airdry massapor water vmass Humidity Specific ω
% Humidity Relative airdry lbper su,h,v,
T ,Tp
bulbwet bulbdry
φ
Properties
ProcessesHeating and coolingCooling and dehumidificationMixingHumidificationZone
Air Handling Unit Systems
Psychrometrics – air water vapor mixtures1) Ideal Mixing2) Ideal Gas Air3) Ideal Gas Water Vapor4) Adiabatic Saturation5) Four Psychrometric Processes
IDEAL MIXING – IDEAL GASES
( )mixmixi
imix
___
iii
iii
V,Tpp Law Daltons - Mixing Ideal
V
TRnp V
TRmp Gas Ideal
∑=
==
+ +…+ =V)(T,
p 1
V)(T,p 2
V)(T,p n
V)(T,p mix
( )mixmixi
imix
___
iii
iii
p,TVV Law Agamats - Mixing Ideal
p
TRnV p
TRmV Gas Ideal
∑=
==
+ +…+ =p)(T,
V 1
p)(T,V 2
p)(T,V n
p)(T,V mix
Binary Ideal Gas Mixture
∑
∑
∑
=
=
=
−
sameTsameV
i
sameTsameV
i
sameTsameV
i
uu
hh
ppDaltonLawGibbs
mixture. theof V and T same at thealonecomponent theof value
property -property partialIdeal Mixing
Real Mixing
componentexcesspA
BA pp +
Afraction x mole
componentexcesspA
Afraction x mole
2
1
2
1
2
1
2
1
2211
23
TT
pp
TT
vv
LAW CHARLES
vpvp LAW BOLYES
)0 and atm (1 STP at gas of /molemolecules 106.023
liters. 22.4 gasany of mole (1) One
LAW SAVOGADRO'
=
=
×=×
×
=
Co
*
IDEAL (PERFECT) GAS LAW
pv RT pV mRT
RRmolecular weight
==
=
o o
p - absolute pressure, psia, kPa T - absolute temperature, R, K
o*
o o
air
3*
o o
ft lbf R R 1545.15 lb mole
ft lbf R ft lbf R R =1545.15 /28.96 = 53.35lb mole lbm
kJ kPa mR 8.314 orkmole K kmole K
mass moles Molecular Weight
=
=
= ×
*
*
m n Molecular Weight
pv R T pV nR T
= ×
=
=
Ideal Gas Law
( )
o
o o
2 2 2
3
o
3
The specific volume of air at 75 F and 14.7 psia
53.35 ft lbf / lbm R 459.69 R 75 FRTvp 14.7 lbf / in 144 in / ft
v 13.476 ft /lb
The specific volume of air at 24 C and 101.325 kPa
.287 kPa m /kgRTvp
× += =
×
=
= =( )o o
2
3
273.15 K 24 F101.325 kPa
v .8417 m /kg
× +
=
12)(3 vv
vRTp and
vRTp ngsubstituti
11)(3 pp
RTVp
RTVp
saturationat or water vapmassor water vapmass actual
gas idealan is ter vapor that waassume saturationat or water vapmass
or water vapmass actualhumidity Relative
w
g
gg
ww
g
w
saturation
g
w
−=φ
==
−=φ
==φ
=φ=
Relative Humidity
( ) ( ) 14b)(3 pp
p6219.pp29
p 18ω
pMW pMW
TMWT/cVp
TMWT/cVp
airdry massor water vapmassω
ppp ,MWT
constantR
gases ideal areapor water vandair assume airdry mass
or water vapmassω Fraction, Mass Humidity, Specific
mixture. theof mass theNOT is NCALCULATIO OF BASIS
airdry kgm ,air dry lb air.dry of mass NCALCULATIO OF BASIS
wambient
w
wambient
w
aa
ww
air
air
water
water
airwaterambient
m
−−
=−×
×=
××
=
×
×
==
+==
=
SPECIFIC HUMIDITY
( )
Tc ωTch gases ideal as steam andair both with
h ωTch properties steam Table and gas, idealan asair with
kgh kgωh kJ/kgh
17)(3 h ωhh
kJ/kg ,BTU/lb HHH
vapor air dry kgmkJ/ vapor,air dry lbBTU/ air.dry of massper apor water vngaccompanyi theofenthalpy
theplusair dry theofenthalpy theis mixture theofenthaply Theair.dry of mass NCALCULATIO OF BASIS
