The wind chill factor represents the equivalent 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
π‘
W(t) = {33 β (10.45+10βπ£βπ£)(33βπ‘) / 2204
33 β 1.5958(33 β π‘)
if 0 β€ v < 1.79
if 1.79 β€ v < 20
if v β₯ 20
where v represents the wind speed (in meters per second) and t represents the air temperature . Compute the wind chill for an air temperature of 15Β°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.) Show your work.
To compute the wind chill for an air temperature of 15Β°C and a wind speed of 12 meters per second, we need to use the wind chill formula and substitute the given values.
Given:
Temperature (t) = 15Β°C
Wind Speed (v) = 12 m/s
First, let's determine the range of wind speed that applies to our given value of v. In this case, 1.79 β€ 12 < 20, so we use the second part of the formula.
Now, we can substitute the values into the formula:
W(t) = {33 β [(10.45+10βvβv)/(33βt)]} / [33 β 1.5958(33 β t)]
W(t) = {33 β [(10.45+10β12β12)/(33β15)]} / [33 β 1.5958(33 β 15)]
Next, let's simplify the formula step by step:
W(t) = {33 β [(10.45+10β12β12)/18]} / [33 β 1.5958(18)]
W(t) = {33 β [(10.45+10β12β12)/18]} / [33 β 28.8744]
Now, let's evaluate the numerator first:
Numerator = (10.45+10β12β12)
Numerator = 10.45 + 10β12 - 12
Numerator = 10.45 + 10(β12) - 12
Numerator = 10.45 + 10(3.464) - 12 (since β12 = 3.464)
Numerator = 10.45 + 34.64 - 12
Numerator = 43.09 - 12
Numerator = 31.09
Now, substitute this value back in the formula:
W(t) = {33 β (31.09/18)} / [33 β 28.8744]
W(t) = {33 - 1.7272} / 4.1256
W(t) = 31.2728 / 4.1256
W(t) β 7.57Β°C
Therefore, the wind chill for an air temperature of 15Β°C and a wind speed of 12 meters per second is approximately 7.57Β°C.