Chapter 12 · Cooling Things Down · Ten playable problems

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Ch 12 · P1 — Why water, not air

PROBLEM 111 · COOLING THINGS DOWN — THE CARRIER CHOICE

Why do large systems move cooling with water rather than air?

Live model

specific heat × density = the whole argumentWhy do big systems move cooling with water instead of air?

Ch 12 · P2 — Two exits, one lever

PROBLEM 112 · COOLING THINGS DOWN — THE MASS BALANCE

Water leaves the tower two ways. Assign what each exit takes with it — and see why only one of them is your lever.

Live model

evaporation distills · blowdown drainsTwo exits from the tower. Assign what each one takes with it.

Ch 12 · P3 — The controller's blind faith

PROBLEM 113 · COOLING THINGS DOWN — SETPOINT ≠ CONTROL

The conductivity controller holds its setpoint perfectly, so the manager declares the chemistry under control. Why might that be wrong, and what is the diagnostic?

Live model

the scale steals its own evidenceThe conductivity controller holds setpoint flawlessly. Why might the chemistry still be out of control?

Ch 12 · P4 — The tower's arithmetic

PROBLEM 114 · COOLING THINGS DOWN — E, B, AND M

A 750-ton chiller, 10°F range, 0.85 evaporation factor. Dial the evaporation — blowdown and makeup at 4 cycles unlock with it.

Live model

Q 11.25M BTU/hr · RECIRC 2,250 GPM

750 tons · 15,000 BTU/hr each · 3 GPM/tonHeat load 11,250,000 BTU/hr, recirc 2,250 GPM, range 10°F. Dial the evaporation.

Ch 12 · P5 — A million and a half gallons

PROBLEM 115 · COOLING THINGS DOWN — 3 CYCLES VS 6

Same 19.1 GPM of evaporation, 4,380 hours a year. Dial the annual water saved by running 6 cycles instead of 3.

Live model

B = E ÷ (C − 1) · M = E + BSame 19.1 GPM evaporation, 4,380 hr/yr. Dial the annual water saved going from 3 to 6 cycles.

Ch 12 · P6 — Two ions, two stories

PROBLEM 116 · COOLING THINGS DOWN — THE DIVERGENT COC

Makeup: Cl 48, Ca 160. Tower: Cl 245, Ca 640. Run both cycle counts and read the verdict.

Live model

the divergence quantifies the scaleChloride COC 5.10, calcium COC 4.00. What is the mass balance saying?

Ch 12 · P7 — Four degrees of fouling

PROBLEM 117 · COOLING THINGS DOWN — THE APPROACH PENALTY

800 tons at 0.60 kW/ton, 4,500 hours, $0.11/kWh — and fouling has added 4°F of approach at 2% energy per degree. Dial the annual penalty.

Live model

4°F × 2%/°F on the clean-condition bill800 tons, 0.60 kW/ton, 4,500 hr at $0.11/kWh, approach up 4°F at 2%/°F. Dial the annual penalty in $k.

Ch 12 · P8 — The cycles ledger

PROBLEM 118 · COOLING THINGS DOWN — 4 CYCLES OR 6

20 GPM evaporation, 4,000 hr/yr. Water $6, sewer $8, chemicals $1.80 vs $2.50 per thousand gallons. Total both columns and dial the net annual savings.

Live model

water and sewer save $8,960 · chemicals give back $2,880Run the table: water $6, sewer $8, chemicals $1.80 vs $2.50 per kgal. Dial the net annual savings in $k.

Ch 12 · P9 — Which limit governs

PROBLEM 119 · COOLING THINGS DOWN — THE CEILING RACE

Makeup: Ca 320, alkalinity 210, chloride 150. Inhibitor limits: Ca 1,400, alkalinity 1,000. Run the cycles up and click the constraint that hits its ceiling first.

Live model

round down to 4 for margin: Ca 1,280 · alk 840 · Cl 600Drag the cycles and watch which bar hits its ceiling first — then name the governing limit.