pp
vp
waterv
wateradryair
va
dryairdryairwair
m
+=
+=
+
=
−+=
+=
++
kJkgkg
kJ
dryairdryair
ENTHALPY
Specific Volume( )mixmix
iimix V,Tpp Law Daltons - Mixing Ideal
∑=
+ =V)(T,
p a
V)(T,p w
V)(T,p atm
airdry /lbft p
TRmVv
pTRmV
3
air
air
air
air
air
airairair
==
×=
airdry /lbft p
TRωm
Vv
waterlbft
airdry lb waterlb
pTRωmV
pTRmV
3
water
water
air
water
3
water
waterairwater
water
waterwaterwater
×==
×=
=
mixwaterair VVV ==
( )
( )
F55.1.2149pat TT28.071094.7.009275.24h
@ThωTch
ft 13.638144.2151
75)(459.6985.84.0092pRTω
mVv
ft 13.676144.215114.7
75)(459.6953.35pRT
mVv
RTpvVVV
airdry water/lblb .0092ω.215114.7
.2151.622ω
ppp
2918ω
psia .2151.4302.5p@75pp
psia 14.69barometer 50%, F,75
ovdp
vp
3
wa
w
3
aa
a
wa
watm
w
w
g
w
o
===
=×+×=
×+×=
=×
+××=×==
=×−+×
===
===
=−
=
−=
=×=
=
=
φ
φ
lb/ft 13.7v
F55Tairdry BTU/lb 28.5h
airdry water/lblb .093ωChart ricPsychromet
3
odp
=
=
==
28.14h13.68v.00924ω
AirH2O EES
===
airdry lbBTU/ 8.511105.2.0252100.24h60% ,100at
airdry BTU/lb 241105.20.100.24h0% ,100at
ωhhh
O
O
vaporairdry
=×+×==
=×+×==
+=
φ
φ
100 F
24 BTU/lbm
51.8 BTU/lbm
( )
( ) ( )
( )( )
( )( )
( )( )
( )( )wbdb
wbfdbg
wbdbpfg2wb
f2g1
21pfg221
fg22f2g1121p
fgf2g2
21pa2a1
f2g22f2g112aa1
g222af21f22g11a1
g222af212g11a1
outvapor airaddedwater invapor air
T,Tfω
21d)(3 hh
TTchωω
hhTTchω
ω
hω)h(hωTTc
hhh
)T(Tchhng,substituti
hhωhhωhh
hωhhωhωhωh
hωhhωωhωh
HHH0ΔPE0,ΔKE 0,W 0,Q
EquationEnergy FlowSteady dryairunit mass 1n calculatio of basis
=
−−
−−=
−
−−=
=−+−
=−
−=−
−=−+−
+=−++
+=−++
=+====
++
Adiabatic Saturation
2wb
1db
( )( )
( ) airdry b water /llb 006789.2.1069
2.7459.1409.343.1103
966624.2.105601369.)T(
)T(h)T(h)TT(c)T(h)T(
)T(
airdry b water /llb .01369.316514.7
.3165.622)(Tpp
)(Tp.622)ω(T
1056.2 34.09 .3165 66 T1103.3 96T
hh h p T
hh
TTchωω
db
wbfdbg
dbwbpwbfgwbdb
wbsaturationatm
wbsaturationwb
wb
db
g fgf
wbfdbg
wbdbpfg2wb
=−
=−
−×+×=ω
−
−+×ω=ω
=−
×=−
×=
−
−−=
96 F db66 F wb14.7 atmSpecific Humidity ?
F 96Tdb =
F 66Twb =)T( wbω
Adiabatic Saturation
( )( ) ( )
g1 db v
g1 g1 db
g1 g2 wb db wb
g1 g db wb db
g1
g1
1) h saturation vapor enthalpy @(T T ,p p )
2) h h @ T
3) h h @ T .45 T T
4) h h @ 0 F .44 T T 1061.8 .44 T
for 75F db,70 F wb1) h 1094.07 BTU/ lb dry air Exact
2) h 1093.8
= = =
=
= + × −
= + × − = +
=
=
g1
g1
3 BTU/lb dry air easiest to use
3) h 1093.91 BTU/lb dry air most accurate approximation
4) h 1094.80 BTU/lb dry air
=
=
dbT
T wbT
s
2
v1h
f2h
g2h
g1h
0T =
34
wdb,
v1
p Tat vaporheatedsuper h =
1
3-10
.004389.203529
.2035.622ω
.00649.2956829
.29568.622ω
Hgin .29568.7392.4p ppp
p.622ω
1g
2
g2v2
vatm
v2
=−
=
=−
=
=×=φ=−
=
( )
( )
airdry lb
waterlb .00323.00326.00649ωω a)
.00326ω3.021079.2
1074.1.0043894035.24ω
35at h40at h35at hωTTc
ω
12
1
1
lv
fg g121p1
=−=−
=−
×+−=
−
+−=
140 F
1g35 F
35 F
.003ω
.005ω.006ω
PsychCD
1
1g
2
=
==
1
2
(6) p
TRωvv
(5) p
RT1vv
VOLUMESPECIFIC
(4) T@p
pHUMIDITYRELATIVE
)3(hh
)T(Tc)h(ωω
)2(pp
p622.
