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Cooling tower at a lower wet bulb: Merkel number, characteristic and off-design cold-water temperature (Leeper 1981, Example 2)

Tool	Cooling Tower Performance
Source	Leeper, S. A. (1981). Wet Cooling Towers: "Rule-of-Thumb" Design and Simulation. EGG-GTH-5775, Idaho National Engineering Laboratory, U.S. Department of Energy, Idaho Falls, ID. Example 2, pp. 17–18.
Level	Undergraduate

Problem

A counterflow mechanical-draft cooling tower is designed to cool 8,950 gpm of water from 110 °F to 84 °F at a 69 °F wet bulb with a water-to-air ratio L/G of 1.30. Find the tower characteristic KaV/L of the design point and the hot- and cold-water temperatures when the wet bulb drops to 60 °F with L/G and the range held constant.

Inputs to Enter

Counterflow; water flow 564.66 L/s (8,950 gpm); hot water 43.33 °C (110 °F), cold water 28.89 °C (84 °F), wet bulb 20.56 °C (69 °F); sea level
L/G entered, 1.30; characteristic KaV/L = C (L/G)^-n passed through the design point with n = 0.6
Off-design: wet bulb 15.56 °C (60 °F), water flow, air flow and heat load 100 % of design
Dry bulb 29.44 °C, 4 cycles of concentration, drift 0.02 %, fan pressure 125 Pa at 70 %, pump head 9 m at 80 % (the tool's own additions; the report gives none)

Open the Cooling Tower Performance tool (loaded with this example)

Answers

Range 14.44 K (26 °F), approach 8.33 K (15 °F), heat load 33,922 kW
KaV/L = 1.5227 by numerical integration and 1.5213 by the four-point Chebyshev rule (book: 1.49 by a hand sum of table enthalpies)
C = 1.5227 × 1.30^0.6 = 1.7823 (the book's 1.49 gives 1.7442 in its Example 3)
At the 15.56 °C wet bulb: cold water 26.43 °C = 79.57 °F, hot water 40.87 °C = 105.57 °F, approach 10.87 K (book, by four trials: 79.5 °F and 105.5 °F)
Effectiveness model: ε = 0.7786 at the design point; cold water 26.21 °C at the off-design point, 0.21 K below the Merkel value
Evaporation 12.15 L/s (2.15 % of the flow), make-up 16.20 L/s at 4 cycles; fan input 71.86 kW, pump input 61.90 kW

Notes

The tool's default inputs are this case in SI units; press Submit. The report's enthalpies come from hand tables and its integrals are hand sums, so the tool reproduces the example to hand accuracy, not to the printed digits: with the printed KaV/L of 1.49 entered as C = 1.7442 the tool gives 79.82 °F. Example 3 of the report (air flow 60 %) follows by entering C = 1.7442 and Air Flow 60 %: the tool gives 89.9 °F against the printed 89.6 °F (test_cooling_tower.php).