Liquid ethanol is a flammable fluid and can release vapors that form explosive
mixtures at temperatures above its flashpoint at \(16.6^{\circ} \mathrm{C}\). In
a chemical plant, liquid ethanol \(\left(c_{p}=2.44 \mathrm{~kJ} / \mathrm{kg}
\cdot \mathrm{K}, \rho=789 \mathrm{~kg} / \mathrm{m}^{3}\right)\) is being
transported in a pipe with an inside diameter of \(5 \mathrm{~cm}\). The pipe is
located in a hot area with the presence of ignition source, where an estimated
\(20 \mathrm{~kW}\) of heat is added to the ethanol. Your task, as an engineer,
is to design a pumping system to transport the ethanol safely and to prevent
fire hazard. If the inlet temperature of the ethanol is \(10^{\circ}
\mathrm{C}\), determine the volume flow rate that is necessary to keep the
temperature of the ethanol in the pipe below its flashpoint.