pp
2918ω
pppHUMIDITYSPECIFIC
)T8.14.2500(ωT005.1h)1()T44.8.1061(ωT24.h
@Thhωhhh
ENTHALPY
vapor
dbvaporvapor
air
dbair
dbsaturation
vapor
wbliquid
db vapor
dbwbpairwbfg
vaporatm
vapor
air
vapor
airvaporatm
dbdb
dbdb
dbgvapor
vaporair
×==
×==
=
−−+×
=
−==
+=
×+×+×=×+×+×=
=
+=
φ
(5) from vfind pT with (4) from find p with
itterationby (3) fromT find ω with
(2) from p find ω with (1) fromT findh with
ω andh select repeatedly pselect
Chart ricPsychromet a Build To
vapordb,
vapor
wb
vapor
db
atm
φ
db
dbwb
andT andTT
ionsSpecificatPoint State HVACCommon
φ
φωvhp
ppTT
air
vapor
atm
wb
db
.44 1.8 c
1.0 4.18 c
.24 1.005air cEnglish Metric
vapor waterp
waterliquid p
p
ω
dbT
ω
dbT
ω
dbT
ω
dbT
Heating-Cooling Cooling-Dehumidification
Mixing Humidification
PSYCHROMETRIC PROCESSES
Heating Cooling
heating
kJ T,18.1m ΔT 1.005 mQ
BTU T,45.m ΔT .24 mQ
BTU kJ, T,cm ΔT c mQΔh mΔh mQ
varyingv,T,constantp
constantω
airdry airdry
airdry airdry
waterpairdry pairdry
rwater vapoairdry airairdry
bulbdry
w
∆+=
∆+=
∆+=
+=
==
=
ω
ω
ω
ω
φ
ω
bulbdry Theating
coolingQ
T (F) P (psia) h (Btu/lbm) Cp (Btu/lbm*R)
33 0.0923 1076.4 0.45134 0.0961 1076.8 0.45135 0.1000 1077.2 0.45136 0.1040 1077.7 0.45137 0.1082 1078.1 0.45138 0.1126 1078.5 0.45139 0.1171 1079.0 0.45140 0.1217 1079.4 0.45141 0.1266 1079.9 0.45242 0.1316 1080.3 0.45243 0.1367 1080.7 0.45244 0.1421 1081.2 0.45245 0.1476 1081.6 0.45246 0.1533 1082.0 0.45247 0.1592 1082.5 0.45248 0.1653 1082.9 0.45349 0.1716 1083.4 0.45350 0.1781 1083.8 0.45351 0.1849 1084.2 0.45352 0.1918 1084.7 0.45353 0.1990 1085.1 0.45354 0.2065 1085.5 0.45355 0.2141 1086.0 0.45456 0.2221 1086.4 0.45457 0.2303 1086.8 0.45458 0.2387 1087.3 0.45459 0.2474 1087.7 0.45460 0.2564 1088.2 0.45461 0.2657 1088.6 0.45462 0.2753 1089.0 0.45563 0.2851 1089.5 0.45564 0.2953 1089.9 0.45565 0.3058 1090.3 0.45566 0.3166 1090.8 0.45567 0.3278 1091.2 0.45568 0.3393 1091.6 0.45669 0.3511 1092.1 0.45670 0.3634 1092.5 0.45671 0.3759 1092.9 0.45672 0.3889 1093.4 0.45673 0.4023 1093.8 0.45674 0.4160 1094.2 0.45675 0.4302 1094.7 0.45776 0.4448 1095.1 0.45777 0.4598 1095.5 0.45778 0.4752 1096.0 0.45779 0.4911 1096.4 0.45780 0.5075 1096.8 0.45781 0.5243 1097.3 0.458
T (F) P (psia) h (Btu/lbm) Cp (Btu/lbm*R)
82 0.5416 1097.7 0.45883 0.5594 1098.1 0.45884 0.5778 1098.6 0.45885 0.5966 1099.0 0.45886 0.6160 1099.4 0.45887 0.6359 1099.9 0.45988 0.6564 1100.3 0.45989 0.6774 1100.7 0.45990 0.6990 1101.1 0.45991 0.7213 1101.6 0.45992 0.7441 1102.0 0.45993 0.7676 1102.4 0.46094 0.7917 1102.9 0.46095 0.8164 1103.3 0.46096 0.8418 1103.7 0.46097 0.8680 1104.2 0.46098 0.8948 1104.6 0.46199 0.9223 1105.0 0.461
100 0.9505 1105.4 0.461101 0.9795 1105.9 0.461102 1.0092 1106.3 0.461103 1.0398 1106.7 0.461104 1.0711 1107.2 0.462105 1.1032 1107.6 0.462106 1.1362 1108.0 0.462107 1.1700 1108.4 0.462108 1.2047 1108.9 0.462109 1.2402 1109.3 0.463110 1.2767 1109.7 0.463111 1.3141 1110.1 0.463112 1.3524 1110.6 0.463113 1.3916 1111.0 0.463114 1.4319 1111.4 0.464115 1.4731 1111.8 0.464116 1.5154 1112.3 0.464117 1.5587 1112.7 0.464118 1.6030 1113.1 0.464119 1.6485 1113.5 0.465
T (C) P (kPa) h (kJ/kg) Cp (J/g*K)
