Chapter 2.4, Problem 59AYU

Wind Chill The wind chill factor represents the air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is

$W=\{\begin{array}{l}t0\le v<1.79\\ 33-\frac{\left(10.45+10\sqrt{v}-v\right)\left(33-t\right)}{22.04}\text{}1.79\le v\le 20\\ 33-1.5958\left(33-t\right)v>20\end{array}$

where $v$ represents the wind speed (in meters per second) and $t$ represents the air temperature $\left(°C\right)$. Compute the wind chill for the following:

(a) An air temperature of ${10}^{\circ }\text{C}$ and a wind speed of 1 meter per second (m/sec)

(b) An air temperature of ${10}^{\circ }\text{C}$ and a wind speed of 5 m/sec

(c) An air temperature of ${10}^{\circ }\text{C}$ and a wind speed of 15 m/sec

(d) An air temperature of ${10}^{\circ }\text{C}$ and a wind speed of 25 m/sec

(e) Explain the physical meaning of the equation corresponding to $0\le v<1.79$.

(f) Explain the physical meaning of the equation corresponding to $v>20$.