1. 1 FLUID PROPERTIES Chapter 2 CE319F: Elementary Mechanics of Fluids

2. 2 Fluid Properties Define “characteristics” (fingerprint) of a fluid Properties expressed by basic “dimensions” –length, mass (or force), time, temperature Dimensions quantified by basic “units” We will consider: systems of units, some important fluid properties, and the dimensions associated with those properties.

3. 3 Systeme International (SI) Length = meters (m) Mass = kilograms (kg) Time = second (s) Force = Newton (N) –Force required to accelerate 1 kg @ 1 m/s 2 –Acceleration due to gravity (g) = 9.81 m/s 2 –Weight of 1 kg at earth’s surface = W = mg = 1 kg × 9.81 m/s 2 = 9.81 kg-m/s 2 = 9.81 N Temperature = Kelvin (K) –273.15 K = freezing point of water –K = 273.15 + o C

4. 4 Systeme International (SI) Work and energy = Joule (J) J = N*m = kg-m/s 2 * m = kg-m 2 /s 2 Power = watt (W) = J/s SI prefixes: G = giga = 10 9 c = centi = 10 -2 M = mega = 10 6 m = milli = 10 -3 k = kilo = 10 3  = micro = 10 -6

5. 5 English System Length = foot (ft) = 0.3048 m Mass = slug or lbm (1 slug = 32.2 lbm = 14.59 kg) Time = second (s) Force = pound-force (lbf) –Force required to accelerate 1 slug @ 1 ft/s 2 Temperature = ( o F or o R) – o Rankine = o R = 460 + o F Work or energy = ft-lbf Power = ft-lbf/s –1 horsepower = 1 hp = 550 ft-lbf/s = 746 W Banana Slug Mascot of UC Santa Cruz

6. 6 Intensive vs. Extensive Property Intensive property: independent of mass of system – temperature, pressure, density Extensive property: value depends on system size –total mass, total volume, total momentum Specific property = extensive property / mass –example: specific volume = V/m

7. 7 Density Mass per unit volume (e.g., @ 20 o C, 1 atm) –Water  water = 1,000 kg/m 3 (62.4 lbm/ft 3 ) –Mercury  Hg = 13,500 kg/m 3 –Air  air = 1.205 kg/m 3 Densities of gases = strong f (T,p) = compressible Densities of liquids are nearly constant (incompressible) for constant temperature Specific volume = 1/density

8. 8 Example A 5-L bottle of carbon tetrachloride (CCl4) is accidentally spilled onto a laboratory floor. What is the mass of carbon tetrachloride that was spilled in lbm. Assume a density of 1,590 kg/m 3 for CCl4.

9. 9 Specific Weight Weight per unit volume (e.g., @ 20 o C, 1 atm)  water = (998 kg/m 3 )(9.81 m/s 2 ) = 9,790 N/m 3 [= 62.4 lbf/ft 3 ]  air = (1.205 kg/m 3 )(9.81 m/s 2 ) = 11.8 N/m 3 [= 0.0752 lbf/ft 3 ]

10. 10 Specific Gravity Ratio of fluid density to density of water or air at STP (e.g., @ 20 o C, 1 atm) –WaterSG water = 1 –MercurySG Hg = 13.6 –AirSG air = 1 Note: SG is dimensionless and independent of system of units

11. 11 Example The specific gravity of a fresh gasoline is 0.80. If the gasoline fills an 8 m 3 tank on a transport truck, what is the weight of the gasoline in the tank?

12. 12 Ideal Gas Law P = absolute (actual) pressure (Pa = N/m 2 ) V = volume (m 3 ) n = # moles R u = universal gas constant = 8.31 J/ o K-mol T = temperature ( o K) R = gas-specific constant R(air) = 287 J/kg- o K

13. 13 Example Calculate the volume occupied by 1 mol of any ideal gas at a pressure of 1 atm (101,000 Pa) and temperature of 20 o C.

14. 14 Example The molecular weight of air is approximately 29 g/mol. Use this information to calculate the density of air near the earth’s surface (pressure = 1 atm = 101,000 Pa) at 20 o C.

