⟵ 12 Cooling Things Down (Narrative) · Contents · 12 Cooling Things Down (Problem Set) ⟶

Cooling Things Down: Engineering Notes

“If you are reading this straight through, you can skip this section and lose nothing essential to the story. These notes are for the operators, engineers, and technicians who need to do the math.”

Why This Matters in the Field

Cooling tower management is fundamentally a water balance problem. If you cannot calculate evaporation, blowdown, and makeup, you cannot set a conductivity target, size a blowdown valve, justify a treatment budget, or explain to a facility manager why their water bill changed.

These calculations are not complicated. But skipping them is how people end up wasting millions of gallons per year - or scaling a condenser in a single summer.

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Core Tools & Constants

Parameter	Value
Density of water	8.34 lb/gal
Specific heat of water	1.0 BTU/lb·°F
Latent heat of vaporization	~970 BTU/lb (1,000 BTU/lb for field calculations)
Standard refrigeration ton	12,000 BTU/hr·ton (heat removed from building)
Cooling tower ton	15,000 BTU/hr·ton (building heat + compressor heat)
Condenser water flow (rule of thumb)	3 GPM per ton at 10°F ΔT
Evaporation rate (rule of thumb)	1% of recirc ≈ 10°F cooling
Full-load chiller power input	0.60 kW/ton (for a 1,000-ton water cooled centrifugal chiller)

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Tower Performance: Range and Approach

Range is the temperature drop of the water across the tower:

Range = T(return) − T(supply)

Typical range: 10–15°F for comfort cooling. Set by heat load and flow rate.

Approach is how close the cold water temperature gets to the ambient wet-bulb temperature:

Approach = T(supply) − T(wet bulb)

Typical approach: 5–10°F.

A smaller approach means a more effective tower, but usually a larger tower with more fill, more fan energy, and higher cost.

Wet-bulb temperature is the lowest temperature achievable solely through evaporative cooling. It is measured using a sling-psychrometer - a thermometer wrapped in a water-soaked cloth that is spun through the air to maximize evaporation. As water evaporates from the cloth, the measured temperature cools.

When relative humidity is 100%, the wet-bulb temperature equals the actual air temperature (dry-bulb). At lower humidity, the wet-bulb temperature is lower than the air temperature because evaporation proceeds faster allowing more cooling.

A cooling tower cannot cool water below the surrounding air’s wet-bulb temperature, because the air has less capacity to accept additional vapor.

This is the same reason swamp coolers work well in dry climates and poorly in humid ones. In dry air, water evaporates readily and the temperature can move significantly downward toward the wet-bulb. In humid air, the evaporation driving force is weaker because the air is already closer to saturation.

A useful way to think about it:

• Dry-bulb temperature tells you how hot the air is
• Wet-bulb temperature tells you how much evaporative cooling potential the air still has
• Approach tells you how effectively the tower is using that remaining potential

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Refrigeration Tons vs. Cooling Tower Tons

This distinction matters for every calculation that follows.

A standard refrigeration ton is defined as 12,000 BTU/hr·ton – the amount of heat the chiller removes from the building. A 1,000-ton chiller at full capacity removes 12,000,000 BTU/hr from the building.

But the cooling tower must reject more than just the building’s heat. The chiller compressor adds heat to the system as it does work. This additional heat is roughly 3,000 BTU/hr per ton (about 25%), which defines a cooling tower ton as 15,000 BTU/hr·tonCT.

The total heat load at the cooling tower for a 1,000-ton chiller is therefore roughly 15,000,000 BTU/hr.

When calculating evaporation, blowdown, or sizing a tower, always use the cooling tower heat load – not the chiller tonnage alone.

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The Cooling Tower Mass Balance Equations

Overall Mass Balance

What enters must equal what leaves:

Makeup = Evaporation + Blowdown + Drift + Leaks

Drift and leaks are generally small. For calculation purposes, we simplify to:

M = E + B

Evaporation Rate

Method 1: From Heat Load

If the heat rejection is known:

E (lb/hr) = Q (BTU/hr)hfg (BTU/lb)

Where:

• Q = heat load (BTU/hr)
• hfg = latent heat (~1,000 BTU/lb in cooling towers)

Example: For a heat load of 6,000,000 BTU/hr

E = 6,000,000 (BTU/hr)1,000 (BTU/lb) = 6,000 lb/hr

Converting to (GPM):

E = 6,000 lb/hr 8.34 lb/gal × 60 min/hr = 12.0 gpm

Method 2: From Recirculation Rate and Range

In practice, the heat load is often unknown. The evaporation rate can be estimated from operating conditions:

E (gpm) ≈ Recirc Rate (gpm) × ΔT × f 1,000

Where:

• Recirc Rate is the water flow through the tower system in GPM. It can be estimated from nominal cooling tower tonnage:

Recirc Rate = CT Tonnage × 3 GPM/ton.