Ch 12 · P10 — The missing thirty percent

PROBLEM 120 · COOLING THINGS DOWN — THE WATER BILL MYSTERY

Cycles hold at 2,400 ÷ 600 = 4, yet the makeup meter runs 30% over the mass balance. Pick three consistent explanations — one option fights the physics.

Live model

0 / 3 PICKED

concentrated losses act like blowdown — conductivity would fallMakeup runs 30% over the mass balance while cycles hold at 4. Pick three consistent explanations. 0 of 3 picked.

Problem set

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Problem 1
Why do large cooling systems move cooling with water rather than air? In your answer, reference specific heat, density, and the practical size of the distribution system.
Authored answer
Air has a specific heat of approximately 0.24 BTU/lb·°F versus water's 1.0, and is roughly 800 times less dense. To move the same BTU load, air-based systems require vastly greater volumetric flow through massive ductwork with high-powered fans. A chilled water system consolidates cooling into a central plant with compact piping – a six-inch chilled water pipe carries the same capacity as a four-foot air duct – with a fraction of the pumping energy and far simpler redundancy.
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Problem 2
In the mass balance, evaporation removes pure water while blowdown removes concentrated water. Explain why this distinction matters for how dissolved solids accumulate, and why the water treater controls blowdown (not evaporation) to manage chemistry.
Authored answer
Evaporation removes only pure water – dissolved solids cannot evaporate and remain behind in the tower. This is why concentration increases even though no solids are being added beyond what arrives in the makeup. Blowdown removes concentrated water, carrying dissolved solids out of the system and relieving the accumulation. The water treater controls blowdown because evaporation is fixed by the heat load. Evaporation cannot be reduced without reducing the cooling demand itself. Blowdown is the only controllable mechanism for managing how concentrated the tower water becomes.
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Problem 3
A facility manager notices that the conductivity controller is holding its setpoint perfectly, and concludes that the cooling tower chemistry must be under control. Explain why this conclusion might be wrong. What diagnostic would you use to verify the mass balance, and what would the results tell you?
Authored answer
Conductivity tracks total dissolved solids but does not distinguish between species. If calcium carbonate is precipitating as scale, its contribution to conductivity disappears – but the controller does not know this. Makeup continues entering, the conductivity setpoint holds, and the true concentration of scaling species drifts from what conductivity reports. The diagnostic is to compare cycles of concentration calculated from a soluble tracer ion (chloride) against cycles calculated from a scaling-risk ion (calcium). If chloride-based COC is significantly higher than calcium-based COC, calcium is leaving the water as scale. The divergence quantifies how much.
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Problem 4
A cooling tower serves a 750-ton chiller (750 refrigeration tons). The tower range is 10°F. Using an evaporation factor of 0.85: Calculate the cooling tower heat load in BTU/hr. Estimate the recirculation rate in GPM. Calculate the evaporation rate in GPM. Calculate blowdown and total makeup at 4 cycles of concentration.
Authored answer
(a) Q = 750 tons × 15,000 BTU/hr per CT ton = 11,250,000 BTU/hr. (b) Recirc = 750 × 3 GPM/ton = 2,250 GPM. (c) E = 2,250 × 10 × 0.85 ÷ 1,000 = 19.1 GPM. (d) B = 19.1 ÷ (4 − 1) = 6.37 GPM. M = 19.1 + 6.37 = 25.5 GPM. Check: M = 19.1 × 4 ÷ 3 = 25.5 GPM. ✓
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Problem 5
Using the evaporation rate from Problem 4, calculate the total annual makeup water (in gallons) at 3 cycles and at 6 cycles, assuming 4,380 hours of operation per year. What is the annual water savings from increasing cycles?
