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Sheet1

Estimate of size of a cooling tower

TL2 Ap TA1 L

= = = =

Cp L/G(=N) TL1 P Hwbt

= = = = = =

Haoh

= =

41.3 C 5.0 C 27.0 C 108 m3/h 0.03 kg/s 4.19 kj/kg 1 32.0 C 101.3 kPa 83.49 kj/kg 19.94 kcal/kg

Water inlet temp. Approach temp. Air wet bulb temp. Water flow rate specific heat Water and air ratio Water outlet temp. Barometric Pressure entalphy at air wet bulb temp.

Hwbt+N x Cpx(TL1-TL2) 122.43 kj/kg 29.24 kcal/kg

entalphy at air outlet temp.

The Tchebycheff method to evaluate NTU t1 = TL2+0.1(TL1-TL2)= t2 = TL2+0.1(TL1-TL2)= t3 = TL2+0.1(TL1-TL2)= t4 = TL2+0.1(TL1-TL2)=

32.93 C 35.72 C 37.58 C 40.37 C

△HG

=

CpxL/Gx(TL1-TL2)=

38.94

HG1 HG2 HG3 HG4

= = = =

Hwbt+0.1 x △HG = Hwbt+0.4 x △HG = (Hwbt+△HG)-(0.4 x △HG) = (Hwbt+△HG)-(0.1 x △HG) =

1/(HL-HG)1 1/(HL-HG)2 1/(HL-HG)3 1/(HL-HG)4

= = = = ∑

NTU(KaV/L) (=U/N)

=

Ka

HL1= HL2= HL3= HL4=

87.38 99.06 106.85 118.53

0.0338 0.0279 0.0241 0.0192 0.1050 Cp x (TL1-TL2) x ------------------------------

0.1050 4

=

1.022

=

14000 kcal/m3 h △Η

1쪽

heat transfer coefficient based on entalphy

Sheet1

V

υ G

E

Qh Qe

= = = = = = = = = = = =

= =

LxNTU --------Ka 7.88 m3 0.8496 m3/kg 91758.01 m3/hr 1529.3 m3/min 108000 kg/hr 30 kg/s G x (x2-x1) ((TL1-TL2)/600) x L x C 1.41 m3/hr 1.64 m3/hr 0.02 %

1168.2 kw 1169.0 kw

2쪽

Volume for fill packing specific volume for inlet moist air Air flow rate

heat exchanger quantity heat load

Sheet1

C Degree -273.00 #REF! -273.00

Density kg/m3 1.1774 #REF! 0.9980

Cp kj/kg C 1.0057 #REF! 1.0090

Viscosity kg/m sx10^5 1.8462 #REF! 2.0750

Kin. Visco. m2/sx10^6 15.69 #REF! 20.76

k W/m C 0.0262 #REF! 0.0300

0.7080 #REF! 0.6970

0 #REF!

-0.1794 #REF! 0.0000 #REF! #REF!

0.0033 #REF! 0.0000 #REF! #REF!

0.2288 #REF! 0.0000 #REF! #REF!

5.0700 #REF! 0.0000 #REF! #REF!

0.0038 #REF! 0.0000 #REF! #REF!

-0.0110 #REF! 0.0000 #REF! #REF!

C Degree -273.00 #REF! -273.00

Density kg/m3 1.1774 #REF! 0.9980

Cp kj/kg C 1.0057 #REF! 1.0090

Viscosity kg/m sx10^5 1.8462 #REF! 2.0750

Kin. Visco. m2/sx10^6 15.69 #REF! 20.76

k W/m C 0.0262 #REF! 0.0300

Pr

3쪽

Pr

0.7080 #REF! 0.6970

Sheet1

0 #REF!

-0.1794 #REF! 0.0000 #REF! #REF!

0.0033 #REF! 0.0000 #REF! #REF!

0.2288 #REF! 0.0000 #REF! #REF!

4쪽

5.0700 #REF! 0.0000 #REF! #REF!

0.0038 #REF! 0.0000 #REF! #REF!

-0.0110 #REF! 0.0000 #REF! #REF!

Sheet1 V HL1 P2 φ2 Ra2 Rv2 Ps2 Pv2 Pa2

1 m3 32.93 C 306.08 K 101.3 kPa 100 % 0.287 Kj/kg K 0.462 Kj/kg K 5.0730 Kpa φ2 x Ps2

h2

= = = =

1.0035T1 + w1(2500 + 1.861 T1) 117.03 kj/kg da 116.96 kj/kg da 27.93 kcal/kg

V HL2 P2

= = = =

φ2 Ra2 Rv2

= = =

Ps2 Pv2

= = = = = = = = = = = = =

mv2

Td2

V υ2 ha2

hv2

Pa2 35 ω2 40 45 ma2 50 55 mv2 60 65 70 Td2

5쪽

barometic pressure(total relative humidity specific gas constant for specific gas constant for saturaed vapor pressure partial pressure for vapor

partial pressure for dry a

= = = = = = = =

ma2

volume for moist air air ambient temp.