15. 15 Vapor Pressure (P vp ) Vapor pressure of a pure liquid = equilibrium partial pressure of the gas molecules of that species above a flat surface of the pure liquid –Concept on board –Very strong function of temperature (P vp up as T up) –Very important property of liquids –When P vp exceeds total air pressure applied at surface, liquid will boil. Pressure at which a liquid will boil for a given temperature –At 10 o C, vapor pressure of water = 0.012 atm = 1200 Pa –If reduce pressure to this value - get boiling of water –Formation of cavitation bubbles –Harm to pipes, pumps, turbines, propellers If P vp > 1 atm compound = gas If P vp < 1 atm compound = liquid or solid

16. 16 Vapor Pressure (P vp ) Vapor pressure of water (and other liquids) is a strong function of temperature. Water

17. 17 Vapor Pressure (P vp ) - continued P vp,H2O = Pexp(13.3185a – 1.9760a 2 – 0.6445a 3 – 0.1299a 4 ) P = 101,325 Pa a = 1 – (373.15/T) T = o K valid to +/- 0.1% accuracy for T in range of -50 to 140 o C Equation for relative humidity of air = percentage to which air is “saturated” with water vapor. How does RH affect drying of building materials, and why? Implications? How does RH affect dust mites? Implications?

18. 18 300  m Dust Mites

19. 19 Example (HW!): Relative Humidity The relative humidity of air in a room is 80% at 25 o C. (a)What is the concentration of water vapor in air on a volume % basis? (b)If the air contacts a cold surface, water may condense (see effects on next slide). What temperature is required to cause water condensation?

20. 20

21. 21 Example: Relative Humidity Continued

22. 22 Elasticity (Compressibility) If pressure acting on mass of fluid increases: fluid contracts If pressure acting on mass of fluid decreases: fluid expands Elasticity relates to amount of deformation for a given change in pressure E v = bulk modulus of elasticity Small dV/V = large modulus of elasticity How does second part of equation come about?

23. 23 Example Given: Pressure of 2 MPa is applied to a mass of water that initially filled 1000-cm 3 (1 liter) volume. Find: Volume after the pressure is applied if E v = 2.2x10 9 Pa

24. 24 Example Based on the definition of E v and the equation of state, derive an equation for the modulus of elasticity of an ideal gas.

25. 25 Surface Tension

26. 26 Surface Tension Below surface, forces act equal in all directions At surface, some forces are missing, pulls molecules down and together, like membrane exerting tension on the surface. surface tension =  magnitude of tension/length   = 0.073 N/m (water @ 20 o C) water air No net force Net force inward Interface

27. 27 Surface Tension Liquids have cohesion and adhesion, both involving molecular interactions –Cohesion: enables liquid to resist tensile stress –Adhesion: enables liquid to adhere to other bodies Capillarity = property of exerting forces on fluids by fine tubes or porous media –due to cohesion and adhesion –If adhesion > cohesion, liquid wets solid surfaces and rises –If adhesion < cohesion, liquid surface depresses at pt of contact –water rises in glass tube (angle = 0 o ) –mercury depresses in glass tube (angle = 130-140 o ) Text section 2-7 (Table 2-4; Appendix A)

28. 28 Example Given: Water @ 20 o C, d = 1.6 mm Find: Height of water W

29. 29 Example Find: Maximum capillary rise of water between two vertical glass plates 1 mm apart. t   h

30. 30 Examples of Surface Tension

31. 31 Example Given: Spherical soap bubble, inside radius r, film thickness t, and surface tension . Find: Formula for pressure in the bubble relative to that outside. Pressure for a bubble with a 4-mm radius?

32. 32 Viscosity Newton’s Law of Viscosity Proportionality constant = dynamic (absolute) viscosity Viscosity Units Water (@ 20 o C):  = 1x10 -3 N-s/m 2 Air (@ 20 o C):  = 1.8x10 -5 N-s/m 2 Kinematic viscosity m 2 /s V V+dvV+dv 1 poise = 0.1 N-s/m 2 1 centipoise = 10 -2 poise = 10 -3 N-s/m 2

33. 33 Effect of Temperature Gases: greater T = greater interaction between molecules = greater viscosity. Liquids: greater T = lower cohesive forces between molecules = viscosity down.

34. 34 See textbook Figure 2-17 (figure) and appendices (tables)

35. 35 Shear in Different Fluids Shear-stress relations for different fluids Newtonian fluids: linear relationship Slope of line = coefficient of proportionality) = “viscosity” Shear thinning fluids (ex): toothpaste, architectural coatings; Shear thickening fluids = water w/ a lot of particles, e.g., sewage sludge; Bingham fluid = like solid at small shear, then liquid at greater shear, e.g., flexible plastics

36. 36 Example: Textbook # 2-43 To be worked on board in lecture.

37. 37 Example A cylindrical weight of 5 lbf falls at a constant velocity inside a cylinder with a diameter of 6.000 inches. The diameter of the weight is 5.995 inches, and its length is 2” as shown in the figure below. The oil film between the weight and cylinder walls is composed of crude oil at 150 degrees F. Determine the velocity of the weight.