# Cooling Tower Design & Thermal Rating Calculator Documentation

# 1. Overview

The Cooling Tower Design & Thermal Rating Calculator is a chemical and utility engineering tool designed to rate, size, and evaluate the performance of Induced-Draft Counterflow Cooling Towers. It computes cooling duty ( $\text{TR}$ and $\text{kW}$ ), cooling approach ( $A$ ), Merkel transfer units ( $\text{NTU}$ / $\text{KaV/L}$ ), active PVC fill surface area ( $A_{total}$ ), total fan static pressure drop ( $\Delta P_{total}$ ), fan motor power ( $P_{fan}$ ), and evaporative/makeup water losses ( $M$ ).

# 2. Fundamental Equations & Chemical Engineering Formulas

# 2.1 Thermal Heat Duty ( $Q$ )

Q = \frac{m_w \cdot C_p \cdot (T_{hot} - T_{cold})}{3600} \quad [\text{kW}]

\text{Duty in TR} = \frac{Q}{3.51685} \quad [\text{TR}]

Where:

$m_w$ : Water mass flow rate ( $\text{kg/h} = \text{Water Flow in m}^3/\text{h} \times 1000$ )
$C_p$ : Specific heat of water ( $4.184 \text{ kJ/kg}\cdot^\circ\text{C}$ )
$T_{hot}$ : Hot water inlet return temperature ( $^\circ\text{C}$ )
$T_{cold}$ : Cold water outlet supply temperature ( $^\circ\text{C}$ )

# 2.2 Range, Approach & Cooling Efficiency

\text{Cooling Range } (\Delta T) = T_{hot} - T_{cold} \quad [^\circ\text{C}]

\text{Cooling Approach } (A) = T_{cold} - T_{WB} \quad [^\circ\text{C}]

\text{Cooling Efficiency } (\eta_{CT}) = \frac{T_{hot} - T_{cold}}{T_{hot} - T_{WB}} \times 100\%

Where $T_{WB}$ is the ambient wet-bulb temperature.

# 2.3 Geometry & PVC Honeycomb Fill Area

\text{Footprint Area } (A_{footprint}) = L \times W \quad [\text{m}^2]

\text{Liquid Flux } (L_{flux}) = \frac{Q_L}{A_{footprint}} \quad [\text{m}^3/\text{m}^2\cdot\text{h}]

\text{Active Fill Volume } (V_{fill}) = A_{footprint} \times H_{fill} \quad [\text{m}^3]

\text{Total Surface Area } (A_{total}) = a_{sp} \times V_{fill} \quad [\text{m}^2]

Where $a_{sp}$ is the specific surface area of the PVC fill blocks ( $\text{m}^2/\text{m}^3$ ).

# 2.4 Merkel Transfer Units ( $\text{NTU}$ ) via 4-Point Chebyshev Rule

\text{NTU} = \frac{K_a \cdot V}{L} \approx \frac{\Delta T}{4} \times \left( \frac{1}{\Delta h_1} + \frac{1}{\Delta h_2} + \frac{1}{\Delta h_3} + \frac{1}{\Delta h_4} \right)

Where $\Delta h_i = h_{s,i} - h_{a,i}$ is the enthalpy driving force evaluated at four intermediate temperatures:

T_i = T_{cold} + c_i \cdot \Delta T \quad \text{for } c_i \in \{0.1, 0.4, 0.6, 0.9\}

# 2.5 Air Pressure Drop & Fan Motor Power

\Delta P_{total} = \Delta P_{fill} + \Delta P_{louver} (3.0) + \Delta P_{drift} (2.5) + \Delta P_{stack} (2.0) \quad [\text{mmWC}]

P_{fan} = \frac{(G / 3600) \cdot (\Delta P_{total} \cdot 9.80665)}{1000 \cdot \eta_{fan} \cdot \eta_{motor}} \times 1.15 \quad [\text{kW}]

# 2.6 Evaporative & Water Balance Losses

Evaporation Loss ( $E$ ):

E = 0.00085 \times Q_L \times \Delta T \times 1.8 \quad [\text{m}^3/\text{h}]

Drift Droplet Loss ( $D$ ):

D = 0.00005 \times Q_L \quad [\text{m}^3/\text{h}]

Blowdown Rate ( $B$ ):

B = \frac{E}{CoC - 1} \quad [\text{m}^3/\text{h}]

Total Fresh Makeup Water ( $M$ ):

M = E + D + B \quad [\text{m}^3/\text{h}]

# 3. Recommended Design Guidelines

Approach Target: Maintain an approach of $4.0 - 9.0^\circ\text{C}$ for efficient thermal sizing.
Liquid Loading Rate: Keep liquid flux rate within $12 - 22 \text{ m}^3/\text{m}^2\cdot\text{h}$ to prevent dry spots or flooding.
Fill Height: Standard PVC honeycomb fill heights range between $1.20 \text{ m}$ and $1.65 \text{ m}$ .