Lec 6: Psychrometrics and Engineering Equation Solver (EES)

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Lec 6 Psychrometrics and Engineering Equation
Solver (EES)
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• For next time
• Read 3-6 to 3-7
• Outline
• Property diagrams
• Psychrometrics and relative humidity
• EES Example
• Important points
• How to use the property tables
• How to plot a process in a property diagram
• How to use relative humidity

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Psychrometrics

• Air may be dealt with as a mixture of
  non-reacting ideal gases.
• Dry air is air with no water vapor.
• Moist air contains water vapor.
• Dry air may be regarded as a mixture of
  nitrogen, oxygen, argon, carbon dioxide, and
  trace amounts of other gases--for example, neon,
  helium and methane.

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Psychrometrics

• A useful model of a mixture of ideal gases is the
  Dalton model
• Each component i behaves as if it were alone in
  the mixture at the temperature T of the mixture
  and volume V occupied by the mixture.

or
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Psychrometrics

• The total number of moles is
• Thus the total pressure exerted by a mixture of
  ideal gases is

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Psychrometrics

• The mole fraction y from chemistry is often used
• It can easily be shown that yi is also equal to

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Psychrometrics

• The mass fraction mf is also important in
  dealing with mixtures, and it is defined as

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Psychrometrics

• One can show that
• Where Mi is the molecular weight of the ith
  component of the mixture and M is the molecular
  weight of the mixture, given by

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TEAMPLAY

• What are the mole fractions of the two
  constituents if 1 lbm of argon is mixed with 1
  lbm of helium?
• What is the molecular weight of the resulting
  mixture?

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Psychrometrics

• These relationships are good for mixtures of
  ideal gases in general.
• The components of air, even the water vapor,
  behave as ideal gases in general.
• (The water vapor behaves as an ideal gas because
  its pressure and temperature are relatively low.)

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Psychrometrics

• However, an additional complication introduced by
  the water vapor is the fact that it will condense
  if its partial pressure pi in the mixture reaches
  the saturation pressure.
• Consider the atmosphere at pressure p to be
  mixture of dry air a and water vapor v.

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Psychrometrics

• Atmospheric cooling may be regarded as a constant
  pressure process from 1 to 2 in the figure below.

pi, psia
0.70
1
0.26
2
T1 90 F
T2 60 F
vi
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Psychrometrics

• Relative humidity ? is a useful parameter in
  discussing human comfort. It is defined as

pi, psia
3
0.70
1
0.26
2
T1 90 F
T2 60 F
vi
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TEAMPLAY

• Work problem 3-58

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Engineering Equation Solver (EES)

• Solves non-linear algebraic equations faster than
  one can do by hand.
• Unknown variable can appear anywhere in the
  equation, even on either side of the equal sign.
• Provides a database of thermodynamic tables such
  as those in your book.

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EES

• Allows parametric studies too tedious to assign
  as homework by hand.
• Parametric tables work much like spreadsheets.
• Allows plotting quickly and easily.

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TEAMPLAY

• Minimize todays lecture and get to the desktop.
• Click on the desktop icon for EES 32, --no
  password is required.
• Click OK until you get a blank screen.
• Click on File and then New.
• The next screen should be an Equations Window.

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TEAMPLAY--EES

• Consider a simple problem y1 mx2 ln x
• If you wanted to know x(y), this was a trial and
  error solution not too long ago, for most folks.
• Enter it into EES thusly y_1mx2 ln (x)

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TEAMPLAY-- EES

• After you have entered the sample equation,
  select Windows, Formatted Equations to see
  how it looks. Notice that the y_1 is now y1,
  etc.
• Return to equations window and enter y110.

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TEAMPLAY--EES

• Go to Calculate and select Solve.

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TEAMPLAY

• Parametric studies
• In the previous TEAMPLAY problem, let us vary y1
  from 1 to 8 in increments of 1 (8 runs) and see
  how x varies.
• Under Tables, select New Parametric Table
• Click and drag the variables you want to see to
  the right--x, y1 and maybe others.

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TEAMPLAY

• See that y1 is not specified in the problem
  statement in the Equations Window.
• Enter y1 via Alter Values under Tables
• Click on the column headings to be able to enter
  units.
• You must solve the table before you can plot it.
• Under Calculate select Solve Table.

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TEAMPLAY

• Under Plot select New Plot Window and X-Y
  Plot.

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Obtaining a copy of EES for your computer

• Available from SELL (Software Evaluation
  Licensing Lab) in Teague 1105.
• Take a blank CD and they will burn one for you.
  May have to return to pick up.
• Alternatively, check out a CD there which you
  must return. Right now, waiting list.
• Everything you need should be on the CD,
  including a manual.
• The copy will expire August 31, 2004.