 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 $5\mu \mathrm{m}$ in diameter supported between prongs.^[ref] Maintaining resistance approximately fixes wire temperature only over the characterized resistance-temperature relation and control bandwidth.

A lumped thermal balance illustrates the mechanism: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 formwhere $E$ 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 $A=1{\mathrm{V}}^2$, $B=0.5{\mathrm{V}}^2(m/s{)}^{-1/2}$ and $n=1/2$, $U=16m/s$ gives $E=\sqrt{3}\mathrm{V}$. Differentiation gives $dU/dE\approx 55.43(m/s)/V$ there, so a small $0.010\mathrm{V}$ error corresponds to about $0.554m/s$ 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.