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

QQ

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