5.0730 kPa P2 - Pv2 96.23 Kpa 0.622 x Pv/(P-Pv) 0.0328 Kg(w)/Kg(a) PaV/RaT 1.0954 kg Pv2V2/Rv2T2=ω2ma2 0.0359 kg 0.0359 kg 307.05 K 5.3562 ep 5.0730 ap 33.90 C ma2(Ra2+ω2Rv2) x T2/P2 1.00 m3 0.91 m3/kg 1.0035 x T1 33.05 kj/kg da 32.99 Kj/kg da 2593.85 kj/kg

ω2

116.96 134.93 148.29 170.70

= = = = = = = = = = = = = = = = = = = =

1 m3 35.72 C 308.87 K 101.3 kPa 100 % 0.287 Kj/kg K 0.462 Kj/kg K 5.9247 Kpa φ2 x Ps2

absolute humidity

mass for dry air per cubic

mass for vapor per cubic

dew point temperature Where, estimate Td by tr mehod until ep is equale

volume for moist air specific volume for moist entalphy for dry air

entalphy for vapor

volume for moist air air ambient temp. barometic pressure(total relative humidity specific gas constant for specific gas constant for

saturaed vapor pressure partial pressure for vapor

5.9247 kPa P2 - Pv2 95.38 Kpa 0.622 x Pv/(P-Pv) 0.0386 Kg(w)/Kg(a) PaV/RaT 1.0759 kg Pv2V2/Rv2T2=ω2ma2 0.0416 kg 0.0416 kg 307.05 K

partial pressure for dry a absolute humidity

mass for dry air per cubic

mass for vapor per cubic

dew point temperature

Sheet1 75 80 85 90 V 95 100 υ2 ha2

= = = = = = = =

5.3562 ep 5.9247 ap 33.90 C ma2(Ra2+ω2Rv2) x T2/P2 1.00 m3 0.93 m3/kg 1.0035 x T1 35.85 kj/kg da 35.78 Kj/kg da 2601.76 kj/kg

h2

= = = =

1.0035T1 + w1(2500 + 1.861 T1) 135.01 kj/kg da 134.93 kj/kg da 32.23 kcal/kg

V HL3

= = = = = = = = = = = = = = = = = = = =

1 m3 37.58 C 310.73 K 101.3 kPa 100 % 0.287 Kj/kg K 0.462 Kj/kg K 6.5589 Kpa

hv2

P2 φ2 Ra2 Rv2 Ps2 Pv2 Pa2

φ2 x Ps2

h2

= = = =

1.0035T1 + w1(2500 + 1.861 T1) 148.38 kj/kg da 148.29 kj/kg da 35.42 kcal/kg

V HL4

= = = = = =

1 m3 40.37 C 313.52 K 101.3 kPa 100 % 0.287 Kj/kg K

mv2

Td2

V υ2 ha2

hv2

P2 φ2 Ra2

6쪽

entalphy for vapor

volume for moist air air ambient temp.

barometic pressure(total relative humidity specific gas constant for specific gas constant for saturaed vapor pressure partial pressure for vapor

partial pressure for dry a

= = = = = = = =

ma2

volume for moist air specific volume for moist entalphy for dry air

6.5589 kPa P2 - Pv2 94.74 Kpa 0.622 x Pv/(P-Pv) 0.0431 Kg(w)/Kg(a) PaV/RaT 1.0624 kg Pv2V2/Rv2T2=ω2ma2 0.0457 kg 0.0457 kg 307.05 K 5.3562 ep 6.5589 ap 33.90 C ma2(Ra2+ω2Rv2) x T2/P2 1.00 m3 0.94 m3/kg 1.0035 x T1 37.71 kj/kg da 37.65 Kj/kg da 2607.03 kj/kg

ω2

Where, estimate Td by tr mehod until ep is equale

absolute humidity

mass for dry air per cubic

mass for vapor per cubic

dew point temperature Where, estimate Td by tr mehod until ep is equale

volume for moist air specific volume for moist entalphy for dry air

entalphy for vapor

volume for moist air air ambient temp. barometic pressure(total relative humidity specific gas constant for

