Chapter 1, Problem 168P

It is well know that at the same outdoor air temperature a person is cooled at a faster rate under windy conditions that under calm conditions due to the higher convection heat transfer coefficients associated with windy air. The phrase wind-chill is used to relate the rate of heat loss from people under windy conditions to an equivalent air temperature for calm conditions (considered to be a wind or walking speed of 3 mph or 5 km/h). The hypothetical wind-chill temperature (WCT), called the wind-chill temperature index (WCTI), is an air temperature equivalent to the air temperature needed to produce the same temperature (WCT), called the wind-chill temperature index (WCTI), is an air temperature equivalent to the air temperature needed to produce the same cooling effect under calm conditions. A 2003 report on wind-chill temperature by the U.S. National Weather Service gives the WCTI in metric units as $\text{WCTI}{(}^{\circ }C)=13.12+0.6215T-11.37V^{0.16}+0.3965T{V}^{0.16}$

Where T is the air temperature in ${}^{\circ }C$ and V the wind speed in km/h at 10 m elevation. Show that this relations can be expressed in English units as $\text{WCTI}{(}^{\circ }F)=35.74+0.6215T-35.75V^{0.16}+0.4275T{V}^{0.16}$

Where T is the air temperature in ${}^{\circ }F$ and V the wind speed in mph at 33ft elevation. Also, prepare a table for WCTI for air temperatures ranging from 10 to $-{60}^{\circ }C$ and wind speeds ranging from 10 to 80 km/h. Comment on the magnitude of the cooling effect of the wind and the danger of frostbite.