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Pasos para calcular las propiedades psicrometricas del aire humedo.Basico para materias donde trabajen con aire
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ELSEVIER
Applied Energy 48 (1994) I lg ~: 1994 Elsevier Science Limited
Printed in Great Britain. All rights reserved 0306-2619/94/$7.00
Psychrometric Properties of Humid Air: Calculation Procedures
Y. O. Devres
T U B I T A K Marmara Research Centre, Food and Refr igera t ion Technology Department ,
P.O.Box 21, 41470 Gebze-Kocaeli ,Turkey
A BSTRA CT
Knowledge of the psychrometric properties is essential during the designing of air conditioning, cold storage, and drying processes where humid air is a working fluid. In this study detailed procedures Jor calculating psychro- metric properties are given. Seven main properties of the psvchrometrics, namely dry-bulb, wet-bulb and dew-point temperatures, atmo~spheric pressure, humidity ratio, relative humidity and enthalpy can be calculated using the given procedures. According to the Gibbs Phase Rule, in the humid air case, any three intensive properties will be sufficient to evaluate the remaining properties. Therefore the combination of three out of seven properties gives a total of 35 different sets. Computer soJhvare has been developed and utilised to obtain the psychrometric properties q/" humid air. It was Jound that given three input parameters, the remaining four parameters could, except in three cases, can be calculated with neglLgible error.
NOTATION
h Enthalpy of humid air (kJ/kg) hs* Enthalpy of humid air at saturation at the thermodynamic wet-bulb
temperature (kJ/kg) hw* Specific enthalpy of condensed water at the thermodynamic wet-
bulb temperature and a pressure of 101 325 Pa (kJ/kg) Pw Partial pressure of water vapour in humid air (Pa) Pws Pressure of saturated pure water (Pa) P Total pressure of humid air (Pa) Ra Gas constant for dry air (J/kg K) T Dry-bulb temperature (°C)
1
2 Y .o . Devres
7* Wet-bulb temperature (°C) TD Dew-point temperature (°C) v Specific volume of humid air (m3/kg) W Humidity ratio of humid air (kg/kg) W S Humidity ratio of humid air at saturation (kg/kg) Ws* Humidity ratio of humid air at saturation at thermodynamic wet-
bulb temperature (kg/kg)
o~ Parameter defined in Table 2 /3 Parameter defined in Table 3 p. Degree of saturation ~b Relative humidity
INTRODUCTION
In the study of the processes of air conditioning, cold storage and drying, a knowledge of the psychrometric properties of the working fluid, that is humid air, is essential. In general, the psychrometric properties of a medium can be predicted either analytically by recourse to the laws for gases or by consulting specially prepared charts and tables. Using these charts, if the atmospheric pressure or altitude is known, it is easy to find the psychrometric properties using two other known properties. However, during the designing, for instance, of a cold store, in most cases its altitude is different from sea level. And yet, most of the charts available in the references are based on sea level properties. Therefore, finding psychrometric properties from zero-altitude charts can create errors. Although the best method for finding these properties is to calculate them analytically using the perfect gas relationships, in many situations, it is often neither convenient nor practical. A realistic solution for these problems is to employ a computer for the numerical solution of the relevant equations: the psychrometric properties being defined in the software.