Sheet1 Rv2 Ps2 Pv2 Pa2 ω2 ma2 mv2

Td2

V υ2 ha2

hv2 h2

= = = = = = = = = = = = = =

0.462 Kj/kg K 7.6203 Kpa φ2 x Ps2 7.6203 kPa P2 - Pv2

= = = = = = = =

93.68 Kpa 0.622 x Pv/(P-Pv) 0.0506 Kg(w)/Kg(a) PaV/RaT 1.0411 kg Pv2V2/Rv2T2=ω2ma2 0.0527 kg 0.0527 kg 307.05 K 5.3562 ep 7.6203 ap 33.90 C ma2(Ra2+ω2Rv2) x T2/P2 1.00 m3 0.96 m3/kg 1.0035 x T1 40.51 kj/kg da 40.44 Kj/kg da 2614.94 kj/kg

= = = =

1.0035T1 + w1(2500 + 1.861 T1) 170.8 kj/kg da 170.70 kj/kg da 40.77 kcal/kg

a m2/sx10^4 0.2216 0.2216 0.2983 0.0767 #REF! 0.0000 #REF! #REF!

a m2/sx10^4 0.2216 0.2216 0.2983

7쪽

specific gas constant for saturaed vapor pressure partial pressure for vapor

partial pressure for dry a absolute humidity

mass for dry air per cubic

mass for vapor per cubic

dew point temperature Where, estimate Td by tr mehod until ep is equale

volume for moist air specific volume for moist entalphy for dry air

entalphy for vapor

Sheet1

0.0767 #REF! 0.0000 #REF! #REF!

8쪽

Sheet1

moist air emp.

essure(total pressure)

1) water inlet condition

constant for dry air constant for vapor por pressure ure for vapor

T1 wq

= = =

41.30 C 108 m3/hr 0.030 m3/s

2) water exit condition

ure for dry air T2

=

mw ρw Cpw

= = =

Qw

= = =

32.0 C

midity 0.03 air per cubic meter

30.000 kg/s 1000.0 kg/m3 4.190 kj/kg C

por per cubic meter

mperature mate Td by trial and error ep is equaled to ap

moist air me for moist air dry air 32.930 kj/kg DA

mw x (hf2-hf1) mw x Cpw x (T2-T1) 1169.0 Kw(kj/s)

21.11 26.67 32.22 37.78 43.33 48.89

4.179 4.179 4.174 4.174 4.174 4.174

C Degree 26.67

Cp kj/kg C 4.179

36.65

4.1745

37.78

4.174

11.1100 9.9800

-0.0050 -0.0499

vapor t + w(2501+1.805xt) 116.890 kj/kg DA

moist air emp.

essure(total pressure)

constant for dry air constant for vapor

46.4287 46.3788 4.1745

por pressure ure for vapor 1) moist air inlet condition

ure for dry air V T1

midity 0.04 air per cubic meter

P1 φ1

= = = = =

1 m3 27.0 C 300.15 K 105 kPa 100 %

por per cubic meter 2) moist air exit condition

mperature

V

9쪽

=

1 m3

Sheet1

mate Td by trial and error ep is equaled to ap

T2 P2 φ2 hw3

moist air me for moist air dry air 35.720 kj/kg DA

Ra1 Rv1 Ps1 Pv1

vapor t + w(2501+1.805xt) 134.846 kj/kg DA

Pa1 ω1 ma1

moist air emp.

mv1

essure(total pressure) Td1

constant for dry air constant for vapor por pressure ure for vapor

V

ure for dry air

υ1 ha1

midity 0.04 air per cubic meter

hv1

por per cubic meter

h1

mperature mate Td by trial and error ep is equaled to ap

V T2 P2 φ2 Ra2 Rv2 Ps2 Pv2

moist air me for moist air dry air 37.580 kj/kg DA

vapor Pa2 t + w(2501+1.805xt) 148.197 kj/kg DA

ω2 ma2

moist air emp.

mv2

essure(total pressure)

