ENGINEERING FLUID MECHANICS Chapter 1.pptx

Fluid Mechanics

1. FLUID MECHANICS

2. FLUID MECHANICS - is the study of the effects of forces and energy on liquids and gases. Like other branches of classical mechanics, the subject subdivides into statics (often called hydrostatics) and dynamics (fluid dynamics, hydrodynamics, or aerodynamics).

3. Fluids are classified into two, namely liquids and gases. The characteristics of fluids are as follows: CHARACTERISTICS LIQUIDS GASES Shape and Volume Take the shape of their containers Have Fixed Volumes regardless of their container volumes Fixed volumes are not greatly affected by temperature and pressure Take the shape of their containers Take the volume of their containers Gas volume varies with temperature and pressure Resistance and Shear Cannot support shear Will deform continuously to minimize shear forces Cannot support shear Will deform continuously to minimize shear forces Compressibility Slight Compressible Incompressible Highly Compressible Resistance to motion Resist instantaneous changes in velocity due to viscosity Resistance to motion stops when the liquid motion stops Cannot resist instantaneous changes in velocity because of very low viscosities

4. CHARACTERISTICS LIQUIDS GASES Pressure The same in all direction The same in all direction Molecular Spacing Molecules are relatively closer together Molecules are held together by strong forces of attraction Molecules have low kinetic energy Distance each molecule travels between collision is small Molecules are relatively far apart Molecules have weak forces of attraction Molecules have high kinetic energy Distance each molecule travels between collision is large

5. TYPES OF FLUIDS Fluids are generally divided into two types, namely, IDEAL FLUIDS and REAL FLUIDS. The characteristics of the two types of fluids are as tabulated: IDEAL FLUIDS REAL FLUIDS No viscosity(i.e. resistance to shear is zero) Viscous Incompressible Compressible Have uniform velocity distribution when flowing Non-uniform velocity distribution No friction between moving layers of fluids Experience friction between moving layers of fluids No eddy currents Turbulent in flow No eddy currents No turbulence

6. Real fluids are further divide into two, namely, Newtonian fluids and Non-Newtonian fluids. Newtonian fluids are fluids that exhibit constant or uniform viscosities while non-Newtonian fluids are those whose viscosities will vary with velocity. DENSITY OF FLUID The density ( ) is defined as mass (m) per unit volume (V).      

7. SPECIFIC VOLUME OF FLUID Specific volume (v) is the volume (V) occupied per unit mass (m) of the fluid. SPECIFIC WEIGHT OF FLUID Specific weight ( ) is defined as weight (W) per unit volume (V).       =  

8. SPECIFIC GRAVITY OF FLUID Specific gravity (SG) is the ratio of the density of a substance to the density of water at a reference temperature of 4 . Sometime called relative density .     Food for the brain: SG of water = 1 SG of mercury = 13.6

9. VISCOSITY OF A FLUID The viscosity of a fluid is a measure of that fluid’s resistance to flow when acted upon by an external force such as a pressure gradient or gravity. v F h fluid stationary surface A

10. FORMULA: Where : F = force on the plate A = cross sectional area of the moving the plate S = shear stress experienced by the fluid = absolute viscosity of the fluid v = velocity of the moving plate h = distance between moving plate and stationary surface (height of fluid)    

11. F A S v h N pa N-s/ or pa-s m/s m lb psi lb-s/ or psi-s in/s in dyne dyne/ dyne-s/ or poise cm/s cm F A S v h N pa m/s m lb psi in/s in dyne cm/s cm

12. KINEMATIC VISCOSITY The kinematic viscosity ( ) is the ratio of the absolute viscosity ( ) of a fluid to its mass density ( ).     or stoke or stoke or Pa-s Food for the brain: 1 poise = 0.1 Pa-s 1 centipoise = 0.01 poise

13. Ex. A sliding-plate viscometer (50 cm x 25 cm) is used to measure the viscosity of a Newtonian fluid. A force of 25 N is required to keep the top plate moving against 1 mm height of fluid at a constant velocity of 5 m/s. What is the viscosity of the fluid? Ans. 0.04 Pa-s

14. Given: A = 50cm x 25cm F = 25 N h = 1 mm v = 5 m/s Solution:  

15. Ex. The viscosity of a fluid with specific gravity 1.3 is measured to be 0.0034 N-s/ . Solve its kinematic viscosity in /s. Ans. 2.615 x  

16. Given: sg = 1.3 Solution: *  

17. Ex. A given oil has a kinematic viscosity of 0.000125 /s and a specific gravity of 0.8. What is the dynamic viscosity? Ans. 0.1 Pa-s  