There are seven main different properties in the psychrometric charts, namely dry-bulb, wet-bulb and dew-point temperatures, atmospheric pressure, humidity ratio, relative humidity and enthalpy. ~ According to the Gibbs Phase Rule, there are four degrees of freedom for a system consisting of humid air, assuming it to be a mixture of nitrogen, oxygen, and water vapour. For all practical purposes the ratio of the masses of oxygen and nitrogen in air is constant, hence the degrees of freedom are reduced to three. Thus any three intensive properties will be sufficient to evaluate the remaining properties. 2 Therefore the combination of three out of seven properties gives a total of 35 different sets. These are shown
TA
BL
E 1
C
om
bin
atio
n S
ets
of
Sev
en P
sych
rom
etri
c P
rop
erti
es,
Eac
h S
et C
om
pri
sin
g T
hre
e P
rop
erti
es
1 T
T*
T D
6 T
T
* P
10
T
T*
W
13
T
T*
¢
15
T
T*
h
16
T*
T D
P
20
T*
T D
W
23
T*
T D
25
T*
T D
h
26
T D
P
W
29
T D
P
¢
31
T D
P
h
32
P W
¢
34
P W
h
1351
w
+ hi
2 T
T
D
P 3
T
P W
7 T
T
D
W
8 T
P
¢
11
T T
D
¢ 12
T
P h
14
T
T D
h
17
T*
P W
21
T*
P ¢
24
T*
P h
27
T D
W
¢
30
T D
W
h
33
P +
hi
4 T
W
¢
9 T
W
h
15IT
+
hi
18
T*
W
22
T*
W
1'9I
T"
+ hi
28
T D
¢
h ]
T
Dry
-bu
lb t
emp
erat
ure
T*
Wet
-bul
b te
mp
erat
ure
T D
D
ew-p
oin
t te
mp
erat
ure
P P
ress
ure
W
Hum
idit
y ra
tio
¢ R
elat
ive
hu
mid
ity
h E
ntha
lpy
'5
4 Y . o . Devres
in Table 1. In this study, each set is used separately in an attempt to find solutions for the remaining unknown variables. In some cases analytical solutions were not found and numerical methods had to be employed.
METHOD
Psychrometric equations
For the determination of psychrometric properties, a knowledge of the water-vapour saturation-pressure is essential. The equations for calculating saturation pressures for the temperature ranges -100°C to 200°C are given in Table 2. The solutions for the saturations vapour-pressure as a function of temperatures were found with REGAN, 3 using polynomial REGression ANalysis on data obtained from ASHRAE. 4 In some cases however, the saturation pressure was known allowing the temperature to be calculated from the data. In such cases, temperatures calculated using saturation pressures where derived from regression analysis are shown in Table 3.
The definition of psychrometric properties can be given very easily where perfect gas relations are employed. ~ As a result, only equations (in total 28 equations) are given in Table 4. In every equation, in order to obtain the property given in the second column, the known properties given in the third column must be replaced in the equation given in the fourth column. The units of each property are shown in the last column.
Recommended procedures for the calculation of psychrometric properties
Calculation procedures are shown in Table 5. With the following steps, it is easy to calculate the unknown properties. In some cases, however, numerical analyses must be employed for solution.
RESULTS AND DISCUSSION
In the computer program, 32 out of the 35 combinations have been solved successfully. In combinations 9, 11 and 26 (see Table 5), the equa- tions could not be solved. In each of these cases, two of the equations differed only by a numerical factor, effectively reducing the number of free parameters and not permitting non trivial solutions.
A computer program was developed in F O R T R A N for calculating the psychrometric properties. Nine subroutines were written for numerical solution. For 32 cases, all the properties were calculated with only small
TA
BL
E 2
C
alc
ula
tio
n o
f W
ate
r-V
ap
ou
r S
atu
rati
on
Pre
ssu
re w
hic
h i
s D
ep
en
de
nt
on
th
e T
em
pe
ratu
re w
ith
in V
ari
ou
s T
em
pe
ratu
re
Ra
ng
es
a=
A.
T2
+B
.T+
C+
D.T
1
Tin
K
Pw~
=
10
00
.
ex
p (
a),
Pw~
in P
a
Tem
per
atu
re
( K)
21
3.1
5 <
T
<
27
3-1
5
27
3.1
5 _
< T
<
32
2-1
5
32
2.1
5 <
T
<
37
3.1
5
37
3.1
5
<_ T
<
4
23
-15
4
23
.15
<
T <
4
73
-15
A
-0.7
29
75
93
70
7
. 10
5
B
+0
-53
97
42
07
27
.
10 2
C
+0
.20
69
88
06
20
. l0
+2
D
-0.6
04
22
75
12
8.
10 +
4
+0
.12
55
00
19
65
.
10 4
-0.1
92
35
95
28
9
. 10
-l
+0
-27
05
10
1
89
9.
10 +
2
0.6
34
40
1
15
77
.
10 +
4
+0
-12
46
73
21
57
.
10 4
-0.1
91
5
46
58
06
.
l0
I
+0
.27
02
38
83
1
5 .
