3. Physical properties of fluids.pptx yd

It s describing fluids properties

1. Physical properties of fluids Lecture 2

2. Density, Specific weight, Specific Volume, Specific gravity, Viscosity. Newton’s Law of viscosity. Surface tension. Compressibility of fluids. Outline

3. The density , or more precisely, the volumetric mass density , of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho). Mathematically, density is defined as mass divided by volume: where ρ is the density, m is the mass, and V is the volume. In SI its units are kg/m 3 In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. Density

4. The specific weight (also known as the unit weight ) is the weight per unit volume of a material. The symbol of specific weight is γ (the Greek letter Gamma). where is the specific weight of the material (weight per unit volume, typically N/m 3 units) is the density of the material (mass per unit volume, typically kg/m 3 ) is acceleration due to gravity (rate of change of velocity, given in m/s 2 , and on Earth usually given as 9.81 m/s 2 ) A commonly used value is the specific weight of water on Earth at 5°C which is 9.807 kN /m 3 or 62.43 lbf/ft 3 . Specific weight

5. Relation between Specific weight and density

6. In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density: Specific volume is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the meter cubed per kilogram (m 3 /kg or m 3 ·kg −1 ). Sometimes specific volume is expressed in terms of the number of cubic centimeters occupied by one gram of a substance. In this case, the unit is the centimeter cubed per gram (cm 3 /g or cm 3 ·g −1 ). To convert m 3 /kg to cm 3 /g, multiply by 1000; conversely, multiply by 0.001. Specific volume

7. Specific gravity is the ratio of the density of a substance to the density (mass of the same unit volume) of a reference substance. It is also called relative density The reference substance is nearly always water for liquids or air for gases. Specific gravity is commonly used in industry as a simple means of obtaining information about the concentration of solutions of various materials such as brines, hydrocarbons, sugar solutions (syrups, juices, honeys, etc.) and acids. True specific gravity can be expressed mathematically as: Specific gravity

8. Specific gravity

9. Problems

10. Problems

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12. Viscosity can be thought as the internal stickiness of a fluid that represents internal friction. Internal friction forces in flowing fluids result from cohesion and momentum interc hange between molecules The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress. For liquids, it corresponds to the informal notion of "thickness". For example, honey has a much higher viscosity than water. A fluid that has no resistance to shear stress is known as an ideal fluid or inviscid fluid . Otherwise all fluids have positive viscosity. If the viscosity is very high, the fluid will appear to be a solid in the short term. Viscosity

13. A liquid whose viscosity is less than that of water is sometimes known as a mobile liquid, while a substance with a viscosity substantially greater than water is called a viscous liquid. Viscosity of a fluid depends on temperature: In liquids, viscosity decreases with increasing temperature (i.e. cohesion decreases with increasing temperature) In gases, viscosity increases with increasing temperature (i.e. molecular interchange between layers increases with temperature setting up strong internal shear) Viscosity

14. Kinematic viscosity for air & crude oil Increasing temp → increasing viscosity Increasing temp → decreasing viscosity

15. If force P is applied on upper plate as shown, the top plate would be displaced through some small distance δ α The vertical line AB would be rotated through the small angle, δβ , to the new position We note that to resist the applied force, P , a shearing stress τ , would be developed at the plate–material interface, for equilibrium to occur, P = τ A , where A is the effective upper plate area It is well known that for elastic solids, such as steel, the small angular displacement, δβ (called the shearing strain), is proportional to the shearing stress , τ , that is developed in the material. Proof for Viscosity

16. When the force P is applied to the upper plate, it will move continuously with a velocity U, as illustrated in Fig. 1.5. A closer inspection of the fluid motion between the two plates would reveal that the fluid in contact with the upper plate moves with the plate velocity, U, and the fluid in contact with the bottom fixed plate has a zero velocity. The top layer causes a shear stress on adjacent lower layer while the lower on top layer. This shear stress is proportional to rate of change of velocity with respect to y. What happens if the solid is replaced with a fluid such as water? Proof for Viscosity

17. A continuation of this experiment would reveal that as the shearing stress, τ , is increased by increasing P (recall that P = τ A) , the rate of shearing strain or velocity gradient is increased in direct proportion—that is, Proof for Viscosity This result indicates that for common fluids such as water, oil, gasoline, and air the shearing stress and rate of shearing strain (velocity gradient) can be related with a relationship of the form where the constant of proportionality is designated by the Greek symbol μ (mu) and is called the absolute viscosity , dynamic viscosity , or simply the viscosity of the fluid.

18. Units of viscosity. Viscosity is a quantitative measure of a fluid’s resistance to flow. μ= F/ [A×(u/h)], μ = τ /(u/h) N-s/m²

19. Kinematic Viscosity :

20. Units of viscosity/ Newton’s Law of viscosity

21. Newtonian fluids: Fluids in which the shear stress is directly proportional to the rate of shear strain are Newtonian fluids. Non-Newtonian fluids: The term non-Newtonian is used to classify all fluids in which the shear stress is not directly proportional to the rate of shear strain. Newton’s Law of viscosity.

