= Hot-wire anemometer
A <hot-wire anemometer> infers fluid motion from the cooling of an electrically heated fine wire. Faster transverse flow generally changes the convective heat loss, changing either the wire's <electrical resistance> or the <power> needed to maintain its <temperature>. The output is converted into flow <speed> through an <instrument calibration>, not by assuming that electrical voltage itself is <velocity>.
A primary manufacturer describes a <constant-temperature hot-wire anemometer> with the wire in one arm of a <Wheatstone bridge>. A servo adjusts heating current to keep the wire resistance approximately fixed. Representative probes use tungsten wires about $1\,\mathrm{mm}$ long and $5\,\mathrm{\mu m}$ in diameter supported between prongs.<Measurement Principles of CTA by Dantec Dynamics>[CTA principles and Probes]{ref} Maintaining resistance approximately fixes wire <temperature> only over the characterized resistance-temperature relation and control <bandwidth>.
A lumped thermal balance illustrates the mechanism:
$$
C_w\frac{dT_w}{dt}=I^2R_w-hA_w(T_w-T_a)-Q_{\rm ends}-Q_{\rm rad}.
$$
Here $C_w$ is the wire's <heat capacity>, $h$ a <heat transfer coefficient>, $A_w$ its exposed area and $T_a$ the surrounding fluid <temperature>. Conduction to supports and radiation are explicitly retained as losses. In a quasi-steady constant-temperature regime, the electrical heating must track the flow-dependent heat loss. In a constant-current arrangement, wire <temperature> and resistance instead vary as the cooling changes.
An empirical calibration often has the form
$$
E^2=A+BU^n,\qquad U=\left(\frac{E^2-A}{B}\right)^{1/n},
$$
where $E$ is a specified bridge output and $A,B,n$ are fitted for the probe, fluid and operating conditions. The coefficient units depend on the chosen units of $U$ and the exponent. For an original model with $A=1\,\mathrm{V^2}$, $B=0.5\,\mathrm{V^2}(\mathrm{m/s})^{-1/2}$ and $n=1/2$, $U=16\,\mathrm{m/s}$ gives $E=\sqrt3\,\mathrm V$. Differentiation gives $dU/dE\approx55.43\,\mathrm{(m/s)/V}$ there, so a small $0.010\,\mathrm V$ error corresponds to about $0.554\,\mathrm{m/s}$ before other uncertainty contributions.
A proposed experiment places the probe in a controlled reference flow, records bridge output over several speeds, measures ambient <temperature> and repeats the calibration after the experiment. Rotating the probe reveals directional sensitivity; a single straight wire does not uniquely resolve an arbitrary three-dimensional <velocity> or the sign of reversed crossflow. <Hot-wire anemometry> therefore needs a stated probe orientation, <frequency> response and data-reduction procedure as well as a steady calibration.
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