10 +
2
0.6
34
09
4 1
63
9
. 10
+4
+0
-12
04
50
76
46
.
10 4
-0.1
86
66
50
55
3
. l0
1
+ 0
.26
8 3
62
94
0 3
.
l0 +
2
-0.6
31
6
97
20
63
.
10 +
4
+0
.10
69
73
01
83
. 10
-4
-0-1
69
89
65
75
4.
10 1
+0
.26
1 4
07
32
98
.
10 +
2
-0.6
22
07
8
12
30
.
10 +
4
TA
BL
E 3
C
alc
ula
tio
n o
f T
em
pe
ratu
re w
hic
h i
s D
ep
en
de
nt
on
Wa
ter
Va
po
ur
Sa
tura
tio
n P
ress
ure
wit
hin
Va
rio
us
Te
mp
era
ture
R
an
ge
s
T-
E
.134
+ F
. ~3
+ G
. ~
2 +
H
. fi
+ K
, T
in K
13 -
In
(p
,J,
p,~
in
Pa
Pre
s,~u
re (
Pa
/
1 _
<p
<6
11
6
1t
_<p
<
12 3
50
12
35
0_
<p
<
10
14
20
1
01
42
0_
<p
<4
76
20
7
47
6 2
07
<-p
<
1 5
55
09
9
e~
-W
E
+0
-10
04
92
65
34
F +
0.1
39
29
1 7
63
3
G
~ 0
.28
15
15
15
74
H
+0
-73
11
62
11
19
K
+0
.21
25
89
37
34
10 2
+
0.5
03
10
62
50
3.
10 2
+
0.1
20
95
12
51
7
. 10
4
+0
.24
67
29
10
16
. 10
I
+0
.27
48
40
24
84
. 10
4
10 2
0
.88
26
77
93
80
. 10
1
-0.3
54
55
42
10
5.
10 +
° -0
.93
67
11
2
88
3.
10 +
° 0
.10
68
66
13
07
. 10
~1
10 +
~ ~
0.1
24
36
88
44
6.
10 *
l +
0.5
02
08
58
47
9.
10 *
l +
0-1
51
41
42
33
4.
10 *
2 +
0.1
74
29
64
96
2.
10 *
2
10 +
1 +
0.3
38
85
34
29
6.
l(Y
I
-0-2
05
03
01
05
0.
10 +
2 0
.98
82
41
75
01
.
10 +
2 -0
.11
61
20
85
32
. 10
~
10 -~
~
0.2
15
00
7 7
99
3
. 10
*~
+0
-27
18
58
54
32
. 10
*~
+ 0
-49
9 5
09
29
4 8
.
10 ~
~
0.5
47
26
1
81
20
.
10 +
~
TA
BL
E 4
C
alcu
lati
on o
f P
sych
rom
etri
c P
rope
rtie
s
Eq.
No.
T
o ob
tain
K
now
n(s)
E
quat
ion
Rem
arks
1 Pw
s T
a=
A
. T
2 +
B.
T+
C
+D
. •l
Pw
s =
10
00
.ex
p(a
)
T i
n K
, Pw
s in
Pa
for
con
stan
ts s
ee T
able
2
2 T
Pw
~ T
=E
. /3
4+
F.
/33+
G.
/32
+ H
. /3
+ K
/3
=ln
(Pw
~)
T i
n K
, Pw
s in
Pa
for
con
stan
ts s
ee T
able
3
3 P
w
To
a=A
. T
t~+
B.
T o
+
C+
D.
To
I Pw
=
10
00
.ex
p(a
)
T O
in K
, Pw
in
Pa
for
con
stan
ts s
ee T
able
2
4 T
O
Pw
T
D=
E./
34
+F
./3
3+
G./
32
+H
./3
+K
/3
= I
n (p
w)
T D
inK
,pw
inP
a fo
r co
nst
ants
see
Tab
le 3
5 p*
s T
* o
t=A
. T
.2+
B
. T
* +
C+
D
. T
* i
P*s
= 1
00
0.e
xp
(a)
T*
in K
, P
*s i
n P
a fo
r co
nst
ants
see
Tab
le 2
6 h
T,
W
h =
T+
W
. (2
501
+ 1-
805.