Authored answer
At 3 cycles: B = 19.1 ÷ (3 − 1) = 9.55 GPM. M = 19.1 + 9.55 = 28.65 GPM. Annual = 28.65 × 60 × 4,380 = 7,529,220 gal/yr ≈ 7.53 Mgal. At 6 cycles: B = 19.1 ÷ (6 − 1) = 3.82 GPM. M = 19.1 + 3.82 = 22.92 GPM. Annual = 22.92 × 60 × 4,380 = 6,023,376 gal/yr ≈ 6.02 Mgal. Savings = 7.53 − 6.02 = 1.51 Mgal/yr. Over 1.5 million gallons saved on a single tower by increasing from 3 to 6 cycles.
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Problem 6
A tower operates at 5 cycles based on conductivity. Lab results show: MAKEUP: Chloride = 48 mg/L; Calcium = 160 mg/L as CaCO₃ TOWER: Chloride = 245 mg/L; Calcium = 640 mg/L as CaCO₃ Calculate the chloride-based COC and the calcium-based COC. Is the mass balance intact? If not, what percentage of calcium is leaving the water as scale? What would you recommend as the next diagnostic step or treatment response?
Authored answer
Chloride COC = 245 ÷ 48 = 5.10. Calcium COC = 640 ÷ 160 = 4.00. The mass balance is not intact. Chloride-based COC exceeds calcium-based COC, meaning calcium is leaving the water as scale. Expected calcium at 5.10 cycles = 160 × 5.10 = 816 mg/L as CaCO₃. Actual = 640 mg/L. Calcium lost = (816 − 640) ÷ 816 = 21.6% precipitating as scale. Next steps: evaluate LSI/RSI at current conditions, check condenser approach temperature for fouling evidence, review scale inhibitor residual and dosing, and consider whether cycles need to be reduced or inhibitor chemistry adjusted.
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Problem 7
An 800-ton chiller operates at 0.60 kW/ton under clean conditions for 4,500 hours per year at $0.11/kWh. Condenser tube fouling has increased the approach temperature by 4°F. Using the upper-end estimate (2% energy increase per °F of approach rise), calculate: Annual energy cost under clean conditions. Annual energy cost under fouled conditions. The annual cost penalty from fouling.
Authored answer
Clean conditions: 800 tons × 0.60 kW/ton = 480 kW. Annual energy = 480 × 4,500 = 2,160,000 kWh. Annual cost = 2,160,000 × $0.11 = $237,600. Fouled conditions: 4°F × 2% = 8% energy increase. Additional power = 480 × 0.08 = 38.4 kW. Total = 518.4 kW. Annual energy = 518.4 × 4,500 = 2,332,800 kWh. Annual cost = 2,332,800 × $0.11 = $256,608. Annual penalty from fouling = $256,608 − $237,600 = $19,008.
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Problem 8
A cooling tower evaporates 20 GPM and operates 4,000 hours per year. The facility is evaluating whether to increase from 4 cycles to 6 cycles of concentration. The following costs apply: Water: $6.00 per 1,000 gallons (Applies to Makeup) Sewer: $8.00 per 1,000 gallons (Applies to Blowdown) Chemical treatment at 4 cycles: $1.80 per 1,000 gallons of makeup Chemical treatment at 6 cycles: $2.50 per 1,000 gallons of makeup Calculate annual blowdown and makeup at each cycle count. Calculate annual water cost, sewer cost, and chemical cost at each cycle count. What is the net annual savings from increasing to 6 cycles? In one or two sentences, explain why the chemical cost increases even though total makeup decreases.
Authored answer
(a) At 4 cycles: B = 20 ÷ (4 − 1) = 6.67 GPM. M = 20 + 6.67 = 26.67 GPM. Annual makeup = 26.67 × 60 × 4,000 = 6,400,000 gal. Annual blowdown = 6.67 × 60 × 4,000 = 1,600,000 gal. At 6 cycles: B = 20 ÷ (6 − 1) = 4.0 GPM. M = 20 + 4.0 = 24.0 GPM. Annual makeup = 24.0 × 60 × 4,000 = 5,760,000 gal. Annual blowdown = 4.0 × 60 × 4,000 = 960,000 gal. (b) At 4 cycles: Water = 6,400 kgal × $6.00/kgal = $38,400. Sewer = 1,600 kgal × $8.00/kgal = $12,800. Chemical = 6,400 kgal × $1.80/kgal = $11,520. Total = $62,720. At 6 cycles: Water = 5,760 kgal × $6.00/kgal = $34,560. Sewer = 960 kgal × $8.00/kgal = $7,680. Chemical = 5,760 kgal × $2.50/kgal = $14,400. Total = $56,640. (c) Net annual savings = $62,720 − $56,640 = $6,080. Water and sewer savings total $8,960. Chemical costs increase by $2,880. The net savings are positive. (d) Higher cycles concentrate every dissolved species in the tower water – calcium, alkalinity, silica, chloride, sulfate – increasing supersaturation and scaling pressure. The treatment program must work harder to keep those species in solution, which requires more aggressive (and more expensive) inhibitor chemistry even though the total volume of water being treated is lower.