Td2

constant for dry air

10 쪽

= = = = =

35 C 308.15 K 100 kPa 100 % 146.68 kj/kg

= = = = = = = = = = = = = = =

0.287 Kj/kg K 0.462 Kj/kg K 3.6081 Kpa

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

φ1 x Ps1 3.6081 kPa P1 - Pv1 101.39 Kpa 0.622 x Pv1/(P1-Pv1) 0.0221 Kg(w)/Kg(a) Pa1V1/Ra1T1 1.1770 kg Pv1V1/Rv1T1=ω1ma1 0.0260 kg 0.0261 kg 301.12 K 3.8179 ep 3.6081 ap 27.97 C ma1(Ra1+ω1Rv1) x T1/P1 1.00 m3 0.85 m3/kg 1.0035 x T1 27.09 kj/kg da 27.05 Kj/kg da 2577.04 kj/kg 1.0035T1 + w1(2500 + 1.861 T1) 83.54 kj/kg da 83.49 kj/kg da 19.94 kcal/kg 1 m3 33.9 C 307.05 K 100 kPa 100 % 0.287 Kj/kg K 0.462 Kj/kg K 5.3562 Kpa φ2 x Ps2 5.3562 kPa P2 - Pv2 94.64 Kpa 0.622 x Pv/(P-Pv) 0.0352 Kg(w)/Kg(a) PaV/RaT 1.0740 kg Pv2V2/Rv2T2=ω2ma2 0.0378 kg 0.0378 kg 307.05 K 5.3562 ep 5.3562 ap

Sheet1

constant for vapor por pressure ure for vapor

V υ2 ha2

ure for dry air

midity 0.05 air per cubic meter

hv2 h2

por per cubic meter

mperature mate Td by trial and error ep is equaled to ap

Q/ma1

mw3/ma1

moist air me for moist air dry air 40.370 kj/kg DA

= = = = = = = =

33.90 C ma2(Ra2+ω2Rv2) x T2/P2 1.00 m3 0.93 m3/kg 1.0035 x T1 34.02 kj/kg da 33.96 Kj/kg da 2596.60 kj/kg

= = = = = = = = = =

1.0035T1 + w1(2500 + 1.861 T1) 124.24 kj/kg da 124.17 kj/kg da 29.66 kcal/kg ha2 - ha1 + w2hv2 - w1hv1 + (w1-w2)hw3 Cpa(T2-T1) + w2hv2 - w1hv1 + (w1-w2)hw3 1.0035 x (T2-T1) + w2hv2 - w1hv1 + (w1-w2) 39.38 kj/kg da w2 - w1 0.0131 kg(w)/kgda

Q/(ma1+mv2)=Q/ma1(1+w) = 34.20 kj/kg MA mw3/ma1+mv1=mw3/ma1(1+w) = 0.0113 kg/kg MA

vapor t + w(2501+1.805xt) 170.597 kj/kg DA

11 쪽

Sheet1

12 쪽

Sheet1

water inlet temperature water flow rate

air ambient temp. mass flow rate for water water density at bulk temp. water density at bulk temp.

### C ### C

heat exchanger quantity from water to air

997.4 995.8 994.9 993.0 990.6 988.8

0 0 0 0 0 0

0.604 0.614 0.623 0.630 0.637 0.644

Density kg/m3 995.8

Viscosity kg/m s 0

k W/m C 0.614

993.3

0.000700

0.628

993.0

0

0.630

-2.80 -27.94

-0.0002 -0.0018

0.0160 0.1597

11063.34 11035.39 993.28

0.0096 0.0078 0.000700

6.8215 6.9812 0.628373

6.78 5.85 5.12 4.53 4.04 3.64

volume for moist air wet bulb temp. for inlet moist air barometic pressure(total pressure) relative humidity

volume for moist air

13 쪽

Sheet1 wet bulb temp. for exit moist air barometic pressure(total pressure) relative humidity saturated water entalphy at

35

C

specific gas constant for dry air specific gas constant for vapor saturaed vapor pressure partial pressure for vapor partial pressure for dry air absolute humidity 0.02 mass for dry air per cubic meter mass for vapor per cubic meter

dew point temperature Where, estimate Td by trial and error mehod until ep is equaled to ap

volume for moist air specific volume for moist air entalphy for dry air 27.000 kj/kg DA entalphy for vapor t + w(2501+1.805xt) 83.436 kj/kg DA

volume for moist air air ambient temp. barometic pressure(total pressure) relative humidity specific gas constant for dry air specific gas constant for vapor saturaed vapor pressure partial pressure for vapor partial pressure for dry air absolute humidity 0.04 mass for dry air per cubic meter mass for vapor per cubic meter

dew point temperature Where, estimate Td by trial and error mehod until ep is equaled to ap

14 쪽

Sheet1

volume for moist air specific volume for moist air entalphy for dry air 33.900 kj/kg DA entalphy for vapor t + w(2501+1.805xt) 124.092 kj/kg DA

w1-w2)hw3 + (w1-w2)hw3 hv1 + (w1-w2)hw3 heat quantity for dry air 1 kg condensated water for dry air 1 kg

heat quantity for mosit air 1 Kg condesated water for moist air 1 kg

15 쪽

Sheet1

16 쪽