The document discusses the fundamentals of cooling tower design and operation. Cooling towers work by evaporating a portion of hot water into unsaturated air, which cools the water. Differential balances are used in the tower, including enthalpy and mass balances. Design equations require integrating these differential equations. The results are used to determine the height of transfer units (HTUs) and number of transfer units (NTUs) needed. NTUs are evaluated using equilibrium data from psychrometric charts, while HTUs are evaluated using operating line and driving force line data and slopes. A minimum air flow is also determined based on an infinite packing height.

1. HUMIDIFICATION FUNDAMENTALS COOLING TOWER DESIGNS http://www.picture-newsletter.com/nuclear/cooling-tower-ub4.jpg

2. COOLING TOWER OPERATION EVAPORATION OF A PORTION OF ENTERING HOT 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

3. PROCESS TEMPERATURE AND HUMIDITY PROFILES FIGURE 10.5-1

4. DIFFERENTIAL BALANCES IN THE TOWER DIFFERENTIAL CROSS-SECTION OF THE TOWER, Sdz ENTHALPY BALANCE IS G y dH y = d (LH L ) d L ≈ 0, G y dH y = Lc L dT L (10.5-3) HEAT TRANSFER RATE FROM LIQUID TO INTERFACE LdH L = Lc L dT L = h L a(T L - T i )dz = G y dH y (10.5-4)

5. DIFFERENTIAL BALANCES IN THE TOWER HEAT TRANSFER RATE FROM INTERFACE TO GAS G’ y c s dT y = h y a(T i - T y )dz (A) MASS TRANSFER RATE OF VAPOR FROM INTERFACE TO GAS G’ y d Ĥ = k y M B a( Ĥ i - Ĥ )dz (B)

6. DIFFERENTIAL BALANCES IN THE TOWER INTEGRATION TO OBTAIN REQUIRED HEIGHT OF PACKED SECTION (A) CAN BE REARRANGED

7. DIFFERENTIAL BALANCES IN THE TOWER DIFFERENTIAL MASS BALANCE: DIFFERENTIAL ENTHALPY BALANCE:

8. DIFFERENTIAL BALANCES IN THE TOWER GAS PHASE ENTHALPY TO MASS TRANSFER RATE: GAS PHASE ENTHALPY TO LIQUID PHASE TEMPERATURE

9. DIFFERENTIAL BALANCES IN THE TOWER AND FOR a h = a m : PACKED HEIGHT:

10. DESIGN EQUATIONS REQUIRES INTEGRATION OF EQUATIONS (C), (D), (E) OR (10.5-13) RESULTS HAVE THE GENERAL FORM Z i = (HTU) i (NTU) I HTU ≡ HEIGHT OF A TRANSFER UNIT NTU ≡ NUMBER OF TRANSFER UNITS TRANSFER UNIT≡ Δ VARIABLE/AVERAGE DRIVING FORCE

11. TRANSFER UNITS NTU ARE EVALUATED AS HTU ARE EVALUATED AS

12. TRANSFER UNIT DESIGN EVALUATION OF NTU’S REQUIRES EQUILIBRIUM DATA NORMALLY OBTAINED FROM PSYCHROMETRIC CHARTS OPERATING LINE DATA INTERGRATE (10.5-13) FOR NTU

13. TRANSFER UNIT DESIGN SLOPE OF OPERATING LINE IS Lc L /G y SLOPE OF DRIVING FORCE LINE IS -h L a/k G aM B P SEE EXAMPLE 10-5-1 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

14. MINIMUM AIR FLOW LIMITING VALUE BASED ON INFINITE PACKING HEIGHT