18. Given: sg = 0.8 Solution: *  

19. Ex. A given oil ( ) is sheared between two parallel plates 0.005 inch apart with the lower plate fixed and the upper plate moving at 13 ft /s. Compute the shear stress oil. Ans. 287  

20. Given: v = 13 ft /s Solution:  

21. COMPRESSIBILITY OF A FLUID (B) - is the fractional change in the volume, of a fluid per unit change in pressure, at constant temperature process. BULK MODULUS (E) - of a fluid is similar to the modulus of elasticity of a solid. Bulk modulus is the reciprocal of compressibility. Bulk modulus is sometimes called coefficient of compressibility .       Food for the brain : If not given, the bulk modulus of water at standard condition is 2.1 GPa

22. Ex. A 0.1 volume of water is observed to be 0.0982 after a pressure is applied. What is that pressure? Bulk modulus of elasticity = 2.1 GPa . Ans. 37.8 Mpa  

23. Given: Solution:  

24. Ex. The compressibility of water is 5 x /N. Find the decrease in volume of 100 mL of water when subjected to a pressure of 15 Mpa . Ans. 0.75 mL  

25. Given: Solution:  

26. Ex. Water in the hydraulic press, initially at 20 psia , is subjected to a pressure of 17 000 psia . Determine the percentage decrease in its volume if the average bulk modulus of elasticity is 365 000 psi. Ans. 4.65 %

27. Given: Solution:  

28. SURFACE TENSION OF A FLUID The membrane or “skin” that seems to form on free surface of a fluid is caused by intermolecular cohesive forces and is known as surface tension . Surface tension is the reason why insects can sit on a pond or a needle can float on the surface of a glass of water. Where: = surface tension (N/m or lb / ft ) = change in pressure r = radius of droplet or bubble   for droplets for bubbles   Food for the brain : If not given, the surface tension of water in air is approximately 0.0756 N/m or 0.00518 lb / ft

29. Ex. A soap bubble has a radius of 5 cm. If the soap solution has a surface tension of 0.03 N/m. What is the gage pressure within the bubble? Ans. 2.4 Pa.

30. Given: Solution:  

31. Ex. The surface tension force of a water in air is approximately 0.00518 lb /ft. If the atmospheric pressure is 14.7 psia , what is the pressure inside a droplet 0.01 inch in diameter? Ans. 14.87 psia

32. Given: Solution:  

33. Ex. A soap bubble 50 mm in diameter contains a pressure (in excess of atmospheric pressure) of 2 bars. Find the surface tension in the soap film? Ans. 1250 N/m2.

34. Given: Solution:  

35. CAPILLARITY OF A FLUID Capillarity action is the name given to the behaviour of a liquid in a thin bore tube. Capillary action is caused by surface tension between the liquid and a vertical solid surface. The liquid tends to climb the wall.   Where: h = height of rise or fall in the tube 𝜃 = contact angle = surface tension d = diameter of the tube 𝛾 = specific weight of fluid  

36. CONTACT ANGLES The angle of contact, 𝜃, indicates whether adhesive or cohesive forces dominate. For angles of contact less than 90º, adhesive forces dominates while for angles more than 90º, cohesive forces dominates MATERIALS ANGLE, 𝜃 Mercury-glass 140º Water-paraffin 107º Water-silver 90º Kerosene-glass 26º Glycerine-glass 19º Water-glass 0º Ethyl alcohol-glass 0º

37. Ex. Water at 20 ºC ( N/m) will rise in a clean 1 mm diameter glass tube a distance of ? Ans. 3 cm  

38. Given: Solution:  

39. Ex. Mercury makes an angle of 130º with respect to the vertical when in contact with clean glass. How far will mercury depress in a clean, 10 m diameter glass tube. If N/m for mercury. Ans. – 0.9 m  

40. Given: Solution: *  

41. Ex. A given liquid has a surface tension of 0.4 N/m. In a 3 mm diameter vertical tube if the liquids rises 6 mm above the liquid outside the tube, calculate the contact angle. Ans. 83.66º

42. Given: Solution:  

43. PRESSURE OF A FLUID Pressure is the force per unit area exerted by a liquid or gas on a body or surface, with the forces acting right angles to the surface uniformly in all directions. Fluid pressure are measured in respect to two pressure references: atmospheric pressure and zero pressure . Atmospheric Pressure is the pressure caused by a gases which composes in the atmosphere. Gage pressure is the pressure measured with respect to the atmospheric pressure or barometric pressure. It is measured using pressure gages and manometers. Absolute pressure is the pressure measured with respect to the true zero pressure reference.

