The Blueprint of Water

Cooling Things Down: Problem Set

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⟵ 12 Cooling Things Down (Engineering Notes) · Contents · 12 Cooling Things Down (Answer Key) ⟶

Cooling Things Down: Problem Set

“These are only provided to reinforce understanding. The Engineering Notes contain some of the information that will be required. Make sure to employ dimensional analysis for all unit conversions.”

Level 1: Conceptual Mastery

  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.

  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.

  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?

Level 2: Applied Thinking

  1. A cooling tower serves a 750-ton chiller (750 refrigeration tons). The tower range is 10°F. Using an evaporation factor of 0.85:

  2. Calculate the cooling tower heat load in BTU/hr.

  3. Estimate the recirculation rate in GPM.

  4. Calculate the evaporation rate in GPM.

  5. Calculate blowdown and total makeup at 4 cycles of concentration.

  6. 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?

  7. 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

  1. Calculate the chloride-based COC and the calcium-based COC.

  2. Is the mass balance intact? If not, what percentage of calcium is leaving the water as scale?

  3. What would you recommend as the next diagnostic step or treatment response?

  4. 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:

  5. Annual energy cost under clean conditions.

  6. Annual energy cost under fouled conditions.

  7. The annual cost penalty from fouling.

Level 3: Optimization

  1. 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

  1. Calculate annual blowdown and makeup at each cycle count.

  2. Calculate annual water cost, sewer cost, and chemical cost at each cycle count.

  3. What is the net annual savings from increasing to 6 cycles?

  4. In one or two sentences, explain why the chemical cost increases even though total makeup decreases.

  5. 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.

  6. What is the maximum number of cycles allowed by the calcium hardness limit?

  7. What is the maximum number of cycles allowed by the alkalinity limit?

  8. Which constraint governs, and at that cycle count, what are the tower concentrations of calcium, alkalinity, and chloride?

  9. 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.

  10. You are called to evaluate a cooling tower that is consuming significantly more water than expected. The conductivity controller is functioning and holding its setpoint. Tower water conductivity reads 2,400 µS/cm; makeup conductivity is 600 µS/cm. However, the makeup meter shows water consumption approximately 30% higher than your mass balance predicts for the calculated COC. Identify at least three possible explanations for the discrepancy and describe how you would investigate each one.

Problem notes

Each problem as its own linked note.

12.1 · 12.2 · 12.3 · 12.4 · 12.5 · 12.6 · 12.7 · 12.8 · 12.9 · 12.10

⟵ 12 Cooling Things Down (Engineering Notes) · Contents · 12 Cooling Things Down (Answer Key) ⟶

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