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Pertemuan 01 - 02 Introduction

Pertemuan 01 - 02 Introduction. INTRODUCTION TO FLUID MECHANICS . 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.

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Pertemuan 01 - 02 Introduction

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  1. Pertemuan 01 - 02Introduction

  2. INTRODUCTION TO FLUID MECHANICS

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

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

  6. 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) Pressure in a Fluid

  7. 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 Pressure in a Fluid

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

  9. Pressure in a Fluid

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

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

  12. 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 Archimedes’ Principle

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

  14. Flotation

  15. Fluids:Statics vs Dynamics

  16. Density The density of a fluid is defined as its mass per unit volume. It is denoted by the Greek symbol, . kg  water= 998 kgm-3 m  = V air =1.2kgm-3 kgm-3 m3 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)

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

  18. Pressure Pressure is the force per unit area, where the force is perpendicular to the area. N pa= 105 Nm-2 F p= Nm-2 (Pa) A 1psi =6895Pa m2 This is the Absolute pressure, the pressure compared to a vacuum. The pressure measured in your tyres is the gauge pressure, p-pa.

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

  20. Pressure Pressure in a fluid acts equally in all directions Pressure in a static liquid increases linearly with depth p= g  h increase in depth (m) pressure increase The pressure at a given depth in a continuous, static body of liquid is constant. p3 p1 = p2 = p3 p1 p2

  21. Measuring pressure (1)Manometers (negligible pressure change in a gas) p1 = px p1 (since they are at the same height) px = py p2=pa z pz= p2 = pa h x y py - pz = gh liquid density  p1 - pa = gh So a manometer measures gauge pressure.

  22. Measuring Pressure (2)Barometers vacuum p1 = 0 A barometer is used to measure the pressure of the atmosphere. The simplest type of barometer consists of a column of fluid. h p2 - p1 = gh p2 = pa pa = gh examples water: h = pa/g =105/(103*9.8) ~10m mercury: h = pa/g =105/(13.4*103*9.8) ~800mm

  23. 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/in2 (psi) 760 Torr (mm Hg) 1013.25 millibars = 101.3 kPascals 1kPa = 1Nt/m2

  24. 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. Units SI - International System Length Meter Time Sec Mass Kg Temp 0K = 0C + 273.15 Force Newton = Nt = 1 kg m / s2 Gravity 9.81 m/s2 Work = Fxd Joule = Nt-m Power = F/t Watt = Joule/sec

  26. Units English Length in Ft Time in Sec lbm (slug) - 1 slug = 32.2 lbm Force - lb Gravity - 32.2 ft/sec2 Work = slug-ft/s2

  27. Properties of Fluids • Density = r (decreases with rise in T) • mass per unit volume ( lbs/ft3 or kg/m3 ) for water density = 1.94 slugs/ft3 or 1000 kg/m3 Specific Weight = g (Heaviness of fluid) • weight per unit volume g = rg for water spec wt = 62.4 lbs/ft3 or 9.81 kN/m3 Specific Gravity = SG • Ratio of the density of a fluid to the density of water SG = rf / rw SG of Hg = 13.55

  28. Ideal Gas Law relates pressure to Temp for a gas P = rRT T in 0K units R = 287 Joule / Kg-0K Pressure Force per unit area: lbs/in2 (psi), N/m2, 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 m = 1.12 x 10-3 N-s/m2 Surface tension - forces between 2 liquids or gas and liquid - droplets on a windshield.

  29. Section 1: Pressure Pressure at any point in a static fluid not fcn of x,y,or z Pressure in vertical only depends on g of the fluid P = gh + Po Gage pressure: relative to atmospheric pressure: P = gh 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. Pressure in a Tank Filled with Gasoline and Water What is the pressure at point A? At point B? gG = 42.43 lbs/ft3 SG = 0.68 gW = 62.4 lbs/ft3 At point A: PA = gG x hG + PO = 42.43 x 10 + PO 424.3 lbs/ft2 gage At point B: PB = PA + gW x hW = 424.3 + 62.4 x 3 611.5 lbs/ft2 gage Converting PB to psi: (611.5 lbs / ft2) / (144 in2/ft2) = 4.25 psi

  31. 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. Manometers - measure DP • 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. Manometers Simple Example: P = gx h + PO Find the pressure at point A in this open u-tube monometer with an atmospheric pressure Po PD = gWx hE-D + Po Pc = PD PB = PC - gHgx hC-B PA = PB

  34. 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 Archimedes’ Principle

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

  36. Flotation

  37. 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 Gases

  38. Boyle’s Law

  39. 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 Boyle’s Law

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

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

  42. 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 105 newtons/meter2 Atmospheric Pressure

  43. Barometers

  44. 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 Buoyancy in a Gas

  45. 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. Bernoulli’s Principle

  47. 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) Bernoulli’s Principle

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

  49. Bernoulli’s Principle

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

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