Chapter 7, Problem 7.23P

The proposed design for an anemometer to determine the velocity of an airstream in a wind tunnel is comprised of a thin metallic strip whose ends are supported by stiff rods serving as electrodes for passage of current used to heat the strip. A fine-wire thermocouple is attached to the trailing edge of the strip and serves as the sensor for a system that controls the power to maintain the strip at a constant operating temperature for variable airstream velocities. Design conditions pertain to an airstream at $T_{\infty }=25°\text{C}$ and $1\le u_{\infty }\le 50\text{m/s,}$ with a strip temperature of $T_s=35°\text{C}\text{.}$

1. Determine the relationship between the electrical power dissipation per unit width of the strip in the transverse direction, $P\text{'}\left(\text{mW/mm}\right),$ and the airstream velocity. Show this relationship graphically for the specified range of $u_{\infty }.$
2. If the accuracy with which the temperature of the operating strip can be measured and maintained constant is $\pm 0.2°\text{C,}$ what is the uncertainty in the airstream velocity?
3. The proposed design operates in a strip constant-temperature mode for which the airstream velocityis related to the measured power. Consider now an alternative mode wherein the strip is provided with a constant power, say, 30 mW/mm, and the airstream velocity is related to the measured strip temperature $T_s.$ For this mode of operation, show the graphical relationship between the strip temperature and airstream velocity. If the temperature can be measured with an uncertainty of $\pm 0.2°\text{C,}$ what is the uncertainty in the airstream velocity?
4. Compare the features associated with each of the anemometer operating modes.