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1
Lec 6: Psychrometrics and Engineering Equation Solver (EES)
2
• 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
3
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.
4
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.
V
RTmp i
i V
TRnp ui
i or
5
Psychrometrics
• The total number of moles is
• Thus the total pressure exerted by a mixture of ideal gases is
V
TnR
V
TRnpp...ppp uu
j
1ii
j
1iij21
j
1ii21 n...nnn
6
Psychrometrics
• The mole fraction y from chemistry is often used
• It can easily be shown that yi is also equal to
n
ny i
i
p
p
n
ny ii
i
7
Psychrometrics
• The mass fraction “mf” is also important in dealing with mixtures, and it is defined as
m
mmf i
i
8
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
iii M
Mmfy
j
1iiijj2211 MyMy...MyMyM
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TEAMPLAYTEAMPLAY
• 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?
10
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.)
11
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”.
va ppp
12
Psychrometrics
• Atmospheric cooling may be regarded as a constant pressure process from 1 to 2 in the figure below.
pi, psia
vi
T2 = 60 °FT1 = 90 °F
12
0.26
0.70
13
Psychrometrics
• Relative humidity is a useful parameter in discussing human comfort. It is defined as
pi, psia
vi
T2 = 60 °F
T1 = 90 °F1
20.26
0.70 3
3
1
Tat sat
v
p
p
p
p
14
TEAMPLAYTEAMPLAY
• 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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TEAMPLAYTEAMPLAY
• Minimize today’s 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--EESTEAMPLAY--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_1=m*x**2 + ln (x)
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TEAMPLAY-- EESTEAMPLAY-- 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 y1=10.
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TEAMPLAY--EESTEAMPLAY--EES
• Go to “Calculate” and select “Solve”.
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TEAMPLAYTEAMPLAY
• 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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TEAMPLAYTEAMPLAY
• 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.”
23
TEAMPLAYTEAMPLAY
• 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.