The nominal tonnage is typically found in the tower’s engineering specifications.

• ΔT is the temperature change across the cooling tower (range) in °F. For most comfort cooling calculations it is typically around 10-15°F, but should be verified in the field.
• f is the evaporation factor – the percentage of cooling that is being accomplished through latent heat transfer (evaporation) vs sensible heat transfer. It is commonly estimated at 0.85, meaning that 85% of the heat transfer is due to evaporation, while 15% is sensible heat transfer. This value is relatively stable for mechanical-draft towers in typical comfort cooling applications, but can shift in extreme humidity or with very high-efficiency fill.
• 1,000 in the denominator is the rounded latent heat value, chosen for ease of field use.

Example: For a 400-ton cooling tower

The nominal cooling tower tons can be found in the design specifications, and shown to be equivalent to the previous example:

400 CT Tons × 15,000 BTU/hr·tonCT = 6,000,000 BTU/hr Heat Load

Based on the CT Tons:

Recirc Rate (gpm) = CT Tonnage × 3 = 1,200 gpm

E ≈ 1,200 (gpm) × 10°F × 0.85 1,000 = 10.2 gpm

Reconciling the Two Methods

Method 1 yields 12.0 gpm. Method 2 yields 10.2 gpm. The difference is the evaporation fraction. Method 1 assumes all heat rejection occurs through evaporation. Method 2 accounts for the ~15% of heat rejected through sensible transfer (direct warming of the air without evaporation).

Dividing Method 2’s result by f confirms this: 10.2 ÷ 0.85 = 12.0 gpm.

Whichever method is used, incorporating the evaporation factor is more accurate for real systems and should be used for field calculations.

The Solids Mass Balance and Cycles of Concentration

The overall mass balance accounts for water flows. But evaporation removes only pure water – dissolved solids stay behind and accumulate in the tower. To account for this accumulation, we need a solids mass balance.

At steady state, the mass of solids entering the tower must equal the mass of solids leaving:

M × CMakeup = B × CTower

Where C represents the concentration of dissolved solids, and the concentrations in the cooling tower and blowdown are equal.

Rearranging this formula:

M = B × C (Tower) C (Makeup)

Where Cycles of Concentration (COC) = C(tower) ÷ C(makeup):

M = B × COC

This is the fundamental relationship linking the water balance to the solids balance.

Blowdown Rate

Substituting M = E + B into M = B × COC:

E + B = B × COC

E = B × COC − B

E = B × (COC − 1)

Solving for blowdown:

B = E (COC - 1)

Example**:** At 4 cycles with an evaporation rate of 10.2 gpm:

B = 10.2 gpm (4 - 1) = 3.4 gpm

Makeup Rate

Substituting the blowdown equation back into M = E + B:

M = E + (E (COC - 1))

M = E × (1 + 1 (COC - 1))

M = E × ((COC -1) + 1 (COC - 1))

M = E × (COC (COC - 1))

Example: At 4 cycles with an evaporation rate of 10.2 gpm:

M = 10.2 × (4 (4 - 1)) = 13.6 gpm

Check: M = E + B = 10.2 + 3.4 = 13.6 gpm ✓

Conductivity and Cycles

In the field, COC is monitored through conductivity:

COC ≈ Tower ConductivityMakeup Conductivity

This works because most dissolved solids contribute to conductivity. A conductivity controller on the blowdown valve maintains the target COC by opening the valve when tower conductivity rises above the setpoint.

The limitation: Conductivity does not account for transformation. If calcium carbonate precipitates out of solution as scale, its contribution to conductivity disappears – but the controller does not know this. Makeup continues, the conductivity setpoint holds, and the true concentration of scaling species drifts from what conductivity reports.

Verifying the Balance: Tracer Ion Comparison

The diagnostic for catching this is to compare cycles calculated from a soluble tracer ion against cycles calculated from a scaling-risk ion:

COC (tracer) = [Cl] (Cooling Tower) [Cl] (Makeup)

COC (scaling) = [Ca] (Cooling Tower) [Ca] (Makeup)

If COC(tracer) ≈ COC(scaling): the mass balance is intact. Solids are accumulating in solution as expected.

If COC(tracer) > COC(scaling): calcium is leaving the water – it is depositing as scale. The divergence quantifies the loss.

If COC(tracer) < COC(scaling): calcium is entering the water from somewhere other than the makeup. This can occur if calcium scale is being dissolved.

Example: If chloride-based COC is 5.0 but calcium-based COC is only 3.8, roughly 24% of the calcium entering the system is precipitating as scale rather than remaining in solution. This is direct evidence that the mass balance is not in balance, and the system is scaling.

