KNS 2113 FLUID MECHANICS

1. KNS 2113 FLUID MECHANICS CHAPTER 1: BASIC PROPERTIES OF FLUID Semester 1 Session 2009/2010

2. What is Fluid Mechanics? Fluid mechanics is concerned with the behavior of liquids and gases at rest and in motion.

3. Menu / Contents Objective Characteristics of Fluid Dimensions and Units Measures of Fluid Mass and Weight Ideal Gas Law Viscosity of Fluid Newtonian/Non-Newtonian Fluid Bulk Modulus and Vapor Pressure Surface Tension

4. Objective • After completion of this chapter, student will be able to identify and define the characteristics and mechanics of fluids. Menu

5. Characteristics of Fluids Table 1: Characteristics of fluid compare to solids Menu

6. Characteristics of Fluids • A fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude. • When common solids are acted on by a shearing stress, they will initially deform (usually very small deformation) but they will not continuously deform (flow). • Common fluids such as water, oil, and air satisfy the definition of a fluid – that is they will flow when acted on by a shearing stress. Figure 1: Fluid will flow when acted by shearing stress. Menu

7. Dimensions and Units • Fluid characteristics can be described qualitatively in terms of certain basic/primary quantities such as length, time, and mass. • The qualitative description is conveniently given in terms of certain primary quantities such as given in Table 2. Table 2: Primary quantities Menu

8. Dimensions and Units • These primary quantities can then be used to provide a qualitative description of any other secondary quantities . Example: area = L2, velocity = LT-1 • British Gravitational (BG) System. In this system, the unit of length is foot (ft), time unit is second (s), force unit is pound (lb) and temperature is the degree Fahrenheit (°F) or the absolute temperature unit is the degree Rankine (°R) • International System (SI) iswidely used. In this system length is meter (m), time is second (s), mass unit is kilogram (kg) and temperature is kelvin (K). Menu

9. Dimensions and Units Table 3: The seven basic dimensions and their SI units Menu

10. Dimensions and Units Table 4: The secondary dimensions with their SI units Menu

11. Dimensional Homogeneity • Dimensions of the left side of the equation must be the same as those on the right side. • FLT and MLT systems • Where L-length, T- time, M-mass • or L-length, T- time, F-force • where Newton’s Law states that force is equal to mass time acceleration, F=MLT-2 or M=FL-1T2

13. Dimensional Homogeneity

14. Measures of Fluid Mass and Weight Density • The density of a fluid, ρ (rho) is defined as its mass per unit volume. • Units: Kilograms per cubic metre, kg/m3 (or kg m-3) • Dimensions: ML-3 • Typical values: Water=1000 kg/m3, Mercury=13546 kg/m3, Air= 1.23 kg/m3 (at pressure = 1.013 x 10-5 N/m2 and Temperature = 288.15 K) Menu

15. Measures of Fluid Mass and Weight Specific weight • Specific weight of a fluid, γ is defined as its weight per unit volume. • Specific weight is related to density through the equation γ=ρg where g is the local acceleration of gravity. • Units: Newton per cubic metre N/m3 • Dimensions: ML-2T-2 Menu

16. Measures of Fluid Mass and Weight Specific gravity • The specific gravity of a fluid, designated as SG, is defined as the ratio of the density of the fluid to the density of water at some specified temperature. • In equation form, Menu

17. Measures of Fluid Mass and Weight Specific volume • Specific volume, ν, is the volume per unit mass and is therefore the reciprocal of the density; that is: ν = 1/ρ Menu

18. Ideal Gas Law • Gases are highly compressible in comparison to liquids, with changes in gas density directly related to changes in pressure and temperature through the equation p=ρRT • The equation above is commonly termed the ideal or perfect gas law. • It is known closely approximate the behavior of real gas under normal conditions when the gases are not approaching liquefication. Menu

19. Ideal Gas Law Question A compressed air tank has a volume of 0.84 ft3. When the tank is filled with air at the gage pressure of 50 psi, determine the density of the air and the weight of air in the tank. Assume the temperature is 70°F and the Atmospheric pressure is 14.7 psi (abs). Menu

20. Ideal Gas Law Solution The air density can be obtain from the ideal gas law as, So that, Menu

21. Ideal Gas Law Note that both the pressure and temperature were changed to absolute values. The weight of the air, W is equal to So that since 1 lb = 1 slug∙ft/s2 Menu

22. Viscosity of Fluid Dynamic Viscosity • Dynamic viscosity, μ is defined as the shear force per unit area (or shear stress, τ) required to drag one layer of fluid with unit velocity past another layer a unit distance away. • Units: Newton seconds per square metre, N s m-1 or kilograms per meter per second, kg m-1s-1 Menu

23. Viscosity of Fluid Kinematic Viscosity • Kinematic Viscosity, ν, is defined as the ratio of dynamic viscosity to mass density. • Units: square metres per second, m2 s-1 Menu

24. Newtonian / Non-Newtonian Fluid • Fluids which the shearing stress is linearly related to the rate of shearing strain are designated as Newtonian fluids. Most fluids are Newtonian. • Fluids for which the shearing stress is not linearly related to the rate of shearing strain are designated as non-Newtonian fluids. Shear thinning fluids viscosity decreases with increasing shear rate. Shear thickening fluids viscosity increases with increasing shear rate. Menu

25. Newtonian / Non-Newtonian Fluid Menu

26. Newtonian / Non-Newtonian Fluid Question Menu

27. Newtonian / Non-Newtonian Fluid Solution Menu

28. Newtonian / Non-Newtonian Fluid Menu

29. Bulk Modulus and Vapor Pressure • A property that is commonly used to characterize compressibility is the bulk modulus, Ev, where dp is the differential change in pressure needed to create a differential change in volume, dV, of a volume V. The negative sign is included since an increase in pressure will cause a decrease in volume. Since a decrease in volume of a given mass, m=ρV, will result in an increase in density, the equation can also be expressed as Menu

30. Bulk Modulus and Vapor Pressure • If a container is closed with a small air space left above the surface, and this space evacuated to form a vacuum, a pressure will develop in the space as a result of the vapor that is formed by the escaping molecules. When an equilibrium condition is reached so that the number of molecules leaving the surface is equal to the number entering, the vapor is said to be saturated and the pressure that the vapor exerts on the liquid surface is termed the vapor pressure. Menu

31. Surface Tension • A liquid, being unable to expand freely, will form an interface with a second liquid or gas. Molecules deep within the liquid repel each other because of their close packing. Molecules at the surface are less dense and attract each other. • Since half of their neighbors are missing, the mechanical effect is that the surface is in tension and cohesive forces in the surface tend to hold the molecules together. The surface behave like membrane or skin, stretched over the fluid. Menu

32. Surface Tension • If the spherical is cut in half, the force developed around the edge due to surface tension is 2πRσ. This force must be balanced by the pressure difference, ∆p, between the internal pressure, pi and the external pressure, pe acting over the circular area, πR2. Thus • It is apparent from this result that the pressure inside the drop is greater than the pressure surrounding the drop. Menu

33. Surface Tension • Surface tension causes a fluid interface to rise or fall in a capillary tube. Menu

34. Surface Tension Menu

35. Surface Tension Question Menu

36. Surface Tension Solution Menu

37. Tutorial 1: Dimensions and Units

38. Tutorial 1: Dimensions and Units

39. Point to remember

40. THANK YOU ANY QUESTION?