1 0.6571 2502.7 1.88532 0.7060 2504.6 1.88633 0.7581 2506.4 1.88744 0.8136 2508.2 1.88845 0.8726 2510.1 1.88946 0.9354 2511.9 1.89047 1.0021 2513.7 1.89158 1.0730 2515.6 1.89269 1.1483 2517.4 1.893610 1.2282 2519.2 1.894711 1.3130 2521 1.895812 1.4028 2522.9 1.896913 1.4981 2524.7 1.89814 1.5990 2526.5 1.899115 1.7058 2528.3 1.900216 1.8188 2530.2 1.901317 1.9384 2532 1.902518 2.0647 2533.8 1.903619 2.1983 2535.6 1.904720 2.3393 2537.4 1.905921 2.4882 2539.3 1.907122 2.6453 2541.1 1.908223 2.8111 2542.9 1.909424 2.9858 2544.7 1.910625 3.1699 2546.5 1.911826 3.3639 2548.3 1.91327 3.5681 2550.1 1.914328 3.7831 2551.9 1.915529 4.0092 2553.7 1.916730 4.2470 2555.5 1.91831 4.4969 2557.3 1.919332 4.7596 2559.2 1.920633 5.0354 2561 1.921934 5.3251 2562.8 1.923235 5.6290 2564.5 1.924536 5.9479 2566.3 1.925937 6.2823 2568.1 1.927238 6.6328 2569.9 1.928639 7.0002 2571.7 1.9340 7.3849 2573.5 1.931441 7.7878 2575.3 1.932942 8.2096 2577.1 1.934343 8.6508 2578.9 1.935844 9.1124 2580.6 1.937345 9.5950 2582.4 1.938846 10.0990 2584.2 1.940347 10.6270 2586 1.941948 11.1770 2587.8 1.943549 11.7520 2589.5 1.9451
THERMODYNAMIC PROPERTIES OF SATURATED WATER VAPOR (NIST)
Mixing
1
2
( ) ( )
( ) ( )
( ) ( )
3 3 1 1 2 2
1 23 1 2
1 2 1 2
1 2m 1 2
1 2 1 2
1 2
1 2 1 2
m h m h m hm mh h h
m m m mm mω ω ω
m m m mm m and scale
m m m m
= +
= ++ +
= ++ +
+ +
3 ω
dbT1
2
m1
2
3
( ) ( )( )( )
1 3 1 3
1 p 3 1 2 p 2 3
2 31
2 3 1
Δq Δqm c T T m c T T
T Tm (does not scale)m T T
→ →=
− = −
−=
−
( ) ( )
( ) ( )
( )
( )
( )
airdry g18.478kJ/khg2519.8kJ/kkg/kg .0033410K kJ/kg 1.005h
hωTchkg/sec 12.443.041812.401m
kg/sec .0418m10)(273.15/kgm kPa 8.314/18
/secm 10kPa .547RT
Vpm
kg/sec 014.12m10)(273.15/kgm kPa .287/secm 10547.kPa 101.325
RTVpm
kPa547.ppp
p .62200334.
kg/kg00334.ωkJ/kg 20.98kJ/kg 2519.8
kJ/kg 2477.7kg/kg .0054105kJ/kgK 1.005ω
@Th@Th@ThωTTc
ω
kg/kg .0054kPa .8721kPa 101.325
kPa .8721.622ω
ppT @.622pω
1
1
v11dbpa1
m
v1
3
3w
v1
a1
3
3a
a1
v
vatm
v
1
1
wbwdbv
wbfgg1dbwbpa1
g1
vatm
wbvg1
=×+×=
×+==+=
=+×
×==
=+×
×−==
=−
=
=−
×+−=
−×+−
=
=−
×=
−=
kJ/kg 30.5h and kg/kg 6ω read
in 1.65819.51312.443in 2.6
mpoint to2point from distance
kJ/kg 30.22h
h19.513
7.07h19.51312.443h
kgdryair/kgwater00575.ω
19.513
7.0719.51312.443ω
mmmωmωmωm
airkJ/kgdry 50.9hkg07.707.7m
07.701.mm
air /secdry kg 7/kgm .858
6m
airdry /kgmixture m .858v
g/kg 10ωChart
mm
m
21m
m
21m
21m
2211mm
2
2
2a2v2
3a2
32
2
==
=×
=
+=
=
ω+ω=
+=+=
==+=
=×=×ω=
==
=
=
Chart
Calculated
( )
( )
Load Total CoilLoad Sensible CoilSHF
FactorHeat Sensible Coil
Factor Bypass Coil ,TTTTb
TT b1T b
T ch since,hh b1h b
balanceenergy
1mmb
1mm
mm
mmmsaturation tocooled mass -m
coolednot and bypassed mass - m
d1
d2
2d1
p
2d1
total
tc
total
tc
total
b
totaltcb
tc
b
=
−−
=
=−+
==−+
=+
=+
=+
1
2 3
tPoin DewApparatus
T dp
23 hhLoad Sensible Coil
−
21 hhLoad Total Coil
−
COILPERFORMANCE
Cooling Dehumidification
( ) ( )
( )
( )
q
q QQ
QSHF Factor,Heat Sensible
)hω(ω)h)(hω(ωq)h(hω)h)(hω(ωhhq
LATENT SENSIBLE
)h)(hω(ω)h(hω)h)(hω(ωhhm
Q)h(hω)h)(hω(ω)h)(hω(ω)hω(ω)hωh(ω
)h(hω)h)(hω(ω)h)(hω(ω-hω)hω(ωhωpaths, Tconstant and ωconstant ngSelectingi path. oft independen are changesProperty
)hω(ωhωhωhhm
Q)hω(ωmQ)hω(hm)hω(hm
sensible
sensible
latentsensible
sensible
fg21l2v121latent
v2v12l2l121a2a1sensible
