Flow calorimeter
= Flow calorimeter
{title2=$P_{\mathrm{fluid}}=\dot m(h_{\mathrm{out}}-h_{\mathrm{in}})$}
A <flow calorimeter> uses a flowing material to carry energy from a measurement region. In a common arrangement, a heated receiver exchanges energy with a coolant stream. Measurements of <mass flow rate> and inlet/outlet <temperatures> determine the stream's enthalpy gain, while the vessel and environmental paths are included in the overall balance.<Water calorimeter power detectors by Gentec-EO>[Publisher explanation, measuring water flow and temperature to determine absorbed power]{ref}
For a steady stream with negligible changes in bulk <kinetic energy> and height,
$$
P_{\mathrm{fluid}}=\dot m(h_{\mathrm{out}}-h_{\mathrm{in}})
\simeq\dot m c_p(T_{\mathrm{out}}-T_{\mathrm{in}}).
$$
The approximation uses a suitable approximately constant <specific heat capacity>. An absorber, inlet and outlet thermometers, and a calibrated flow measurement turn this equation into an apparatus rather than just a temperature reading.
For a synthetic example, let $\dot m=0.010\,\mathrm{kg\,s^{-1}}$ and $c_p=4000\,\mathrm{J\,kg^{-1}\,K^{-1}}$. A $0.60\,\mathrm K$ rise gives $P_{\mathrm{fluid}}=24\,\mathrm W$. If a 30-watt electrical reference produces this response under matched conditions, the observed response fraction is $0.8$. Under an explicitly tested proportional-response assumption, a later 36-watt fluid reading would correspond to a 45-watt source.
A single calibration point does not establish that assumption at every power. The full balance includes receiver storage and other losses:
$$
P_{\mathrm{source}}=P_{\mathrm{fluid}}+\frac{dU_{\mathrm{receiver}}}{dt}+P_{\mathrm{loss}}.
$$
Warm-up, leakage, thermometer offsets and transport delays can all affect a time-varying measurement. <Calorimeter calibration> and <electrical calorimetry> can test the response across a range, with the same <thermodynamic system> boundary used for calibration and the unknown source.