The heat flow rate is computed from the nameplate water flow rate and the temperature rise across the heat exchanger using an empirical water heat capacity coefficient. The constant \(k_{water} = 251045\) \([\unit{\kJ\per\cubic\meter\per\K\minute\per\hour}]\) is derived from \(8.34\ \text{lb/gal} \times 1\ \text{Btu/(lb·°F)} \times 60\ \text{min/hr}\).

\begin{equation}\label{eq:steam-reduction-water-heat-flow} \dot{Q}_{water} = k_{water} \cdot \dot{V}_{water} \cdot (T_{out} - T_{in})\end{equation}

\begin{equation}\label{eq:steam-reduction-water-energy} E_{use} = \frac{k_{units} \cdot \dot{Q}_{water} \cdot t_{op}}{\eta_{sys} \cdot \eta_{boiler}}\end{equation}

Symbols

\(\dot{Q}_{water}\)	Water heat flow rate \([\unit{ \kJ\per\hour}]\)
\(k_{water}\)	Water heat capacity coefficient (251045) \([\unit{ \kJ\per\cubic\meter\per\K\minute\per\hour}]\)
\(\dot{V}_{water}\)	Nameplate water flow rate \([\unit{ \cubic\meter\per\minute}]\)
\(T_{out}\)	Outlet temperature \([\unit{ \degreeCelsius}]\)
\(T_{in}\)	Inlet temperature \([\unit{ \degreeCelsius}]\)
\(E_{use}\)	Annual energy use \([\unit{ \kJ\per\year}]\)
\(k_{units}\)	Quantity multiplier (number of identical units) \([\unit{ \unitless}]\)
\(t_{op}\)	Annual operating hours \([\unit{ \hour\per\year}]\)
\(\eta_{sys}\)	System efficiency \([\unit{ \unitless}]\)
\(\eta_{boiler}\)	Boiler efficiency \([\unit{ \unitless}]\)