l1v121v2v12l2l121a2a1dryair
v2v12l2l121l1v121l221v22v11
v2v12l2l121l1v121v11l221v22
2 liquid21v22v11a2a1dryair
l221av22a2av11a1a
latentq+=
+=
−=−−=−+−−+−=
−−+−+−−+−=
−+−−+−−=−−−−−−−−−−=−+
−−−+−=
−+++=+
Q
Δω
21
2apparatusdpT
1
humidity. relative 95% F, 40ohumidity t relative 60% F, 80 fromcation dehumidifi and Cooling
( )
.369.3365.2
5.2qq
qSHR
airdry Btu/lb 9.336q8.)(1096..0045)(.0131q
)hω(ω)h)(hω(ωq
airdry lbBtu/ 5.2.394.00784.8q1078.5)(1096.00458)(48.0045)(.013140)(80.24q
)h(hω)h)(hω(ωhhq
airdry lb water/ lb .0045.6.106414.7
.6.1064.622ω
airdry lb water/ lb .0131.6.304214.7
.6.3042.622ω
ppp
2918ω
latentsensible
sensible
latent
latent
fg21l2v121latent
sensible
sensible
v2v12l2l121a2a1sensible
2
1
vatm
v
=+
=+
=
=−×−=
−=−−=
=++=−×+−×−+−×=
−+−−+−=
=×−
××=
=×−
××=
×−×
=φ
φ
8. 48. h1078.5 1096. h.1064 .3042p
95% 60% 40 80 T2 1Pt
PROPERTIES
l
v
v
φ
Adiabatic Humidification
=sensibleQ
( ) ( )( ) ( ) h water washh ωωQ
tionhumidifica steam hh ωωQ
ΔhωmΔhmQ
liquid 1 vapor212latent
vapor1 vapor212latent
rwater vapo1airdry airairdry sensible
−−=
−−=
+=
1
2
1
2
BTU/lb 1164hsteam psi 30
w =
BTU/lb 0h waterF32
w
o
=
1 2
( )a 1 w w a 2
1 2 1 w 2
2 1w
2 1
w
m h +m h =m h (3-36)h + ω -ω h =hh -h =h (3-38b)ω -ωΔh =h (3-39)Δω
Conditioned Space
S - supply
R - return,space conditions
( )
( )
latentsensible
sensible
RfgSR
liquidR
vaporRSR
airdry
latent
airdry
waterliquidpSRairdry
vaporwaterpSairdry
airp
vaporwaterSair
airdry
sensible
liquid SS vaporRRrwater vapoSairairdry
sensible
condensaterwater vapoairdry
QQQSHF Factor,Heat Sensible
)hω(ω)h)(hω(ωmq
ΔTcωωΔT cω ΔT c ΔhωΔhmq
hω-hωΔhωΔhmq
ΔHΔHΔHQ
airdry mass
watermass ω,gainwater
+=
−=−−=
−++=+=
++=
++=
∆=
fgf
fgf
fgf
xvvv
xuuu
xhhh
+=
+=
+=
fv
( )
−=
+=
×+−=
=
+=
+=
fg
f
fgf
gf
g
gglf
gf
vvvx
xvvv
vxvx1vmm
x
vmvmmv
VVV
gv
Two Phase Real Gas Properties
l l fg
s s l
s
l s
fg
fg fg
fg
fg fg
fg
q Δh Δω h
q Δh Δh ΔhqSHF
q qΔh Δω h
SHFΔω h Δh Δω h
Δh hΔωSHF Δh h h
ΔωhΔh
Δω SHF 1
= =
= = −
=+
−=
+ −
−=
+ −
=−
lqsq
q
Conditioned Space
S - supply
R - return,space conditions
( )
( )
latentsensible
sensible
RfgSR
liquidR
vaporRSR
airdry
latent
airdry
waterliquidpSRairdry
vaporwaterpSairdry
airp
vaporwaterSair
airdry
sensible
vaporSS vaporRRrwater vapoSairairdry
sensible
condensaterwater vapoairdry
QQQSHF Factor,Heat Sensible
)hω(ω)h)(hω(ωmq
ΔTcωωΔT cω ΔT c ΔhωΔhmq
hω-hωΔhωΔhmq
ΔHΔHΔHQ
dryair mass watermass ω,gainwater
+=
−=−−=
−++=+=
++=
++=
∆=
SHF
Pre-coolwater coil Cool
Reheatwater coil
O
R
1 2 3
3
S
2
O
RS
1
Combined Air ProcessesSummermixingcoolingdehumidifcationheatingconditioned space
pump
Pre-heat Heat Humidify
O
R
1 2 3 S
O
RS
Combined Air ProcessesWinterheatingmixinghumidification conditioned space
Winter - Heating
Pre-heat Heat Humidify
O 1 23
S
O1
2
R
RS
cool
SR
O2
4
3
4
Combined Air Processes
Winter - Heating Summer - Cooling
o
o
Outside ait at 90 F db and 75 F wb is mixed with return air in a mass proportion of 1/3 outside air to 2/3 return air and cooled in a coil to supply conditions. Return conditions are 75 F, 50% relative humidity. The space cooling load is 100,000 but/hr and the space sensible heat factor is .8. The supply temperature is 55 F. Determine the coil load in Btu/hr.