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Problem 9
Your makeup water contains 320 mg/L calcium hardness as CaCO₃, 210 mg/L alkalinity as CaCO₃, and 150 mg/L chloride. Your scale inhibitor is rated for a maximum of 1,400 mg/L calcium hardness and 1,000 mg/L alkalinity in the tower water. What is the maximum number of cycles allowed by the calcium hardness limit? What is the maximum number of cycles allowed by the alkalinity limit? Which constraint governs, and at that cycle count, what are the tower concentrations of calcium, alkalinity, and chloride? Explain why the actual maximum safe cycle count may be lower than the value you calculated, considering pH, temperature, and the interactions between scaling parameters.
Authored answer
Calcium limit: 1,400 ÷ 320 = 4.38 cycles. Alkalinity limit: 1,000 ÷ 210 = 4.76 cycles. Calcium governs – round down to 4 cycles for safety margin. At 4 cycles: calcium = 320 × 4 = 1,280 mg/L as CaCO₃; alkalinity = 210 × 4 = 840 mg/L as CaCO₃; chloride = 150 × 4 = 600 mg/L. The actual safe maximum may be lower because CO₂ stripping in the tower drives pH upward. At 840 mg/L alkalinity, pH will likely exceed 8.3, shifting the carbonate equilibrium strongly toward CO₃²⁻ and increasing CaCO₃ supersaturation beyond what calcium hardness alone would suggest. The LSI will be significantly positive. Additionally, condenser tube surface temperatures are higher than bulk water temperature, and inverse solubility means calcium carbonate is least soluble exactly where heat transfer matters most. The true operating limit is determined by the interaction of hardness, alkalinity, pH, and temperature – not by any single parameter.
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Problem 10
You are called to evaluate a cooling tower that is consuming significantly more makeup water than expected. The conductivity controller is functioning and holding tower conductivity at 2,400 µS/cm. Makeup conductivity is 600 µS/cm. Based on the calculated cycles, the makeup meter shows water consumption approximately 30% higher than the mass balance predicts. Identify at least three possible explanations for the discrepancy and describe how you would investigate each one.
Authored answer
Tower cycles are 2,400 ÷ 600 = 4 cycles. If the tower is truly holding 4 cycles, then excessive drift or a tower-water leak would not normally explain makeup above the predicted value. Those losses remove concentrated tower water, so they act like uncontrolled blowdown. The conductivity controller should respond by reducing controlled blowdown, and total makeup should remain governed by evaporation and cycles. If the concentrated losses became larger than the required blowdown, tower conductivity would fall below setpoint. More consistent explanations are: (1) Evaporation is higher than assumed. The heat load, condenser water flow, tower range, or operating hours may be higher than the values used in the calculation. Investigate by verifying condenser water flow, entering and leaving condenser water temperatures, tower range, and chiller load. (2) The makeup meter is over-reading. The meter may have an incorrect multiplier, scaling error, installation issue, or mechanical problem. Investigate by checking the meter setup and comparing it against a portable flow meter or controlled fill test. (3) Some metered makeup water is not actually reaching the tower. A branch line, hose bib, washdown connection, or other user may be connected downstream of the meter. Investigate by tracing the piping and isolating branch lines. (4) A makeup-line leak may exist downstream of the meter but upstream of the tower. This would increase metered water use without changing tower conductivity. Investigate by closing the tower makeup isolation valve and checking whether the meter continues to move.
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