Properties - eng.buffalo.edu · CHARLES LAW p v p v BOLYES LAW STP (1 atm and 0 ) 6.023 10...

79
air dry mass apor water v mass Humidity Specific ω % Humidity Relative air dry lb per s u, h, v, T , T p bulb wet bulb dry f Properties Processes Heating and cooling Cooling and dehumidification Mixing Humidification Zone Air Handling Unit Systems

Transcript of Properties - eng.buffalo.edu · CHARLES LAW p v p v BOLYES LAW STP (1 atm and 0 ) 6.023 10...

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

× +

=

tCoefficien JT=

∂∂

hpT

h=constant

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 ==

Metric Psychrometric Chart

h

v

φ

ω

dbT

wbT

( )

( )

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

USCU Psychrometric Chart

(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

→ →=

− = −

−=

JW1

Slide 29

JW1 3.26 edition 5James Wulf, 1/27/2006

( ) ( )

( ) ( )

( )

( )

( )

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

h

2

f DV L fh =

kμ c

P ,AmG

PcG

hj

pr

32

rp

ave

==

=

µρ

=VDN h

RE

f

j

ReN

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

1

2

Total

Sensible

Latent

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

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

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

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

Program

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)

Help

Ventilation Sensible Heat Recoveryheating season

Ventilation Sensible and Latent heat recoveryheating season

( )

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