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A constant-temperature hot-wire anemometer is a hot-wire anemometer whose electrical feedback adjusts wire heating to keep a chosen wire resistance approximately constant. The resistance acts as a temperature indicator; increasing flow cooling calls for increased electrical power. The primary manufacturer's arrangement places the wire in a Wheatstone bridge controlled by a servo amplifier.^[ref]

A simple resistance-temperature calibration illustrates the setpoint. If the cold resistance at fluid temperature $T_a$ is $R_a$, approximateFor stipulated $R_a=5\Omega$, $R_w=7.5\Omega$ and ${\alpha }_R=0.004{\mathrm{K}}^{-1}$, the overtemperature is $125\mathrm{K}$. At ambient $20{}^{\circ }\mathrm{C}$, that corresponds to wire temperature $145{}^{\circ }\mathrm{C}$ in this linear model. These parameters are illustrative, not universal tungsten specifications. A fixed resistance setpoint and a fixed overtemperature require different adjustments when ambient temperature changes.

At steady state, the heating balances convective, support-conduction and radiative losses. The observed bridge output must be calibrated against known flow with the same probe, fluid and operating conditions. A bridge output squared may follow an empirical relation $E^2=A+B{U}^n$ over a limited range, but circuit ratios and losses matter before identifying that output with wire power. The manufacturer's technical account separately treats velocity, directional and temperature calibration.^[ref]

Finite-bandwidth thermal feedback in hot-wire anemometry can be explored with an original local model. Let a temperature perturbation satisfywhere $C_w>0$ is wire heat capacity, $K>0$ a linearized thermal-loss coefficient and $F>0$ the incremental cooling per speed change. An ideal proportional power controller applies $\delta P=-K_c\delta T$, with $K_c>0$. HenceA cooling perturbation first lowers temperature, causing the controller to raise power. Finite feedback gain leaves a residual temperature perturbation and gives DC power sensitivity $F{K}_c/(K+K_c)$.

For $C_w=10^{-8}J/K$, $K=10^{-4}W/K$ and $K_c=9\times 10^{-4}W/K$, the model's thermal time constant changes from $100$ to $10\mu \mathrm{s}$ and its half-power frequency from about $1.59$ to $15.9\mathrm{kHz}$. The closed-loop DC response is $0.9F$. This calculation assumes an instantaneous controller; real amplifier and cable dynamics can add phase lag and limit usable gain.

A proposed characterization calibrates the steady speed response, then applies a small electrical test perturbation and examines settling and ringing while measuring ambient temperature. Check the response over the intended flow range and verify that the measuring electronics do not clip. The primary practical guide describes the feedback bridge as part of the complete measuring chain.^[ref] A fast electrical response alone does not establish spatial resolution or uniquely determine the direction of a reversing flow.

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.