O
1
S R
55 75 90
( )
38.291100.4.0151790.24hT @ hωTch
.0151743.071100.4
1050.9.0186890)(75.24ω
hhT @ hω)T(Tc
ω
.01868.4301614.7
.430172918
Tp14.7@Tp
2918ω
Fwb Fdb,75 90 OOutside,
O
db OvOdb OpO
O
wbldb v
wbfggdbwbpO
wbv
wbvg
=×+×=
×+=
=−
×+−×=
−
×+−×=
=−
=−
=
.001120.00921632.01517
31ω
32ω
31ω
31.4828.083238.29
31h
32h
31h
1Point 28.081093.9.00921675.24h
T @hωTch.009216ω
.43016.514.7.43016.5
2918
75 @ p14.775 @p
2918ω
.50 db, F 75 RReturn,
RO1
RO1
R
R vRRpR
R
v
vR
=+=+=
=+=+=
=×+×=
×+×==
×−×
=×−
×=
=
φφ
φ
ermssmaller t ignoringby error 2%
)00489.24(.)T(TmLOADSHF1).0081)(.00955.45.0081(.24)T(TmLOADSHF
)c)ω(ωcω(c)T(TmLOADSHF.0081ω chart, ricpsychromet thefrom
)T(Tc)ω(ωm)T(Tcωm)T(TcmLOADSHFBALANCE ENERGY SENSIBLE SSPAE
T @h)ω(ωLOADSHF)(1BALANCE ENERGY LATENT SPACE
SRaspace
SRaspace
l pSR vpSa pSRaspace
S
SRl pSRSSR vpSaSRa paspace
R fgSRspace
+×−×=×
×−+×+×−×=×
×−+×+×−×=×=
−××−×+−×××+−××=×
×−=×−
Btu/hr 309,155)21.92(31.5816141.9)h(hmQ21.921085.3.00803755.24h
16141.91050.9.008037)(.009216
20,000m
.008037ωω.009215.009215ω.45.244203.6ω-38.46
1))ω(.009216.45ω(.2420,000
1050.9)ω09216100,000(.0.8ng,substituti
1))ω(.009216.45ω(.24)T(Tm
100,000.8
)T(Tc)ω(ωm)T(Tcωm)T(TcmLOADSHFBalanceEnergy Sensible Space
9.1050)ω(.00921620,000m
h)ω(.009216m100000.8)(1 @Th)ω(ωmLOADSHF)(1
BALANCE ENERGY LATENT SPACESOLUTION USSIMULTANEO
S1acoil
S
S
S
SSS
SSS
SSSRa
SRl pSRaSR vpSaSRa paspace
Sa
fgSa
R fgSRaspace
=−×=−×==×+×=
=×−
=
=×−+×+=
×−+×+=×−×
×−+×+=−×
×
−××−×+−×××+−××=×
×−=
×−×=×−
×−×=×−
X (75-55)
3-63
O S
R
Coolingcoil
Heatingcoil
1 2S msm 1/3
sm 2/3
( )
( )
mix/min5571ftQ
air/60dry mix/lbft 13.37air/hrdry lb 25,000Q
air/hrdry 25,000lb6575.24
60,000m
TTc m.51200,000.qRS Conditons Space
50% ,conditions reasonableconditon" to"
3supply
3s
as
rspassensible
=
×=
=−
=
−=×=→
=⇒ φ
( ) ( )( )
( ) ( )BTU/hr500,287q
2031.525,000hhmq21 Cooling
BTU/hr 84,78878884,000q5165.45.0055165.2425,000q
S2Reheat
21s
Reheat
Reheat
=−=−=
→=+=
−××+−×=→
31.5h28.1(2/3)38.3(1/3)h
h(2/3)h(1/3)hlb/hr 16,668.833225,000m
cfm 197114.19/608,332Qlb/hr 8,33225,000/3m
RO Mixing
1
1
RO1
R
o
o
=×+×=
×+×==−=
=×===
→
SR
O
2
1
51T2 = 65Ts =
.005ωS =
38.3hO =
28.1hR =
3-62 BY CHART
O S
R
1 2
( )
( ) ( )
( )
( )( )
( )Btu/hr 462,500)6.1927(500,62q
hq d)
lb49,705Btu/29.3-15.542,323q
hmq c)84,29.cfm11.95/6042,323vmV
lb/hr 2,3234m 4607cfm13.7/6020,177vmV
lb/hr 20,177m 19.662,50015.5m62,50028.2m
hmhmhm mmm b)
cfm60/11.14500,62vmV
lb/hr 62,5009575.24
300,000TTc
qm
TTcmq a)
4.375300
300qq
q SHF Space
heat
2Sheat
preheat
O1Opreheat
ooo
O
RRR
R
RR
sSOORR
SOR
sss
O1p
ss
O1pss
ls
s
=−×=−=
=×=
−==×=×=
==×=×=
=×=×−+
=+=+
=×=×=
=−
−=
−=
−=
−=+−
−=
+=
hm
h
S
O
R
S
1
2
14.11 v .27h 13.7 v 28.2h
6.19h 15.5h
/lb95ft.11 vBtu/lb 9.3h
SS
RR
2
1
3oO
====
==
==
h
/lb12.51ftv
144..05065)(14.7460)(3553.35
pRTv
9.321076.3.0008635.24h
.00086.0506514.7.05065.622ω
.05065.1013.2pO Outside, - PROPERTIES
/lb13.686ftv
144.2175)(14.7450)(7553.35
pRTv
28.22h1093.85.0093475.24h
@ThωTch
.00934.217514.7.2175.622ω
p14.7p.622ω
.2175.435.5p
@TPpR,Return - PROPERTIES
4.375300
300qq
q SHF Space
3O
air
OO
O
O
vO
3R
air
RR
R
R
RvaporRRpR
R
vR
vRR
vR
RgvR
ls
s
=
×−+×
==
=×+×=
=−×
=
=×=
=
×−+×
==
=×+×=
×+=
=−×
=
−×=
=×=
×=
−=+−
−=
+=
φ
3-62 BY CALCULATION