T
) T
in °
C,
hin
kJ
/kg
h -
25
01
. W
7
T
h,W
T
- 1
+ 1-
805.
W
T
in
°C,
h in
kJ/
kg
e~
h-T
8
W
h, T
W
=
T i
n °C
, h
in k
J/k
g
2501
+
1-80
5.
T
9 W
P
, Pw
W
= 0
.621
98
- Pw
P
and
Pw
in
Pa
P -
Pw
10
P
Pw
, H
/ P
= 0.
621
98
• ~
"+
p,,
P an
d p
,~ i
n P
a W
11
p~
P,
W
12
W~
P,
Pw~
13
P
Pw
~, W
~
14
Pw~
P,
W~
15
~7
P, P
*~
16
p *
14'*
P
,,vs
~
.
17
p~
P
, W
~
18
W*
h,
W,
T*
P.W
P
w
W
+ 0.
621
98
W,
= 0-
621
98
. P
'~
P -
Pw~
P =
0-62
1 98
•
py~
+ P
w~
w~
p,,~
=
0.62
1 98
•
e W
~ +
0.62
1 98
p*~
14 7
= 0-
621
98
• --
--
p -
p*
P 0.
621
98
• p*
~ t
p*~
w*
P.
W*
p*
~-
W*
+
0.62
1 98
w,*
= h
*-h
+
W
h*
Pan
dp
~in
P
a
P an
d P
w~
in P
a
P an
d p
,~.~
in P
a
P an
d p
,,,~
in P
a
P an
d p
{~ i
n P
a
P an
d p
*~ i
n P
a
P an
d p
*~ i
n P
a
/7":
T
* +
(250
1 +
1.8
05
. T
*).
W
*
h*
=4
.18
6.
T*
h, h
* h
* i
n k
J/k
g,
T*
in °
C
ca
7
TA
BL
E
4--
-co
ntd
Eq.
No.
T
o ob
tain
K
no
wn
(s)
Equ
atio
n R
ema
rks
19
W
W.*
,h,
T*
W-
h-h
*+
W
*
h*
20
W
Ws*
, T
, T
* W
=
(250
1 -
2.38
1 .
T*
).
W*
-
(T-
T*
)
25
01
+
1.80
5 .
T-
4.1
86
. T
*
21
T*
W~
, W
, T
T
* =
22
W*
W
, T
, T
*
23
T
W,
T*,
W
~*
24
th
Pw,
Pw~
25
pw
4,, p
w~
26
Pws
4~, P
w
27
/.z
IV,
W s
28
v T
,P,
W
25
01
. (W
s* -
W
) -
T.
(1
+ 1
-80
5.
W)
2.3
81
. W
*
-4.1
86
. W
- 1
Ws ,
_- (
2501
+
1.80
5 .
T
- 2-
381
. T
*).
W
+
(T
- T
*)
25
01
-
2.38
1 .
T*
T=
(2
501
- 2.
381
. T
*).
W
*
- (2
501
- 4-
186
. T
*).
W
+
T*
~b =
PJP
ws
P~
= 4
). P
ws
Pw
s =
Pw
/q~
R a
. T
Y
z
__
1 +
1.8
05
. W
- (1
+
1-60
78.
W)
P
h*
=
T*
+
(2 5
01
+ 1
.80
5.
T*
).
IV*
hw*
-- 4
.18
6
. T
*
h, h
* *
T*
°C
s,
hw
in
kJ/
kg
, in
T a
nd
T
* i
n °C
T a
nd
T
* i
n °C
T a
nd
T
* i
n °C
Tan
d
T*
in°C
Pw a
nd
Pw
s in
Pa
Pw a
nd
Pw
~ in
Pa
Pw a
nd
Pw
s in
Pa
R a
--
287-
055
J/k
g.
K
v in
m3/
kg,
T i
n K
, P
in P
a
e~
Psychrometric properties 0[" humid air 9
TABLE 5 Recommended Procedures for the Calculation of Psychrometric Properties
Proc. Known Step To Use Remarks no. properties no. obtain eqn(s)
1 T, T*, TD 1 Pws 1 2 p*s 5 3 Pw 3 4 P 9, 15, 18 Replace eqns (9) and (15) in eqn (18), then solve
the resulting equation using numerical analysis
2 T, TD, P
3 T , W , P
4 T , W , d )
5 W 9 6 W s 12 7 w* 15 8 h 6 9 ~b 24
1 Pws 1 2 Pw 3 3 W 9 4 W S 12 5 T* 15, 21
6 P*s 5 7 Ws* 15 8 h 6 9 ~ 24
1 Pw~ 1 2 Pw 11 3 TD 4 4 W s 12 5 T* 15, 21
6 P*s 5 7 W* 15 8 h 6 9 4~ 24
1 Pws 1 2 Pw 25 3 P 10 4 TD 4 5 W s 12 6 T* 15, 21
7 P*s 5 8 ~ 15 9 h 6
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
I C~mtinued)
10 E O. Devres
TABLE 5--contd
Proc. Known Step To Use Remarks no. properties no. obtain eqn(s)
5 T , (o ,h 1 Pw~ 1 2 Pw 25 3 W 8 4 P I0 5 T D 4 6 W s 12 7 T* 15, 21 Replace eqn (15) in eqn (21), then solve the
resulting equation using numerical analysis
6 T , T * , P
7 T, TD, W
8 T ,c~ ,P
8 P*s 5 9 W* 15
1 Pws 1 2 P*s 5 3 W* 15 4 W 20 5 W~ 12 6 Pw 11 7 T D 4 8 h 6 9 ~b 24
1 Pw~ 1 2 Pw 3 3 P 10 4 W, 12 5 T* 15, 21
6 p*~ 5 7 W* 15 8 h 6 9 cb 24
1 Pws 1 2 Pw 25 3 W 9 4 W~ 12 5 T o 4 6 T* 15, 21
7 Pw*~ 5 8 W* 15 9 h 6
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Psychrometric properties o f humid air 11
TABLE 5---contd.
Proc. Known Step To Use Remarks no. properties no. obtain eqn ( s )
9 T, IV, h UNRESOLVABLE
10 T, T*, W 1 p,,, 1 2 p*~ 5 3 w* 22 4 P 16 5 w~ 12 6 p,, 11 7 T D 4 8 h 6 9 4' 24
11 T, TD, 05 UNRESOLVABLE
12 T, h, P 1 p,,~ 1 2 W 8 3 p,,. 11 4 T D 4 5 w~ 12 6 T* 15, 21
13 T, T*,05
14 T, tl, T D
7 p*.~ 5 8 W* 15
s
9 4' 24
1 p,,,~ 1 2 p,, 25 3 T D 4 4 p*~ 5 5 P 9, 20
6 W 9 7 w~ 12 8 w~ 15 9 h 6
1 Pws 1 2 W 8 3 Pw 3 4 P 10 5 w, 12 6 T* 15, 21
7 p*~ 5 8 w~* 15 9 4' 24
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (9) in eqn (20), then solve the resulting quadratic equation
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
{ ' iO l l f t l l l i , d ,
12 Y.O. Devres
TABLE ~-contd.
Proc. Known Step To Use Remarks no. properties no. obtain eqn(s)
15 T, T*, h 1 Pws 1 2 W 8 3 P*s 5 4 W* 22 5 P 16 6 p~ 11 7 T D 4 8 W s 12 9 ~ 24
16 T*, T D, P 1 Pw 3 2 p*~ 5 3 W* 15 4 W 9 5 T 23 6 P,,,s 1 7 W s 12 8 h 6 9 ~b 24
17 T*, P, W 1 Pw 11 2 TD 4 3 p*s 5 4 W* 15 5 T 23 6 Pw~ 1 7 Ws 12 8 h 6 9 ~b 24
18 T*, W, 1 p*~ 2 7"
3 Pws 4 P 5 ws 6 w* 7 Pw 8 TD 9 h
5 1, 10, 20, Replace eqn (25) in eqn (10), then solve the
25 resulting equation with eqns (1) and (25) using numerical analysis
1 10, 25
12 15 11 4 6
Psychrometric properties o f humid air 13
TABLE 5---contd.