44. Negative gage pressure Positive gage pressure (Absolute Vacuum)

45. Food for the brain: Unless otherwise specified, the term pressure, means gage pressure . Where: = absolute pressure = atmospheric pressure = gage pressure     Standard Atmospheric Pressures: = 14.7 psi = 101.325 Kpa = 1 atm or 1 atmosphere = 760 mm Hg = 29.92 in Hg = 760 torr = 1.013 bar

46. Ex. The pressure 8 ft below the free surface of a liquid is 2.4 psi. What is the specific gravity of the liquid? Ans. 0.692

47. Given: Solution:  

48. Ex. The gage on a condenser shows a vacuum of 24 inches of mercury. What is the absolute pressure in psi? Ans. 2.91 psi

49. Given: Solution:  

50. Ex. What is the gage pressure in the tank of water 2 m below the water surface? Ans. 19.62 KPa

51. Given: Solution:  

52. Ex. How high does a mercury barometer stand on a day when atmospheric pressure is 98.6 KPa ? Ans. 739 mm

53. Given: Solution: *  

54. VARIATION OF PRESSURE WITH DEPTH IN A FLUID

55. Note: FFS stands for Free Fluid Surface which refers to fluid surface subject to zero gauge pressure.  

56. PRESSURE RELATION DUE TO DIFFERENT LEVELS OF FLUID h c h b h a P 1 P 2 Fluid a Fluid b Fluid c +   Where: = pressure at level 1 (top of fluid) = pressure at level 2 (bottom of fluid) = specific weight of the given fluid h = head of the given fluid  

57. Ex. An open tank contains 9.4 ft of water beneath 1.8 ft of oil (SG = 0.85). Find the gage pressure at the bottom of the tank. Ans. 4.736 psig Solution: * Note: The oil on the top is understood to be at open atmosphere, thus zero gauge  

58. Ex. A pressure gage 19 ft above the bottom of a tank containing a liquid reads 13.19 psi, another gage at height 14 ft reads 15.12 psi. Compute the specific gravity of liquid. Ans. 0.891 Given: Solution:  

59. PASCAL’S LAW Pascal's law is a principle in fluid mechanics given by Blaise Pascal that states “ that a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere”.

60. PRESSURE HEAD Pressure head is the height “h” of a column of homogeneous liquid of unit weight “ ” that will produce an intensity of pressure “p”. To convert Pressure Head (height) of liquid A to B or or          

61. To Convert Pressure Head (height) of any liquid to water, just multiply its height by its specific gravity MANOMETER A manometer is a tube, usually bent in a from of U, containing a liquid of known specific gravity, the surface of which moves proportionally to changes of pressure. It is used to measure pressure. TYPES OF MANOMETER OPEN TYPE – Open manometer is a tube bent into a U-shape to contain one or more fluids of different specific gravities. It is used to measure gage pressure.  

62. DIFFERENTIAL TYPE – without an atmospheric surface and capable of measuring only differences of pressure. PIEZOMETER – The simplest form of open manometer. It is a tube tapped into a wall of a container or conduit for the purpose of measuring pressure. The fluid in the container or conduit rises in this tube to form a free surface. LIMITATIONS OF PIEZOMETER Large pressures in the lighter liquids require long tubes Gas pressure can not be measured because gas can not form free surface.

63. (a) Open Manometer (b) Differential Manometer (c) Piezometer

64. STEPS IN SOLVING MANOMETER PROBLEMS Ordinarily, it is easier to work in units of pressure head rather than pressure for solving any manometer problem. Draw a sketch of the manometer approximately to scale. Decide on the fluid of which head are to be expressed. Water is more desirable. In most cases, we suggest to use head in water even if there is no water in the system. Starting at a point of know pressure head, number in order the levels of contact of fluids of different specific gravities. Proceed from level to level, add pressure head in going down and subtract pressure head in going up with due regard to the specific gravity of the fluids.

65. Ex. For the tank shown in the Fig., h 1 = 3 m and h 3 = 4 m. Determine the value of h 2. OIL SG = 0.84 WATER WATER       Ans. = 1.19 m  

66. Solution:

67. Ex. In the figure shown what is the static pressure in KPa in the air chamber. OIL SG = 0.80 WATER Ans.   AIR 2 m 3 m 4 m 2 m

68. Solution:

69. Ex. Determine the value of y in the manometer shown in the fig.

70. Solution:

71. Ex. For the manometer setup shown, determine the difference in pressure between A and B.

72. Solution:

73. HYDRAULIC PRESSURE In a hydraulic pressure at both ends are equal, thus its force is directly proportional the cross sectional area of its piston.  

74. Ex. What is the radius of the small piston of a hydraulic press when a force of 20 lbs on it produces a force of 8,000 lbs on the large piston whose diameter is 20 inches? Neglect friction

75. Note: In a hydraulic press, the pressure under the large piston is equal to the pressure under small piston Solution: