psychrometrics 1) ideal mixing 2) ideal gas air 3) ideal ...1 psychrometrics 1) ideal mixing 2)...
TRANSCRIPT
1
Psychrometrics
1) Ideal Mixing2) Ideal Gas Air3) Ideal Gas Water Vapor4) Adiabatic Saturation
22
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
TnRpV
TRpv
WeightMolecular nm WeightMolecular molesmass
Kkmole
m kPaorKkmole
kJ8.314R
lbmoleRlbf/lbm 1545.15 R
weightmolecular RR
KR, re, temperatuabsolute - T kPa psia, pressure, absolute - p
mRTpV RTpv
LAW GAS (PERFECT) IDEAL
*
*
o
3
o*
o*
*
oo
=
=
×=×=
=
=
=
==
Ideal Gas Law
3
( )
( )
/kgm .8417vkPa 101.325
C24K273.15/kgm kPa .287p
RTv
kPa 101.325 and C24at air of volumespecific The
/lbft 13.476v/ftin 144lbf/in 14.7
F75R459.69R lbf/lbmft 53.35p
RTv
psia 14.7 and F75at air of volumespecific The
3
2
oo3
o
3
222
oo
o
=
+×==
=
×+×
==
4
tCoefficien JT=
∂∂
hpT
h=constant
5
( )
(12.44) vv
pp
RTpV
RTpV
saturationat or water vapmassor water vapmass actual
saturationat or water vapmassor water vapmass actualhumidity Relative
(12.43) pp29
p 18ω
TMW pTMW p
RTpV
RTpV
airdry massor water vapmassω
airdry massor water vapmassω Fraction, Mass Humidity, Specific
airdry kgm 1 air,dry lb 1 -n calculatio of Basis
w
g
g
w
saturation
wambient
w
airair
waterwater
air
water
m
==φ
==φ
=φ=
−=
=
==
=
Specific and Relative Humidity
Tc ωTch ωTch ωhh
kJ/kg ,BTU/lb HHH
pvpvpva
dryairdryairwair
+=+=+=
+=
6
Metric Psychrometric Chart
Moran Table A-9, A-9E
7
( ) ( )
( )
33
vvvapor
33
aaair
vatm
v
watma
w
gw
g
w
air
o
kg/m .842.58491
K 289.15Km
kPa .4615001. v
T/pωRv v
kg/m .843.58491100
K 289.15Km
kPa .287 v
T/pRv vc).58491100
1.5849.622pp 29
p 18ω b)
kPa 98.415ppp kPa 1.5849p
1698.3.5pp
pp a)
volumespecific b)ω humidity, specific c)
p a) :Find
kPa. 100barometer %, 50 C, 25 Given,
=×
×=
==
=−
×=
==−
=−
=
=−==
×=×=
=
=
φ
φ
φ
ω
v
8
( )
F55.11.21508pat TT
(check)air dry lb water / lb .00924mm
lb .00067575)(459.6985.766
1ft144.21508RT
Vpm
.0731lb75)(459.6953.35
1ft144.21508)(14.69RT
Vpm
ft 13.685144.2150814.6975)(459.6953.351
pRTmV
RTpvVVV
airdry lb water / lb .00924ω.2150814.69
.21508.622pp
p2918ω
psia .21508.43016.5p
75at pp
,,,p :Findpsia 14.69barometer 50%,
F,75 air,moist lb :Given
ovdp
a
v
3vv
v
3aa
a
3a
wa
watm
w
w
g
w
w,
o
===
=
=+×
××==
=+×
××−==
=×−+×
==
=
===
−=
−=
=×=
=
=
φ
ωφ
vaa mmv
lb/ft 13.68v
F55Tairdry BTU/lb 28.5h
airdry water/lblb .093ωChart ricPsychromet
3
odp
=
=
==
9
Adiabatic Saturation
( )
( )( )
( )( )
( )( )
( )wbfdbv
wbdbpfg2wb
f2v1
12pfg221
fg22f2v1112p
fgf2v2
21pa2a1
v222afg212v11a1
outvapor airaddedwater invapor air
hhTTchω
ω
hhTTchω
ω
hω)h(hωTTc
hhh
)T(Tchhng,substituti
hωhhωωhωh
EEEEquationEnergy FlowSteady
dryairunit mass 1n calculatio of basis
−
−−=
−
−−=
=++−
=−
−=−
+=−++
=+ ++
( )( ) ( )
airdry /lb1094.80BTUh 4) accuratemost air dry /lb1094.05BTUh 3)
use easiest toair dry BTU/lb 1093.9h 2)Exactair dry lbBTU/ 1094.07h 1)
wbF db,70 75Ffor
T.441061.8TT.44F 0 @hh 4)
TT.45T @hh 3)
T @hh 2))pp,T@(Tenthalpy vapor saturationh 1)
v1
v1
v1
v1
dbwbdbgv1
wbdbwbgv1
dbgv1
vdbv1
====
×+=−×+=
−×+=
====
dbT
T wbT
s
2wb
1db
2
1v1h
f2h g2h
g1h
0T =
34
10
( )
( )( )
( )( )
( )( )
( )wbfdbv
wbdbpfg2wb
f2v1
21pfg221
fg22f2v1121p
fgf2v2
21pa2a1
v222afg212v11a1
outvapor airaddedwater invapor air
hhTTchω
ω
hhTTchω
ω
hω)h(hωTTc
hhh
)T(Tchhng,substituti
hωhhωωhωh
EEEEquationEnergy FlowSteady
dryairunit mass 1n calculatio of basis
−
−−=
−
−−=
=++−
=−
−=−
+=−++
=+ ++
Adiabatic Saturation
2wb
1db
11
( ) airdry b water /llb 0063.52.1069
2.7946.1308.336.1102
966524.5.10560132.)ω(T
)(Th)(Th)T(Tc)(Th)ω(T
)ω(T
airdry b water /llb .0132.3057814.7
.30578.622)(Tpp
)(Tp.622)ω(T
1056.5 33.08 .30578 65 T1102.6 95T
hh h p T
db
wbfdbg
dbwbpwbfgwbdb
wbsaturationatm
wbsaturationwb
wb
db
g fgf
=−
=−
−×+×=
−−+×
=
=−
×=−
×=
95 F db65 F wb14.7 atmSpecific Humidity ?
F 95Tdb =
F 65Twb =
)T( wbω
12
dbT
T wbT
s
2
1v1h
f2h g2h
g1h
0T =
34
( )( ) ( )
airdry /lb1094.80BTUh 4) accuratemost air dry /lb1094.05BTUh 3)
use easiest toair dry BTU/lb 1093.9h 2)Exactair dry lbBTU/ 1094.07h 1)
wbF db,70 75Ffor
T.441061.8TT.44F 0 @hh 4)
TT.45T @hh 3)
T @hh 2))pp,T@(Tenthalpy vapor saturationh 1)
v1
v1
v1
v1
dbwbdbgv1
wbdbwbgv1
dbgv1
vdbv1
====
×+=−×+=
−×+=
====
133-10
airdry lb
waterlb .00323.00326.00649ωω
addedwater
.00621.145314.7
.1453.622ω
Hgin .1453.36335.4pppp
p.622ω
12
2
g2v2
vatm
v2
=−=−
=−
=
=×=×=
−=
φ
( )
( )
airdry lb water/ lb .00314ω3.0041078.7
1073.5.004264035.24ω
35at h40at h35at hωTTc
ω
.00426.0999814.7
.09998.622ω
1
1
lv
fg g121p1
1g
=−
×+−=
−
+−=
=−
=
140 F
1g35 F
35 F
1
2
Air at 40 F db, 35F wb is heated andhumidified to 70 F db, 40 % relativehumidity at 14.7 psia. Find the mass of water added.
14
USCU Psychrometric Chart
15(6)
pTRωvv
(5) p
RT1vv
VOLUMESPECIFIC
(4) T@p
pHUMIDITYRELATIVE
)3(hh
)T(Tc)h(ωω
)2(pp
p622.
pp
2918ω
pppHUMIDITYSPECIFIC
)T8.18.1061(ωT005.1h)1()T44.8.1061(ωT24.h
@Thh
ωhhh ENTHALPY
vapor
dbairvapor
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 φ 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
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
16
ω
dbT
ω
dbT
ω
dbT
ω
dbT
Heating-Cooling Cooling-Dehumidification
Mixing Humidification
PSYCHROMETRIC PROCESSES
17
Heating Cooling
heating
BTU kJ, ΔT,.45ωm ΔT .24 mQ
BTU kJ, ΔT,cωm ΔT c mQ
Δh ω mΔh mQΔHΔHΔHQ
varyingv,Tφ,constantp
constantω
airdry airdry
waterpairdry pairdry
rwater vapoairdry airairdry
waterair
bulbdry
w
+=
+=
+=+==
==
=
ω
bulbdry Theating
coolingQ
18
Cooling Dehumidification
QSHF Factor,Heat Sensible
h)ωω()h)(hωω(Q
ΔTc)ωω(ΔT c ω ΔT c Q
)h(h)ωω()h(hωΔh mq
)h(h)h-(h)ωω(ΔhωΔhm
q
ΔHΔHΔHQ
dryair kg waterkg ,ωωcondensate
latentsensible
sensible
1fg21
liquid 1
vapor121latent
airdry water
liquid p21airdry vapor waterp2airdry
airpsensible
liquid2
liquid121v2v12air
airdry
sensible
liquid 2
liquid 1
liquid1
vapor121rwater vapo2air
dryair
condensaterwater vapodryair
21
+=
−=−−=
−++=
−−+−+=
−+−++=
++=
−=
1
2 1
2
Q
Δω
21
apparatusdpT
19
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
+=
−=−−=
−++=+=
++=
++=
∆=
20
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
( )
w
w12
12
2w121
2awa1a
2w1
hΔωΔh
hωωhh
hhωωhhmhmhm
HHH
=
=−−
=−+=+
=+
BTU/lb 1164hsteam psi 30
w =
BTU/lb 0h waterF32
w
o
=
1 2
21
1SHFh
ΔωΔh
hhΔωΔh
hΔωΔh
SHF
h ΔωΔhh Δωh ΔωΔh
SHF
qqqSHF
ΔhΔhΔhq
h ΔωΔhq
fg
fgfg
fg
fgfg
fg
sl
s
lss
fgl
−=
−+
−=
−+−
=
+=
−==
==
lqsq
q
22
Mixing
1
2
( ) ( )
( ) ( ) 221
21
21
1m
221
21
321
1m
2211mm
21m
ωmm
mωmm
mω
hmm
mhmm
mh
hmhmhmHHH
++
+=
++
+=
+=+=
3 ω
dbT
1
2
m1
2
3
( ) ( )( )( )1m
m2
2
1
m2p21mp1
m1m1
TTTT
mm
TTcmTTcmΔqΔq
−−
=
−=−= →→
233-26
( ) ( )
( ) ( )
( )
( )
( )
kJ/kg 18.56hkJ/kg 2519.2kg/kg .0033810K kJ/kg 1.005h
hωTchkg/sec 12.427.066812.36m
kg/sec .066810)(273.15/kgm kPa .4615
/secm 10kPa .8725RT
Vpm
kg/sec 12.36m10)(273.15/kgm kPa .287
/secm 10kPa .8725kPa 101.325RT
Vpm
kg/kg .00338ωkJ/kg 21.02kJ/kg 2510.1
kJ/kg 2489.1kg/kg .0054105kJ/kgK 1.005ω
@Th@Th@ThωTTc
ω
kg/kg .0054kPa .8725kPa 101.325
kPa .8725.622ω
ppT @.622pω
wbc 5 db, c 10 - 1Pt
1
1
v11dbpa1
m
3
3a
v1
a1
3
3a
a1
1
1
wbwdbv
wbfgg1dbwbpa1
g1
vatm
wbvg1
=×+×=
×+==+=
=+×
×==
=+×
×−==
=−
×+−=
−
×+−=
=−
×=
−=
kJ/kg 30.5h and 6g/kgω read
in 1.68619.42812.361in 2.65
mpoint to2point from distance
kJ/kg 30.25h
kJ/kg 50.919.36
7kJ/kg 18.5619.3612.36h
kg/kg .00577ω
.01019.36
7.0033819.3612.36ω
ωmmω
mmω
mmmωmωmωm
kJ/kg 50.9h
kg/sec 7/kgm .858
6m
/kgm .858v
g/kg 10ω wbC 18 db, C 25 2Pt Chart,
mm
m
m
m
m
2m
21
m
1m
21m
2211mm
2
32
32
2
==
=×
=
×+×=
=
×+×=
+=
+=+=
=
==
=
=
MixingChart
Mixing Calculated
10 cubic meters per second of 10 C db, 5 C wbair is mixed with 6 cubic meters per second of air at 25 C db and 18 C wb. Compute the mixtureconditions and compare them to results fromthe psychrometric chart.
24
25airdry lbBTU/ 84.511104.7.0252100.24h
60% ,100at airdry BTU/lb 241104.70.100.24h
0% ,100at
ωhhh
O
O
vaporairdry
=×+×==
=×+×==
+=
φ
φ
100 F
24 BTU/lbm
51.8 BTU/lbm
26
R
1
2
3
1 Outside airR Return air from
conditionded space2 After mixing3 After dehumidifucationS Supply S
Combined Processes - mixing, cooling and dehumidification,reheating, conditioned space.
1
R
22 3 S
QQ water
dbT
ω
27Pre-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
28
Air water vapor out
Air water vapor in
Hot water
Cold water
makeup blowdown
( )inoutairmakeup
outairdown blowwatercold
inairmakeuphot water
airoutinair
ωωmm
ωmmm
ωmmmout water massin water mass
mmBalance Mass
−=
++=
++−
=
rwater vapoairby gainedenergy water liquidby lost energy net
BalanceEnergy
+=
Natural DraftCooling Tower
29
( ) ( )
( )
( )
( ) ( )( ) ( )
( )( ) ( )lb/hr 876.6 up make
.01876.0357851,504ωωm up maker51,504lb/hmω1mωmair mass
air/hrdry lb 50,556m
m19.78QQQ1,000,000m17.3Q
88.1104.7.01876.03578mQ
hhωωmQ
m.0844Q
90)(100.45.01876mΔTcωmQ
m2.490100.24mΔTcmQF110at blowdown and makeup Assume
TU/hr1,000,000BΔQΔQBalanceEnergy and Mass
airdry water/lb.03578lb.95052.8214.329
.95052.8218ω
airdry water/lblb .01876ω
.69904.614.329.69904.618
p.614.329
p.618ω
12a
a1a1a
a
aΔωωdrtair
aΔω
aΔω
F120 fF100 v12aΔω
aω
ap1aω
aapadryair
owater air
2
1
Fg90
Fg901
1
oo
1
1
o
o
=−×=−×=
=×+=×+=
=
×=++=
×=−×−×=
−×−×=
×=
−×××=×××=
×=−××==
==
=×−×
××=
=
×−×××
=×−×
××=
2100 F82%
190 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 F90at 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