Cooling Tower Thermal Design & Water Balance Calculator (Merkel Method)

Cooling Tower Thermal Design & Water Balance Calculator

This industrial-grade tool performs a complete Thermal Sizing and Water Balance for open cooling towers. It integrates Psychrometric Analysis to calculate air flow requirements, solves the Merkel Equation ($KaV/L$) for thermal difficulty, and estimates the Total Cost of Operation including water, chemicals, and energy.

Quick Load Scenarios:

1. System Configuration

Mode & Units

Unit System

Calculation Mode

Water Quality & Design

Cycles of Concentration (COC)

Design L/G Ratio

2. Thermal Conditions

Temperatures & Air

Hot Water Inlet ($T_{in}$)

Cold Water Outlet ($T_{out}$)

Wet Bulb ($T_{wb}$)

Dry Bulb ($T_{db}$)

Site Altitude [ft or m]

Load & Costs

Water Flow Rate [GPM]

Fan Static Pressure [in.wg or Pa]

Water Cost [$/kGal or $/m³]

Drift Loss [%]

Performance Analysis

Thermal & Hydraulic Metrics

Parameter	Value	Unit

Design Check:

Temperature Gradient Diagram

● Range ($T_{in}-T_{out}$) ● Approach ($T_{out}-T_{wb}$)

Step-by-Step Engineering Calculation

Evaporation calculated via Enthalpy Balance if possible, else approximation. Merkel Number estimated via 4-point Chebyshev integration.

Engineering Insights: Cooling Tower Fundamentals

1. The Merkel Equation ($KaV/L$)

The Merkel Equation is the industry standard for sizing cooling towers. It represents the difficulty of the cooling task.

$$\frac{KaV}{L} = \int_{T_{out}}^{T_{in}} \frac{C_p \, dT}{h_w - h_a}$$

Where $h_w$ is the enthalpy of saturated air at the water temperature, and $h_a$ is the enthalpy of the air stream.
High $KaV/L$: Hard duty (Close approach, large range). Requires more fill, taller tower.
Low $KaV/L$: Easy duty. Smaller tower.

2. Psychrometrics & Airflow

Cooling occurs by evaporating water into air. The capacity of air to absorb water depends on its Enthalpy.
L/G Ratio: The ratio of Water Mass Flow ($L$) to Air Mass Flow ($G$). Typical design values are 0.8 to 1.5.
If you reduce airflow (increase L/G), the air saturates faster, and the tower performance drops (Approach increases).

3. Where Does the Water Go?

Cooling towers consume water to reject heat.

Evaporation ($E$): Pure water vapor leaves the tower carrying latent heat. Approx 1% of flow for every 7°C (12.5°F) of cooling range.
Drift ($D$): Small droplets of liquid water entrained in the air stream. Contains dissolved solids/chemicals. Modern eliminators limit this to <0.005%.
Blowdown ($B$): Intentional bleed-off to remove concentrated minerals. Since only pure water evaporates, minerals (Ca, Mg, Silica) stay behind and concentrate. If not bled off, they form scale.

Total Make-up = E + D + B.

4. Cycles of Concentration (COC)

COC represents how concentrated the tower water is compared to the make-up water.

$$COC = \frac{\text{Chlorides}_{Tower}}{\text{Chlorides}_{MakeUp}} \approx \frac{MakeUp}{Blowdown}$$

Higher COC saves water (less blowdown) but increases scaling risk.
COC 2.0 -> You blow down 1 gallon for every 1 gallon evaporated (50% water wasted).
COC 5.0 -> You blow down 0.25 gallons for every 1 gallon evaporated (Excellent efficiency).
Most industrial towers aim for 3.0 to 7.0 depending on water treatment.

5. The Vital Difference: Range vs. Approach

Range ($T_{in} - T_{out}$): This is determined strictly by the Heat Load and Water Flow ($Q = \dot{m} C_p \Delta T$). The cooling tower cannot "control" the range; physics dictates it. If you reduce water flow, range increases.
Approach ($T_{out} - T_{wb}$): This is determined by the Tower Size/Efficiency and the ambient Wet Bulb temperature. It is the measure of performance. A larger tower provides a closer approach (colder water). It is thermodynamically impossible for the outlet temperature to equal or go below the wet bulb temperature (Approach = 0 is impossible).