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Water Savings vs. Cycles

Impact of cycles on blowdown makeup for a tower evaporating 25 GPM:

Cycles	Evap (GPM)	BD (GPM)	MU (GPM)	Annual MU (Mgal)	Savings vs 3
2	25	25.0	50.0	26.3	-
3	25	12.5	37.5	19.7	Baseline
4	25	8.3	33.3	17.5	2.2 Mgal
6	25	5.0	30.0	15.8	3.9 Mgal
8	25	3.6	28.6	15.0	4.7 Mgal
10	25	2.8	27.8	14.6	5.1 Mgal

(Assumes 8,760 hr/yr operation and negligible drift. Annual values rounded.)

Key insight: moving from 3 to 6 cycles saves nearly 4 million gallons per year on a single tower. Moving from 6 to 10 saves only 1.2 million more. The biggest gains come first.

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Condenser Performance and Approach Temperature

The condenser approach temperature is one of the most important ways to gain insight into the heat transfer efficiency of the condenser. It calculates the difference between the Leaving Condenser Water Temperature (LCWT) and the Condenser Saturated Refrigerant Temperature (CSRT):

Condenser Approach (°F) = LCWT (°F) - CSRT (°F)

The difference between these two values reflects the theoretical lowest that the Condenser Refrigerant can be cooled. It is important to note that approach temperatures will vary based on load, incoming water temperature, water flow, refrigerant charge, and scaled and/or fouled tubes.

The best practice is to monitor the approach at full load, where a normal range for a clean condenser is typically 1–3°F approach. This can change dramatically if the heat transfer surface becomes fouled, reducing the heat transfer ability of the system.

As fouling builds, the compressor must work harder to provide a suitable gaseous refrigerant to the condenser. This is reflected in a rough field rule:

1°F rise in approach ≈ 1.5–2% increase in chiller energy consumption

Example: A 1,000-ton chiller running at full load for 4,000 hours/year where fouling has increased the approach temperature +5°F, assuming $0.10/kWh.

Baseline Electrical Cost Estimate:

1,000 tons × 0.60 kW/ton = 600 kW

600 kW × 4,000 hr/yr = 2,400,000 kWh/yr

2,400,000 kWh/yr × $0.10/kWh=\ast \ast$240,000/yr**

Fouling Penalty from 5°F increase to Approach (upper end):

600 kW × (5 × 2%) = 60 kW excess power draw

660 kW × 4,000 hr/yr × $0.10/kWh\ast \ast =$264,000/yr**

The fouled condenser requires ~$24,000 more per year to operate, which is why scale and biofilm on condenser tubes are not just water problems - they’re energy problems too.

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Worked Cooling Tower Mass Balance

Scenario: You are servicing a cooling tower connected to a 500-ton chiller. Makeup water conductivity is 400 µS/cm. You want to operate at 5 cycles of concentration. What are your targets?

Step 1: Determine Cooling Tower Heat Load

The 500-ton chiller rating is in standard refrigeration tons. The cooling tower must reject the building load plus compressor heat:

Q = 500 tons × 15,000 BTU/hr·tonCT = 7,500,000 BTU/hr

Step 2: Estimate Recirculation Rate

Recirc Rate = 500 CT tons × 3 GPM/ton = 1,500 gpm

Step 3: Estimate Evaporation Rate

Assuming 10°F range across the tower and f = 0.85:

E = Recirc Rate (gpm) × ΔT × f 1,000 = 1,500 (gpm) × 10°F × 0.85 1,000 = 12.75 gpm

Step 4: Calculate Blowdown at 5 Cycles

B = E (COC - 1)= 12.75 gpm (5 - 1) = 3.19 gpm

Step 5: Calculate Makeup

M = E × (COC (COC - 1)) = 12.75 × (5(5 - 1)) = 15.94 gpm

Check: M = E + B = 12.75 + 3.19 = 15.94 gpm ✓

Step 6: Set Conductivity Target

Target tower conductivity = Makeup conductivity × COC = 400 × 5 = 2,000 µS/cm

Set the conductivity controller to open the blowdown valve at 2,000 µS/cm.

Step 7: Verify with Tracer Ion

At your next water analysis, compare:

• Chloride COC = Cl⁻ (tower) ÷ Cl⁻ (makeup)
• Calcium COC = Ca²⁺ (tower) ÷ Ca²⁺ (makeup)

If both are near 5.0, the balance is holding. If calcium COC is significantly lower, scale is forming and the treatment program needs adjustment.

Annual Water Budget:

At 5 cycles, running 8,760 hr/yr:

• Evaporation: 12.75 gpm × 60 min/hr × 8,760 hr/yr = 6.70 Mgal/yr
• Blowdown: 3.19 gpm × 60 min/hr × 8,760 hr/yr = 1.68 Mgal/yr
• Total makeup: 8.38 Mgal/yr

If this tower were running at 3 cycles instead of 5, blowdown would be 6.38 gpm and total makeup would be 10.07 Mgal/yr.

The difference: 1.69 million gallons per year saved by running 5 cycles instead of 3.

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⟵ 12 Cooling Things Down (Narrative) · Contents · 12 Cooling Things Down (Problem Set) ⟶