14,600cfm14.074/6062,500vmV
/lb14.074ft.09019)(14.7
460)(9553.35v
.09019pp - 14.7
p.622.00384ω
27.021102.45.0038495.24hSsupply,PROPERTIES
.00384ω)1091.65ω93462,500(.00375,000
)hω(ωmQlatent space, - BALANCEENERGY
air/hrdry lb 62,50095).24(75
300,000m
)T(T)cω(ω)T(Tcω)T(TcmQ
sensible space, - BALANCEENERGY15.3351087.3.0008660.24h
hωTch1point PROPERTIES
SSS
3S
vS
vS
vSS
S
S
S
fg@752RaL
S
RSliquidp2RRS
vaporp2RSpSS
1
v1O1p1
=×=×=
=−
+×=
=
==
=×+×=−
=−=
−=
=−
−=
−−+−+−=
=×+×=
+=−
Btu/hr 446,875Q19.88)(27.0362,500Q
)h(hmQHeater - BALANCEENERGY
Btu/hr 244,047.Q
9.32)(15.33540,573Q
)h(hmQPreheater - BALANCEENERGY
heater
heater
2SSheater
preheat
preheat
O1Opreheat
=−×=
−×=
=
−×=
−=
bdryair19.88Btu/lhh62,50015.35540,53728.2221,963
hmhmhm8459.cfm12.5140,537vmV
y/hr40,537lbdrm62,500m5009cfm13.686/6021,963vmV
y/hr21,963lbdrm.0038462,500.00086)m(62,500.00934m
ωmωmωmmixingBALANCEENERGY
2
2
2S1ORR
OOO
RO
RRR
R
RR
SSOORR
=×=×+×
=+
=×=×==−=
=×=×==
×=×−+×=+
−
3-62 BY CALCULATION cont’d
heater preheater mixing
sensible space latent space
ncesEnergyBala 5vh,ω,,p 4times EquationsProperty v−
( ) ( )
( ) ( )
( ) ( )
( )lss
SRSpaSs
S2
s2
preheater2Spw222Spa2preheater
SSSR1
222pw222pa2
2R1,RpwRRRpaR1pw111pa1
O1
O1
OpreO1paOOO1paOpre
q/qqSHF
m TTcmq balanceenergy allover SPACE DCONDITIONE
ωω mm
q TTcωmTTcmq balanceenergy allover PREHEATER
m ωmmm balance lmass tota
m,T TcωmTcm
ω,m m TcωmTcmTcωmTcm balanceenergy overallPROCESSMIXING
ωω balance massvapor mm balance mass total
m,q TTcωmTTcmq balanceenergy allover KNOWNS UN PREHEATER
+=
−=
==
−+−=
=+
+=
+++
==
−+−=
3-62 Heat and Energy Balances10 equations, 10 unknowns
S
R
1 2O
Pre-heater Heater
EQUATION SUMMARY
( )( )
or water vapofheat specific average theisKkg
kJ 1.88
C0at or watwr vapofenthalpy theiskgkJ 2500.5
units Metric )T1.88(2500.5 ωT Kkg
kJ 1.005h
or water vapofheat specific average theisFlb
BTU .45
F0at or water vapofenthalpy theislb
BTU 1061.8
itsEnglish Un )T .45ω(1061.8T Flb
BTU .24h
res) temperatungconditioniair of range over the valueaverage
an from 1%isc ( accuracy less with OPTIONan As tablessteam theusing Tat vapor staurated h
h ωhh
T and Tgiven hh
TTc)h (ωω
φ and Tgiven )p(p
p2918ω
T @ pressure vapor saturationpressurevapor
pp
O
O
dbdbOv
O
O
dbdbOv
p
dbv
vairdry
wbdb wbfdbv
wbdbair pwbfg
vbarometer
v
dbg
v
++=
++=
±=
+=
−
−−=
−=
==φ
latentsensibletotal
total
l22v11latent
v2v1dbpsesnible
rwater vapoairdry sesnible
2m
21
m
1m
2m
21
m
1m
qq /mqΔh /mq
hωhω /mq
)hω(hΔTc /mq
ΔhΔh /mq
hmmh
mmh
ωmmω
mmω
+=
=
−=
−+=
+=
+=
+=
Spitler 3-62 EES"
"INPUT PARAMETERS"
pamb=14.7
Qsensible=-300000
Qlatent=375000
To=35
TR=75
Ts=95
T1=60
Ro=.2
RR=.5
"Point O, outside"
ho=enthalpy(AirH2O,T=To,p=pamb,R=Ro)
wo=humrat(AirH2O, T=To,p=pamb,R=Ro)
"Point R, return"
hR=enthalpy(AirH2O,T=TR,p=pamb,R=RR)
wR=humrat(AirH2O, T=TR,p=pamb,R=RR)
"Point 1"
w1=wo
h1=enthalpy(AirH2O,T=T1,p=pamb,w=w1)
h1=15.34
h2=19.71
ho=9.32
hR=28.13
hs=26.93
mo=41148
mR=21352
ms=62500
pamb=14.7
Qfurnace=451259
Qlatent=375000
Qpreheat=247674
Qsensible=-300000
Ro=0.2
RR=0.5
SHFspace=-4
T1=60
To=35
TR=75
Ts=95
w1=0.0008472
w2=0.003712
wo=0.0008472
wR=0.009234
ws=0.003712
Point S, supply"ws=w2Qsensible+Qlatent=ms*(hR-hs)SHFspace=Qsensible/(Qsensible+Qlatent)SHFspace=.24*(TR-Ts)/(hR-hs)hs=enthalpy(AirH2O,p=pamb,T=Ts,w=ws)"Mixing Energy Balance"mR+mo=msmR*hR+mo*h1=ms*h2mR*wR+mo*w1=ms*w2
