Chapter 1, Problem 1.25P

A common procedure for measuring the velocity of an airstream involves the insertion of an electrically heated wire (called a hot-wire anemometer ) into the airflow, with the axis of the wire oriented perpendicular to the flow direction. The electrical energy dissipated in the wire is assumed to be transferred to the air by forced convection. Hence, for a prescribed electrical power, the temperature of the wire depends on the convection coefficient, which, in turn, depends on the velocity of the air. Consider a wire of length $L=20\text{mm}$ and diameter $D=0.5\text{mm,}$ for which a calibration of the form $V=6.25\times {10}^{-5}{h}^2$ has been determined. The velocity V and the convection coefficient h have units of m/s and ${\text{W/m}}^{\text{2}}\cdot \text{K,}$ respectively. In an application involving air at a temperature of $T_{\infty }=25°\text{C,}$ the surface temperature of the anemometer is maintained at $T_s=75°\text{C}$ with a voltage drop of 5 V and an electric current of 0.1 A. What is the velocity of the air?