Chapter 1, Problem 1.25P

A common procedure for measuring the velocity of anairstream involves the insertion of an electrically heatedwire (called a hot-wire anemometer) into the airflow,with the axis of the wire oriented perpendicular to the flow direction. The electrical energy dissipated inthe wire is assumed to be transferred to the air by forcedconvection. Hence, for a prescribed electrical power, thetemperature 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 Vand the convection coefficient h have units of m/s and ${\text{W/m}}^{\text{2}}\cdot \text{K}$ , respectively. In an application involving air ata temperature of T. = 25°C, the surface temperature ofthe anemometer is maintained at $T_{\infty }=75°\text{C}$ with a voltage drop of 5 V and an electric current of 0.1 A. What isthe velocity of the air?