Density

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Density

• Density, ? mass/unitvolume Slugs/ft3kg/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, ? 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
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LV5
R is different for each gas and is determined
from RRu/M where Ru is the universal gas
constant, Ru8.314 kJ/kmol.K1.986 Btu/lbmol. R
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 stresst occurs at the plate-material
interface at equilibrium, PtA velocity
gradient, du / dy U/b Fluid sticks to the
wallno-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,EVp For Isoentropic
process, EVkp
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
• Malt1, subsonic Magt1, supersonic

For isoentropic process ,
For air at 60 0F, k1.40 and R1716 ft. lb/slug.
oR c1117 ft/s
For water at 20C, Ev 2.19 GN/m2, ? 998.2
kg/m3 c 1481 m/s or 4860 ft/s