Presentation on theme: "Density, ρ= mass/unitvolume –Slugs/ft3;kg/m3"— Presentation transcript:
1 Density, ρ= mass/unitvolume –Slugs/ft3;kg/m3 • Specific volume(volume per unit mass),• Specific weight=weight/volume(lb/ft3; N/m3)• Specific Gravity =density of thefluid/density of water
2 Example 1 The specific gravity of mercury at 80 0C is 13.4. Determine its density and specificweight at this temperature in both BGand SI units,
3 Figure 1.1 (p. 10)Density of water as a function of temperature.
4 Ideal/Perfect Gas Law /Equation of State • Gases are highly compressible, gas density changes with pressure and temperature as,where p is the absolute pressure, ρ the density, T isabsolute temperature, and R is gas constantPressure units: lb/ft2 (psf) ; lb/in2 (psi); N/m2 (Pa)Standard sea-level atmospheric pressure – 14.7 psi; kPaGage pressure + atmospheric pressure = absolute pressure
5 Ts are expressed in Kelvin or Rankine Lisa Vink, 1/11/2007 R is different for each gas and is determined from R=Ru/M where Ru is the universal gas constant, Ru=8.314 kJ/kmol.K=1.986 Btu/lbmol. RLV5Ts are expressed in Kelvin or Rankine Lisa Vink, 1/11/2007
7 Example 2A compressed air tank has a volume of 0.84 ft 3. When the tank is filled with air at a gage pressure of 50 psi, determine the density of the air and the weight of air in the tank.
8 Example 3Determine the density, specific gravity and mass of the air in a room whose dimensions are 4 m x 5 m x 6 m at 100 kPa and 25 C
9 Viscosity Viscosity is a measure of a fluid's resistance to flow. It describes the internal friction of a moving fluid.A fluid with large viscosity resists motionbecause its molecular makeup gives it a lot ofinternal friction.• A fluid with low viscosity flows easily becauseits molecular makeup results in very little frictionwhen it is in motion.
11 Fluid motion can cause shearing stresses Figure 1.2 (p. 13)(a) Deformation of material placed between two parallel plates. (b) Forces acting on upper plate.
12 Figure 1.3 (p. 14)Behavior of a fluid placed between two parallel plates.Shear stressτ occurs at the plate-material interface at equilibrium, P=τAvelocity gradient, du / dy =U/bFluid sticks to the wall=no-slip conditionasRate of shearing strain
13 Figure 1.4 (p. 15) Newtonian Fluids Linear variation of shearing stress with rate of shearing strain for common fluids.; μ= absolute or dynamic viscosity
14 Figure 1.5 (p. 16)Variation of shearing stress with rate of shearing strain forseveral types of fluids, including common non-Newtonian fluids.Units of Viscosity –lb.s/ft2; N.s/m2
15 Figure 1.6 (p. 17)Dynamic (absolute) viscosity of some common fluids as a function of temperature.For gases,For liquids,Kinematic viscosityunits are / ft2 ; m2 /s
16 Example 4 Reynolds number A Newtonian fluid having a viscosity of 0.38 N.s/m2 and a specific gravity of 0.91 flows through a 25 mm diameter pipe with a velocity of 2.6 m/s. Determine the values of the Reynolds number using (a) SI and (BG) units
17 Figure E1.5 (p. 19) velocity , profile 1. What is the shearing stress atthe bottom wall?2. The shearing stress on a planeparallel to the walls and passingthrough the centerline?at2. Along the midplane. whereShearing stress;
18 Compressibility of Fluids Page 20.How the density of a fluid change with pressure?Bulk , modulusunits of bulk modulus , lb/in2 ( psi ) or N/m2 (Pa)Liquids are considered incompressible
19 Compression and expansion of Gases Isothermal process :For isentropic process ;For an isothermal process,EV=p; For Isoentropic process, EV=k·pA cubic foot of helium at an absolute pressure of 14.7 psi is compressed isentropically to ½ ft3. What is the final pressure?
20 Speed of Sound • Acoustic velocity, speed of sound, c • Depends on change in pressure and density• Mach number, Ma = velocity of air/velocity of sound• Ma<1, subsonic; Ma>1, supersonicFor isoentropic process ,For air at 60 0F, k=1.40 and R=1716 ft. lb/slug. oR; c=1117 ft/sFor water at 20C, Ev =2.19 GN/m2, ρ = kg/m3; c =1481 m/s or 4860 ft/s