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**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 the fluid/density of water

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**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,

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Figure 1.1 (p. 10) Density of water as a function of temperature.

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**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; kPa Gage pressure + atmospheric pressure = absolute pressure

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

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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.

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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

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**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.

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**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.

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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=τA velocity gradient, du / dy =U/b Fluid sticks to the wall=no-slip condition as Rate of shearing strain

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**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

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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

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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

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**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

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**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;

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**Compressibility of Fluids**

Page 20. 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

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**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?

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**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 = kg/m3; c =1481 m/s or 4860 ft/s

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Statics CEE 331 July 14, 2015 CEE 331 July 14, 2015

Statics CEE 331 July 14, 2015 CEE 331 July 14, 2015

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