Proc. Known Step To Use Remarks no. properties no. obtain eqn(s)
19 T*, ~b, h 1 P*s 5 2 T 8, 9, 15, Replace eqns (9) and (25) in eqn (8) and solve
18, 25 for P(T), then substitute P(T) in eqn (18) with eqn (15) and solve the resulting equation using numerical analysis Use P(T) found in step 2
20 T*, TD, W
21 T*, 4', P
22 T*, W, h
3 P 4 Pw~ 1 5 w, 12 6 Pw 25 7 T D 4 8 W 9 9 W* 15
1 Pw 3 2 P 10 3 p*~ 5 4 W* 15 5 T 23
6 Pws 1 7 W~ 12 8 h 6 9 4~ 24
1 p*~ 5 2 w* 15 3 T 9, 20, 25
4 Pw~ 1 5 W~ 12 6 W 9 7 Pw 25 8 T D 4 9 h 6
1 P*s 5 2 T 7
3 Pws 1 4 W* 22 5 P 16 6 Pw 11 7 T D 4 8 w, 12 9 ¢b 24
Replace eqns (9) and (25) in eqn (20) and solve the resulting equation using numerical analysis
; ( )mlmued)
14 Y.O. Devres
TABLE 5 contd.
Proc. Known Step To Use Remarks no. properties no. obtain eqn(s)
23 T*, T D,4~ 1 Pw 3 2 p*s 5 3 Pws 26 4 T 2 5 P 9, 15, 20 Replace eqns (9) and (15) in eqn (20) and solve
the resulting quadratic equation
24 T*, P, h
25 T*, T D, h
26 TD, P, W
27 T D, W , ~
6 W 9 7 W* 15 8 W~ 12 9 h 6
1 p*~ 5 2 w* 15 3 W 19 4 Pw 11 5 TD 4 6 T 7 7 Pw~ 1 8 W~ 12 9 ~ 24
1 P*s 5 2 Pw 3 3 P 9, 15, 18
4 W 9 5 T 7 6 Pws 1 7 W~ 12 8 W* 15 9 4~ 24
UNRESOLVABLE
1 Pw 3 2 Pw~ 26 3 T 2 4 P l0 5 W~ 12 6 T* 15, 21
7 P*s 5 8 w * t5 9 h 6
Replace eqns (9) and (15) in eqn (18) and solve the resulting quadratic equation
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Psychrometric properties q f humid air 15
TABLE ~ c o n t d
Proc. Known Step To Use Remarks no. properties no. obtain eqn(s)
28 T D, oh, h 1 Pw 3 2 Pws 26 3 T 4 W 8 5 P 10 6 W~ 12 7 T* 15, 21 Replace eqn (15) in eqn (21), then solve the
resulting equation using numerical analysis
29 TD, P, c~
30 T D, W, h
31 TD, P , h
8 p*~ 5 9 W* 15
1 Pw 3 2 Pw~ 26 3 T 2 4 W 9 5 w~ 12 6 T* 15, 21
7 P*s 5 8 w* 15 9 h 6
1 Pw 3 2 P 10 3 T 7 4 Pws 1 5 W~ 12 6 T* 15, 21
7 P*s 5 8 W* 15 9 4~ 24
1 Pw 3 2 W 9 3 T 7 4 Pw~ 1 5 w~ 12 6 T* 15, 21
7 P*s 5 8 w* 15 9 ~h 24
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
r ~ o H l i t i l l c d !
16 Y.O. Devres
TABLE 5~contd.
