of x,y,or z Pressure in vertical only depends on  of the fluid P =  h + P o Gage pressure: relative to atmospheric pressure: P =  h Thus for h = 10 ft, P = 10(62.4) = 624 psf This becomes 624/144 = 4.33 psi P = 14.7 psi corresponds to 34 ft 10 ft

30. Bina Nusantara What is the pressure at point A? At point B?  G = 42.43 lbs/ft 3 SG = 0.68  W = 62.4 lbs/ft 3 At point A: P A =  G x h G + P O = 42.43 x 10 + P O 424.3 lbs/ft 2 gage At point B: P B = P A +  W x h W = 424.3 + 62.4 x 3 611.5 lbs/ft 2 gage Converting P B to psi: (611.5 lbs / ft 2 ) / (144 in 2 /ft 2 ) = 4.25 psi Pressure in a Tank Filled with Gasoline and Water

31. Bina Nusantara Measurement of Pressure Barometer (Hg) - Toricelli 1644 Piezometer Tube U-Tube Manometer - between two points Aneroid barometer - based on spring deformation Pressure transducer - most advanced

32. Bina Nusantara Manometers - measure  P Rules of thumb:  When evaluating, start from the known pressure end and work towards the unknown end  At equal elevations, pressure is constant in the SAME fluid  When moving down a monometer, pressure increases  When moving up a monometer, pressure decreases  Only include atmospheric pressure on open ends

33. Bina Nusantara Manometers Find the pressure at point A in this open u- tube monometer with an atmospheric pressure P o P D =  W x h E-D + P o P c = P D P B = P C -  Hg x h C-B P A = P B Simple Example: P =  x h + P O

34. Bina Nusantara Archimedes’ Principle An immersed body is buoyed up by a force equal to the weight of the fluid it displaces. If the buoyant force on an object is greater than the force of gravity acting on the object, the object will float The apparent weight of an object in a liquid is gravitational force (weight) minus the buoyant force

35. Bina Nusantara Flotation A floating object displaces a weight of fluid equal to its own weight.

36. Bina Nusantara Flotation

37. Bina Nusantara Gases The primary difference between a liquid and a gas is the distance between the molecules In a gas, the molecules are so widely separated, that there is little interaction between the individual moledules IDEAL GAS Independent of what the molecules are

38. Bina Nusantara Boyle’s Law

39. Bina Nusantara Boyle’s Law Pressure depends on density of the gas Pressure is just the force per unit area exerted by the molecules as they collide with the walls of the container Double the density, double the number of collisions with the wall and this doubles the pressure

40. Bina Nusantara Boyle’s Law Density is mass divided by volume. Halve the volume and you double the density and thus the pressure.

41. Bina Nusantara Boyle’s Law At a given temperature for a given quantity of gas, the product of the pressure and the volume is a constant

42. Bina Nusantara Atmospheric Pressure Just the weight of the air above you Unlike water, the density of the air decreases with altitude since air is compressible and liquids are only very slightly compressible Air pressure at sea level is about 10 5 newtons/meter 2

43. Bina Nusantara Barometers

44. Bina Nusantara Buoyancy in a Gas An object surrounded by air is buoyed up by a force equal to the weight of the air displace. Exactly the same concept as buoyancy in water. Just substitute air for water in the statement If the buoyant force is greater than the weight of the object, it will rise in the air

45. Bina Nusantara Buoyancy in a Gas Since air gets less dense with altitude, the buoyant force decreases with altitude. So helium balloons don’t rise forever!!!

46. Bina Nusantara Bernoulli’s Principle

47. Bina Nusantara Bernoulli’s Principle Flow is faster when the pipe is narrower Put your thumb over the end of a garden hose Energy conservation requires that the pressure be lower in a gas that is moving faster Has to do with the work necessary to compress a gas (PV is energy, more later)

48. Bina Nusantara Bernoulli’s Principle When the speed of a fluid increases, internal pressure in the fluid decreases.

49. Bina Nusantara Bernoulli’s Principle

50. Bina Nusantara Bernoulli’s Principle Why the streamlines are compressed is quite complicated and relates to the air boundary layer, friction and turbulence.

51. Bina Nusantara Bernoulli’s Principle

52. Bina Nusantara REVIEW

53. Bina Nusantara Fluid Mechanics Pressure Pascal’s Law Archimedes’ Principle Fluid Dynamics Bernoulli’s Equation

54. Bina Nusantara Pressure Fluids apply a compressive force to submerged objects from all sides. This means that the force is spread out over a surface area. Pressure: Force per unit area (1 Pa = 1 N/m 2 ) If pressure varies over the area:

55. Bina Nusantara Example – Q14.2 Both dams have the same height and width. Which needs to be stronger?

56. Bina Nusantara (a)What is the force experienced by your finger; what is the force experienced by your thumb? (b)Your thumb holds the pointy end. What is the pressure on the thumb; what is the pressure on your finger? Example You hold a thumb tack between your index finger and thumb with a force of 10 N. The needle has a point that is 0.1mm in radius whereas the flat end has a radius of 5 mm.

57. Bina Nusantara Variation of Pressure with Depth Pressure exerted by a liquid increases with depth. Pressure at sea level is taken to be 1 atmospheres (atm)

58. Bina Nusantara Example – 14.4 F = ?

59. Bina Nusantara Pascal’s Law A change in the pressure applied to a fluid is transmitted to every point of the fluid and to the walls of the container.

60. Bina Nusantara Example 14.2 d 1 = 5.00 cm d 2 = 15.0 cm mg car = 13300 N F 1 = ? P = ?

61. Bina Nusantara Buoyant Forces – Archimedes’ Principle Archimedes’ Principle: The magnitude of the buoyant force on an object equals the weight of the fluid displaced by the object.

62. Bina Nusantara Example – 14.5 Weight in air = 7.84 N Weight in water = 6.84 N

63. Bina Nusantara Totally Submerged Objects a is upward if  f >  obj a is downward if  f <  obj

64. Bina Nusantara Floating Objects

65. Bina Nusantara Example Consider an object that floats in water but sinks in oil. When the object floats in water, half of it is submerged. If we slowly pour oil on top of the water so it completely covers the object, the object 1. moves up. 2. stays in the same place. 3. moves down.

66. Bina Nusantara Fluid Dynamics We now put the fluid in motion (flow). Here are several assumptions about the fluid and its flow: – The flow is to be laminar (steady) not turbulent. – The fluid is non-viscous (negligible internal friction). Think water, not honey. – The fluid in incompressible. – The flow irrotational (no angular momentum).

67. Bina Nusantara Equation of Continuity The product of the velocity of flow and the area of the pipe remains constant.

68. Bina Nusantara Example A blood platelet drifts along with the flow of blood through an artery that is partially blocked by deposits. As the platelet moves from the narrow region to the wider region, its speed 1. increases. 2. remains the same. 3. decreases. What about the pressure?

69. Bina Nusantara Bernoulli’s Equation Using conservation of energy:

70. Bina Nusantara Example – 14.9 d 1 = 5 cm d 2 = 3 cm v 2 = 15 m/s V out in 10 min = ? v 1 = ? P 1 - P 2 = ?

71. Bina Nusantara Review Pascal’s Law: A change in the pressure applied to a fluid is transmitted to every point of the fluid and to the walls of the container. Archimedes' Law: The magnitude of the buoyant force on an object equals the weight of the fluid displaced by the object. Equation of Continuity: Bernoulli’s Equation: Pressure: Fluid Dynamics