# 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 & Crossflow Cooling Towers. It computes cooling duty ( $\text{TR}$ and $\text{kW}$ ), cooling approach ( $A$ ), Merkel transfer units ( $\text{NTU}$ / $\text{KaV/L}$ ), active fill volume ( $V_{\text{fill}}$ ), fan static pressure drop ( $\Delta P_{\text{total}}$ ), fan motor power ( $P_{\text{fan}}$ ), water balance losses ( $E, D, B, M$ ), and provides fill selection options for Timber Splash Grids, PVC Inverted V-Bar, and PVC Honeycomb Film Fills.

# 2. Fundamental Equations & Chemical Engineering Formulas

# 2.1 Thermal Heat Duty ( $Q$ )

Q = \frac{m_w \cdot C_p \cdot (T_{\text{hot}} - T_{\text{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 ( $4.184 \text{ kJ/kg}\cdot^\circ\text{C}$ )
$T_{\text{hot}}$ : Hot water inlet return temperature ( $^\circ\text{C}$ )
$T_{\text{cold}}$ : Cold water outlet supply temperature ( $^\circ\text{C}$ )

# 2.2 Range, Approach & Cooling Efficiency

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

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

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

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

# 2.3 Geometry & Active Fill Surface Area

\text{Footprint Area } (A_{\text{footprint}}) = \frac{Q_L}{L_{\text{flux}}} \quad [\text{m}^2]

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

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

Where:

$Q_L$ : Circulating water flow rate ( $\text{m}^3/\text{h}$ )
$L_{\text{flux}}$ : Design liquid flux ( $\text{m}^3/\text{m}^2\cdot\text{h}$ )
$H_{\text{fill}}$ : Height of active fill packing ( $\text{m}$ )
$a_{sp}$ : Specific surface area density of fill media ( $\text{m}^2/\text{m}^3$ )

# 2.4 Merkel Transfer Units ( $\text{NTU}$ ) & Fill Characteristic Demand

\text{NTU}_{\text{req}} \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)

Available Fill Transfer Characteristic:

\left( \frac{KaV}{L} \right)_{\text{avail}} = C_{\text{fill}} \cdot \left( \frac{L}{G} \right)^{-m} \cdot H_{\text{fill}}^n

\text{Thermal Reserve / Capability Ratio \%} = \frac{(KaV/L)_{\text{avail}}}{\text{NTU}_{\text{req}}} \times 100\%

# 3. Fill Media Technology Comparison

The calculator models three standard industrial fill media types:

Parameter / Feature	PVC Honeycomb (Film Fill)	PVC Inverted V-Bar (Splash)	Timber Splash Grid (Wood)
Media Mechanism	Corrugated cellular film pack	Offset triangular splash bars	Wooden laths & timber grids
Specific Surface Area ( $a_{sp}$ )	$150 – 250 \text{ m}^2/\text{m}^3$ (Default: $220$ )	$75 – 110 \text{ m}^2/\text{m}^3$ (Default: $90$ )	$35 – 55 \text{ m}^2/\text{m}^3$ (Default: $45$ )
Typical Fill Height ( $H_{\text{fill}}$ )	$0.90 – 1.80 \text{ m}$ (Default: $1.55\text{ m}$ )	$1.80 – 2.80 \text{ m}$ (Default: $2.10\text{ m}$ )	$2.40 – 4.50 \text{ m}$ (Default: $3.00\text{ m}$ )
Design Liquid Flux ( $L_{\text{flux}}$ )	$16 – 25 \text{ m}^3/\text{m}^2\cdot\text{h}$	$12 – 18 \text{ m}^3/\text{m}^2\cdot\text{h}$	$8 – 14 \text{ m}^3/\text{m}^2\cdot\text{h}$
Pressure Drop Coeff ( $C_{dp}$ )	$1.50 \text{ mmWC/m}$ at $2.2\text{ m/s}$	$1.15 \text{ mmWC/m}$ at $2.2\text{ m/s}$	$0.85 \text{ mmWC/m}$ at $2.2\text{ m/s}$
Merkel Constants ( $C, m, n$ )	$C=2.45, m=0.65, n=1.00$	$C=1.65, m=0.55, n=0.95$	$C=1.25, m=0.50, n=0.90$
Fouling Tolerance	Low (Clean / filtered water only)	Moderate (Tolerates suspended solids)	High (Immune to turbid/dirty water)

# 4. Air Pressure Drop & Fan Power Sizing

\Delta P_{\text{total}} = C_{dp} \cdot H_{\text{fill}} \cdot \left( \frac{v_{\text{air}}}{2.2} \right)^{1.45} + 2.5 \quad [\text{mmWC}]

P_{\text{fan}} = \frac{(G / 3600) \cdot (\Delta P_{\text{total}} \cdot 9.80665)}{1000 \cdot \eta_{\text{fan}} \cdot \eta_{\text{motor}}} \times 1.10 \quad [\text{kW}]

# 5. 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}]

# 6. Reference Standards

CTI Code ATC-105: Acceptance Test Code for Water Cooling Towers, Cooling Technology Institute.
Marley Cooling Tower Fundamentals: SPX Cooling Technologies Handbook.
Perry, R.H. & Green, D.W.: Perry's Chemical Engineers' Handbook, Section 12.