22. Viscosity: Newtonian vs. Non-Newtonian Newtonian Fluids are Linear Relationships between stress and strain: Most common fluids are Newtonian. Non-Newtonian Fluids are Non-Linear between stress and strain Corn Starch Latex Paint Toothpaste Newtonian fluid : shear stress is proportional to shear strain – Slope of line is dynamic viscosity Shear thinning : ratio of shear stress to shear strain decreases as shear strain increases (toothpaste, catsup, paint, etc.) Shear thickening : viscosity increases with shear rate (glass particles in water, gypsum-water mixtures).

23. Problems

24. Problems

25. Problems

26. Problems

27. Vapor Pressure

28. Vapor Pressure Vapor pressure: the pressure at which a liquid will boil. All liquids tend to evaporate when placed in a closed container Vaporization will terminate when equilibrium Is reached between the liquid and gaseous states Of the substance in the container i.e. # of molecules escaping liquid surface = # of incoming molecules Vapor pressure ↑ when temperature increases At atmospheric pressure, water at 100 °C will boil

29. Vapor pressure of liquids Water can boil at lower temperatures if the pressure is lower When vapor pressure > the liquid’s actual pressure Under this equilibrium we call the vapor pressure, saturation pressure At any given temperature, if pressure on liquid surface falls below the saturation pressure, rapid evaporation occurs (i.e. boiling) For a given temperature, the saturation pressure is the boiling pressure

30. What’s happening here? – Bug is walking on water Why is this possible? – It doesn’t weigh much – It’s spreading its weight out – The downward forces are less than the effects of surface tension Surface tension

31. A molecules in the interior of a liquid is under attractive force in all direction. However, a molecule at the surface of a liquid is acted on by a net inward cohesive force that is perpendicular to the surface. Hence it requires work to move molecules to the surface against this opposing force and surface molecules have more energy than interior ones Higher forces of attraction at surface Creates a “stretched membrane effect” The intensity of the molecular attraction per unit length along any line in the surface is called the surface tension and is designated by the Greek symbol σ (sigma). Surface Tension

32. Surface Tension

33. For a given liquid the surface tension depends on temperature as well as the other fluid it is in contact with at the interface. The dimensions of surface tension are FL -1 with BG units of lb / ft and SI units of N/m . Surface tension, σ s : the force resulting from molecular attraction at liquid surface [N/m] surface tension varies with temperature F s = σ s L F s = surface tension force [N] σ s = surface tension [N/m] L = length over which the surface tension acts [m] Surface Tension

34. Surface Tension on Liquid Drop The pressure inside a drop of fluid can be calculated using a free-body diagram: Real Fluid Drops Mathematical Model Surface tension force This force is balanced by the pressure difference D p : Applied to Area Applied to Circumference

35. Surface tension Consider inserting a fine tube into a bucket of water: Meniscus Surface tension vector (acts uniformly along contact perimeter Between liquid and tube) Adhesion of water molecules to the tube dominates over cohesion Between water molecules giving rise to and causing fluid to rise within tube - radius of tube

36. - unit vector in direction of - surface tension (magnitude of ) Given conditions in previous slide, what is ?

37. (weight vector of water) Equilibrium in y-direction yields: Thus with

38. Surface Tension Problems

39. Surface Tension Problems

40. Capillarity Rise and fall of liquid in a capillary tube is caused by surface tension. Capillarity depends on the relative magnitudes of the cohesion of the liquid to walls of the containing vessel. When the adhesive forces between liquid and solid are larger than the liquid's cohesive forces, the meniscus in a small diameter tube will tend to be concave If adhesive forces are smaller than cohesive forces the meniscus will tend to be convex, for example mercury in glass . water mercury concave convex

41. Surface Tension: Capillary Action h is the height, R is the radius of the tube, q is the angle of contact. “Wetted” “Non-Wetted” The weight of the fluid is balanced with the vertical force caused by Surface tension. Adhesion > Cohesion Cohesion > Adhesion Adhesion Cohesion Adhesion Cohesion

42. Surface Tension: Capillary Action Free Body Diagram for Capillary Action for a Wetted Surface: For clean glass in contact with water, q  0°, and thus as R decreases, h increases, giving a higher rise. For a clean glass in contact with Mercury, q  130°, and thus h is negative or there is a push down of the fluid. Equating the two and solving for h:

43. Differences between adhesive & Cohesive A distinction is usually made between an adhesive force, which acts to hold two separate bodies together (or to stick one body to another) and a cohesive force, which acts to hold together the like or unlike atoms, ions, or molecules of a single body.

44. Capillarity Problems

45. Capillarity Problems

46. Capillarity Problems

47. Compressibility of fluids All fluids compress if pressure increases resulting in an increase in density Compressibility is the change in volume due to a change in pressure A good measure of compressibility is the bulk modulus (It is inversely proportional to compressibility)

48. Compressibility of fluids

49. Compressibility From previous expression we may write For water at 15 psi and 68 degrees Fahrenheit, From above expression, increasing pressure by 1000 psi will compress the water by only 1/320 (0.3%) of its original volume Thus, water may be treated as incompressible (density is constant) In reality, no fluid is incompressible, but this is a good approximation for certain fluids