Density

1. Density • Specific volume (volume per unit mass), Density, ρ= mass/unitvolume –Slugs/ft3;kg/m3 • Specific weight= weight/volume (lb/ft3; N/m3) • Specific Gravity = density of the fluid/density of water

2. Example 1 • The specific gravity of mercury at 80 0C is 13.4. Determine its density and specific weight at this temperature in both BG and 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 is absolute temperature, and R is gas constant Pressure units: lb/ft2 (psf) ; lb/in2 (psi); N/m2 (Pa) Standard sea-level atmospheric pressure – 14.7 psi; 101.33 kPa Gage pressure + atmospheric pressure = absolute pressure

5. LV5 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.R Ts are expressed in Kelvin or Rankine Lisa Vink, 1/11/2007

7. Example 2 A 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 3 Determine 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 motion because its molecular makeup gives it a lot of internal friction. • A fluid with low viscosity flows easily because its molecular makeup results in very little friction when 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 stressτoccurs at the plate-material interface at equilibrium, P=τA velocity gradient, du / dy =U/b Fluid sticks to the wall=no-slip condition as Rate 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 for several 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 viscosity units 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 at the bottom wall? 2. The shearing stress on a plane parallel to the walls and passing through the centerline? at 2. Along the midplane. where Shearing stress;

18. Page 20. Compressibility of Fluids How the density of a fluid change with pressure? Bulk , modulus units 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·p A 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, supersonic For isoentropic process , For air at 60 0F, k=1.40 and R=1716 ft. lb/slug. oR; c=1117 ft/s For water at 20C, Ev =2.19 GN/m2, ρ = 998.2 kg/m3; c =1481 m/s or 4860 ft/s