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HUMIDIFICATION

FUNDAMENTALS

COOLING TOWER

DESIGNS

http://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpg

http://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpghttp://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpghttp://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpghttp://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpg

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COOLING TOWEROPERATION

EVAPORATION OF A PORTION OF ENTERINGHOT WATER INTO UNSATURATED AIR

COOLING OF THE WATER STREAM

PACKED BED CONTACTOR SEE FIGURE 10.5-2 FOR FLOWSHEET

http://www.ges-inc.com/CoolingTower.gif

http://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpghttp://www.youtube.com/watch?v=ooWOaMpEcPo&NR=1http://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.youtube.com/watch?v=ooWOaMpEcPo&NR=1

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PROCESS TEMPERATURE ANDHUMIDITY PROFILES

FIGURE 10.5-1

TOP OF TOWER BOTTOM OF TOWER

i

i

G

GWATER

VAPOR WATER

VAPOR

TL

WATER

VAPOR

TL

TGTGLIQ. SENS.

HEAT

LIQ. SENS.

HEAT

LATENT HT IN GAS

LIQ. SENS.

HEAT

LIQ. SENS.

HEAT

LATENT HT IN GAS

GAS SENS. HT

GAS SENS. HT

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DIFFERENTIAL BALANCES IN THETOWER

DIFFERENTIAL CROSS-SECTION OF THETOWER, Sdz

ENTHALPY BALANCE IS GydHy = d (LHL) dL 0, GydHy = LcLdTL (10.5-3)

HEAT TRANSFER RATE FROM LIQUID TOINTERFACE LdHL = LcLdTL = hLa(TL - Ti)dz = GydHy

(10.5-4)

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DIFFERENTIAL BALANCES IN THETOWER

HEAT TRANSFER RATE FROM INTERFACETO GAS

GycsdTy = hya(Ti - Ty)dz (A)

MASS TRANSFER RATE OF VAPOR FROMINTERFACE TO GAS Gyd = kyMBa(i - )dz (B)

http://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gif

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DIFFERENTIAL BALANCES IN THETOWER

INTEGRATION TO OBTAIN REQUIREDHEIGHT OF PACKED SECTION

(A) CAN BE REARRANGED

)(CdzLcah

TTdT

L

L

iL

L

)('

DdzcG

ah

TT

dT

Sy

y

yi

y

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DIFFERENTIAL BALANCES IN THETOWER

DIFFERENTIAL MASS BALANCE:

DIFFERENTIAL ENTHALPY BALANCE:

)('

EdzG

aMk

HH

Hd

y

By

i

)('

FG

Lc

dT

dH

y

L

L

y

http://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gif

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DIFFERENTIAL BALANCES IN THETOWER

GAS PHASE ENTHALPY TO MASSTRANSFER RATE:

GAS PHASE ENTHALPY TO LIQUID PHASETEMPERATURE

)125.10(' dzG

aMk

HH

dH

y

BG

yyi

y

)145.10(

PaMk

ah

TT

HH

BG

L

Li

yyi

http://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gif

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DIFFERENTIAL BALANCES IN THETOWER

AND FOR ah = am:

PACKED HEIGHT:

y

LL

BG

L

Li

yyi

h

ch

PaMk

ah

TT

HH

)135.10(

2

10

y

y

H

H yyi

y

GB

z

HH

dH

aPkM

Gzdz

http://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gif

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DESIGN EQUATIONS

REQUIRES INTEGRATION OF EQUATIONS(C), (D), (E) OR (10.5-13)

RESULTS HAVE THE GENERAL FORMZi = (HTU)i(NTU)I

HTU HEIGHT OF A TRANSFER UNIT

NTU NUMBER OF TRANSFER UNITS TRANSFER UNIT VARIABLE/AVERAGE

DRIVING FORCE

http://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gifhttp://www.ges-inc.com/CoolingTower.gif

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L2

L1

L

y2

y1

y

2

1

y2

y1

y

T

T LiL

LT

T

T yyi

y

T

H

H i

H

H

H yyi

y

H

TT

dTN

TT

dTN

HH

HdN

HH

dHN

TRANSFER UNITS NTU ARE EVALUATED AS

HTU ARE EVALUATED AS

ah

cGH

ah

cG'H

aMk

G'

HH

L

LLT

y

Sy

T

BG

y

HH

Ly

y

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TRANSFER UNIT DESIGN

EVALUATION OF NTUS REQUIRES EQUILIBRIUM DATA NORMALLY OBTAINEDFROM PSYCHROMETRIC CHARTS

OPERATING LINE DATA

INTERGRATE (10.5-13) FOR NTU

EQUILIBRIUM LINE

OPERATING

LINE

LIQUID TEMPERATURETi1 TL2

H*y2

H*y1

Hy2

Hy1

Hy2i

Hy1i

TL1 Ti2

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TRANSFER UNIT DESIGN

SLOPE OF OPERATING LINE IS LcL/Gy SLOPE OF DRIVING FORCE LINE IS

-hLa/kGaMBP

SEE EXAMPLE 10-5-1INVERSE DRIVING FORCE VS TL

0.00E+00

1.00E-05

2.00E-05

3.00E-05

4.00E-05

5.00E-05

28.0 32.0 36.0 40.0 44.0

LIQUID TEMP (C)

1/(Hyi-

Hy

TL 1/(Hyi - Hy)

29.4 4.41E-05

32.2 4.02E-05

35.0 3.39E-05

37.7 2.83E-05

40.5 2.29E-05

43.3 1.82E-05

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MINIMUM AIR FLOW

LIMITING VALUE BASED ON INFINITEPACKING HEIGHT

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