Qpreheat=mo*(h1-ho) "c)"Qfurnace=ms*(hs-h2) "d)"
3-62 EES Code
[ ] [ ] [ ]
( ) ( ) ( )[ ] [ ] [ ] [ ]1113443234432344321
11144
332
44
332
44
3321
444
333
222
1
444
333
222
1
444
333
222
1
444
333
222
1
3R
321O
4R444O4
3R333O3
2R222O2
1R111O1
dcbcbcbddbdbcdcdcbaD
dcbcbcb
ddbdb
cdcdc
baD
cbacbacba
ddbadbadba
cdcadcadca
bdcbdcbdcb
aD
DDω
DDm
DDT
DDω
kω dm cT bω akω dm cT bω akω dm cT bω a
kω dm cT bω a
−+−−+−−−=
−+−
+−=
−+−=
====
=+++=+++=+++=+++
4444
3333
1222
1111
4
4444
3333
2222
1111
3
4444
3333
2222
1111
2
4444
3333
2222
1111
1
4444
3333
2222
1111
kcbakcbakcba
kcba
D
dkbadkbadkba
dkba
D
dckadckadcka
dcka
D
dcbkdcbkdcbk
dcbk
D
dcbadcbadcba
dcba
D
==
===
LINEAR EQUATION SOLUTION BY DETERMINANTS
Air water vapor out
Air water vapor in
Hot water
Cold water
makeup blowdown
( ) down blowinoutairmakeup
watercoldhot water
outairdown blow watercoldinairmakeuphot water
airoutinair
mωωmmmm for
ωmmmωmmmout watwer massin water mass
mmBalance Mass
+−==
++=++−
=rwater vapoairby gainedenergy
water liquidby lost energy net BalanceEnergy
+=
Natural DraftCooling Tower
( ) ( )
( )
( )
( ) ( )( ) ( )
( )( ) ( )lb/hr 866.7 up make
.01934.0357352,878ωωm up maker53,900lb/hmω1mωmair mass
air/hrdry 52,878lbm
m18.9115QQQ1,000,000m16.673Q
87.921105.2.01934.03573mQ
hhωωmQ
m.0783Q
91)(100.45.01934mΔTcωmQ
m2.1691100.24mΔTcmQF110at blowdown and makeup Assume
TU/hr1,000,000BΔQΔQBalanceEnergy and Mass
airdry water/lb.03573lb.9492.8214.329
.9492.8218ω
airdry water/lb.01934lbω
.7204.614.329.7204.618
p.614.329
p.618ω
psia 14.3at atmospherean Assume
12a
a1a1a
a
aΔωωdrtair
aΔω
aΔω
F120 lF100 v12aΔω
aω
ap1aω
aapadryair
owater air
2
1
Fg91
Fg911
1
oo
1
1
o
o
=−×=−×=
=×+=×+==
×=++=×=
−×−×=
−×−×=
×=
−×××=×××=
×=−××==
==
=×−×
××=
=
×−×××
=×−×
××=
2100 F82%
191 F60%
110 F
120 F
2
1
water.makeup ofquantity theb) and rate flowair thea) Calculate humidity. relative 82% and
100at leavesair theand humidity, relative 60%and F91at tower cooling theentersAir F.110 to
F120 from reduced is water theof re temperatuTheflow. water a fromBTU/hr 101 removes
towercoolingair wcounterflo eevaporativAn
o
o o
o
6×
Cooling Tower Example
COOLING TOWER MASS BALANCE
( ) Down lowBmlower) (typically F 110 UpMake
22a +ω−ω×
( )22am ω−ω×
F 110Down owBl
F 120 mwater
F 110 mwater
RunProgramPS3-3 2012"
"INPUT"T1=60R1=.3T2=110R2=.30Vol1=2000ps=5 +14.7patm=14.7
"SOLUTION"h1=enthalpy(AirH2O, T=T1,R=R1,p=patm)w1=humrat(AirH2O,T=T1,R=R1,p=patm)v1=volume(AirH2O,T=T1,R=R1,p=patm)hl1=enthalpy(steam,T=T1,x=0)hv1=enthalpy(steam,T=T1,x=1)
h2=enthalpy(AirH2O, T=T2,R=R2,p=patm)w2=humrat(AirH2O,T=T2,R=R2,p=patm)
hsteam=enthalpy(Steam,p=ps,x=1)
ma=60*Vol1/v1"ENERGY BALANCE"ma*H1+Qcoil+ma*(w2-w1)*hsteam=ma*h2mwater=ma*(w2-w1)Qlatent=(w2-w1)*(hv1-hl1)Qsensible=Qcoil-QlatentQsensible=ma*(h3-h1)T3=tempeature(AirH2O,h=h3,w=w1,p=patm)
( )
in coldinhot
out coldin cold
in coldinhot
outhot inhot
coldhot
in coldinhot cold
outhot inhot hot
TTTTalso
TTTTessEffectiven
gas ideal ,mmFor hhm
)h(hmessEffectiven
TransferHeat Possible MaximumTransferHeat ActualessEffectiven
−−
−−
=
=−×−×
=
=
)Outside(T inhot
out coldT
in coldT (Return)
outhot T
Cooling Season