Proc. Known Step To Use Remarks no. properties no. obtain eqn(s)
32 P, W, ~h 1 Pw 11 2 T D 4 3 Pws 26 4 T 2 5 Ws 12 6 T* 15, 21 Replace eqn (15) in eqn (21), then solve the
resulting equation using numerical analysis 7 P*s 5 8 W* 15 9 h 6
33 P, ~, h 1 T 6, 9, 25
34 P, W,h
35 w, 4~,h
2 Pws 1 3 W~ 12 4 Pw 25 5 T D 4 6 W 9 7 T* 15, 21
8 P*s 5 9 W* 15
1 T 7 2 Pws 1 3 Pw 11 4 T D 4 5 Ws 12 6 T* 15, 21
7 P*s 5 8 w * 15 9 q~ 24
1 T 7 2 Pws 1 3 Pw 25 4 T D 4 5 P 10 6 W s 12 7 T* 15, 21
8 p*~ 5 9 W* 15
Replace eqns (9) and (25) in eqn (6) and solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
Replace eqn (15) in eqn (21), then solve the resulting equation using numerical analysis
TA
BL
E 6
R
esul
ts o
f P
rope
rtie
s fo
r D
iffe
rent
Com
bina
tion
Set
s
Pro
per
ty
Ca
lcu
lati
on
s
Co
mb
ina
tio
n
Co
mb
ina
tio
n
Co
mb
ina
tio
n
Co
mb
ina
tio
n
Co
mb
ina
tio
n
set
no.
6 se
t no
. 12
se
t no
. 19
se
t no
. 2
7
set
no.
33
T (
°C)
20-0
00*
20.0
00*
19-9
99
20.0
00
20.0
00
T*
(°C
) 15
.000
" 15
.000
15
.000
" 15
.000
15
-000
T
D (
°C)
11.7
55
11.7
55
11.7
55
11.7
55"
11.7
55
P (P
a)
101
325"
000*
10
1 32
5"00
0*
101
323"
823
101
324-
057
101
325"
000*
W
(g/
kg)
8-58
9 8"
589
8"58
9 8"
589*
8"
589
~"
4~ (%
) 59
"008
59
"009
59
"008
* 59
"008
* 59
"008
* "4
h
(kJ/
kg)
41 "7
91
41 "
791"
41
"79
1 *
41 "7
91
41-7
91 *
~
p,~
(Pa)
2
338.
879
2 33
8-87
9 2
338.
879
2 33
8.90
0 2
338-
894
p*~
(Pa)
1
705.
505
1 70
5.51
8 1
705.
505
1 70
5.52
4 1 7
05.5
18
,~.
p,~.
(Pa)
1
380.
122
1 38
0.14
2 1
380.
126
1 38
0.13
8 I 3
80.1
35
W~
(g/k
g)
14.6
96
14.6
96
14.6
97
14-6
97
14.6
96
W*
(g/k
g)
10.6
48
10.6
48
10.6
49
10.6
49
10.6
48
* K
now
ns.
-7,
18 Y.O. Devres
errors. In some cases, however, especially when P was not known, a maximum + 0.5% error occurred. In the other cases, errors considerably smaller than this were obtained.
The results of different combination sets are given in Table 6. In com- bination set no. 6, the properties are calculated without any numerical analysis procedures. In combination sets 12, 19, 27 and 33, however, numerical analysis techniques were employed (see Table 5). In the columns of Table 6, '*' following the data indicates the known psychrometric properties. The calculated values are shown with three digits for comparison. However, no significant differences between any combination sets were found.
CONCLUSION
When humid air is used as a working fluid, it is essential to use reliable data for any necessary calculations. A good method to perform these calculations is by the use of computer software embodying the properties of perfect gases. In this study such software has been developed and utilised to obtain the psychrometric properties of humid air. It was found that given three input parameters, the remaining four parameters could, except in three cases, be calculated with negligible error.
R E F E R E N C E S
1. ASHRAE, Fundamentals Handbook, Psychrometrics. American Society of Heating, Refrigeration and Air-Conditioning Engineers, New York, 1981, Chapter 5, pp.l-10.
2. Agrawal, K.K. & Rao, H.V., A computer model of psychrometric properties of air. ASAE Transactions, 17 (1) (1974) 67-9.
3. Devres, Y.O., Curve-fitting (regression analyses) VAX package computer programme using least-square methods. TI[IBITAK Marmara Research Centre, Food and Refrigeration Technology Publications No.121, Gebze-Kocaeli, 40 p.
4. ASHRAE, Fundamentals Handbook, Psychrometric Tables. American Society of Heating, Refrigeration and Air-Conditioning Engineers, New York, 1981, Chapter 6, pp.l-16.