Water Cooling Heat Loss Calculator

Detailed Description

This calculator estimates the heat removed by water cooling systems, using flow rate, inlet and outlet temperatures, and a correction factor. It accounts for water density variation with temperature and converts between SI and U.S. Customary units as needed. The algorithm is suitable for modeling cooling losses in industrial furnaces, ovens, and similar systems.

The calculation follows a top-down approach:

1. Total Heat Loss - Calculate heat removed by water based on flow rate and temperature rise
2. Water Density - Compute temperature-dependent water density for accurate mass flow calculation

Total Water Cooling Heat Loss

---

Total heat loss due to water cooling.

The heat loss is calculated by multiplying the water flow rate, water density, temperature rise, and correction factor. Water density is temperature-dependent and calculated using the Tanaka correlation. The factor of 60 converts from gallons per minute to gallons per hour.

\begin{equation}\label{eq:water-cooling-heat-loss} Q_\text{cool} = FR \cdot 60 \cdot \rho_{w,lb/gal} \cdot \Delta T \cdot CF\end{equation}

Symbols

\(Q_\text{cool}\)	Water cooling heat loss \([\unit{ \btu\per\hour}]\)
\(FR\)	Water flow rate \([\unit{ \gallon\per\minute}]\)
\(60\)	Minutes per hour (GPM to GPH conversion) - see physics::conversions::kMinutesPerHour \([\unit{ \unitless}]\)
\(\rho_{w,lb/gal}\)	Water density \([\unit{ \pound\per\gallon}]\)
\(\Delta T\)	Temperature rise (outlet - inlet) \([\unit{ \degreeFahrenheit}]\)
\(CF\)	Correction factor \([\unit{ \unitless}]\)

Water Density Calculation

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Temperature-dependent water density calculation.

This formula from Tanaka et al. (2001) calculates the density of water as a function of temperature. The base density of 1000 kg/m³ (see physics::si::kWaterDensityBase) is adjusted by a temperature-dependent correction factor. The result is converted to lb/gal using physics::conversions::kKgPerM3ToLbPerGal.

\begin{equation}\label{eq:water-density-tanaka} \rho_w = 1000 \left[1 - \frac{(T_C + 288.9414)}{508929.2 (T_C + 68.12963)} (T_C - 3.9863)^2 \right]\end{equation}

Symbols

\(\rho_w\)	Water density \([\unit{ \kilogram\per\meter\cubed}]\)
\(T_C\)	Average water temperature \([\unit{ \degreeCelsius}]\)
\(1000\)	Base water density - see physics::si::kWaterDensityBase \([\unit{ \kilogram\per\meter\cubed}]\)

Note

For heat losses due to liquid cooling see Liquid Cooling Heat Loss Calculator or for gas cooling see Gas Cooling Heat Loss Calculator.

See also

Perry's Chemical Engineers' Handbook; NIST Engineering Statistics; Tanaka et al. (2001)

physics::si::kWaterDensityBase for the base water density constant

physics::conversions::kMinutesPerHour for time conversion

physics::conversions::kKgPerM3ToLbPerGal for density unit conversion

Modules
	Water Cooling Heat Loss Formula
	Total heat loss due to water cooling.
	Water Density Calculation Formula
	Temperature-dependent water density calculation.

Files
file	water_cooling_heat_loss.h

Namespaces
namespace	water_cooling_heat_loss
	Calculates heat loss due to water cooling in process heating equipment.

Functions
double	water_cooling_heat_loss::totalHeatLoss (double flowRate, double initialTemperature, double outletTemperature, double correctionFactor)
	Calculates the total heat loss due to water cooling in process heating equipment.

Function Documentation

totalHeatLoss()

double water_cooling_heat_loss::totalHeatLoss	(	double	flowRate,
		double	initialTemperature,
		double	outletTemperature,
		double	correctionFactor
	)

This function computes the heat loss removed by water cooling, based on flow rate, initial temperature, outlet temperature, and a correction factor. The calculation assumes no phase change and uses sensible heat only.

Parameters

[in]	flowRate	Cooling water flow rate \([\unit{\gallon\per\minute}]\)
[in]	initialTemperature	Initial/inlet water temperature \([\unit{\degreeFahrenheit}]\)
[in]	outletTemperature	Outlet water temperature \([\unit{\degreeFahrenheit}]\)
[in]	correctionFactor	Correction factor \([\unit{\unitless}]\)

Returns

Total heat loss \([\unit{\btu\per\hour}]\)

See also

• Water Cooling Heat Loss Formula