Wind chill problem

May 2012
8
0
Norway
\(\displaystyle T_{wc} = 13.12 + 0.6212 \cdot T_a - 11.37 \cdot V^{0.16} + 0.3965 \cdot T_a \cdot V^{0.16}\)

This is the wind chill formula, see Wind chill - Wikipedia, the free encyclopedia
T is temperature, V is the wind velocity.

Let T = -10 C centigrade at some time and V = 10 m/s. At what rate must V be reduced for W to remain constant when T is reduced by 1 C centigrade per hour?
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey mathlearner100.

Have you tried to calculate the derivatives of W with respect to Ta and V? The total differential will be 0 if T_wc doesn't change (i.e. remains constant).

This is when these things vary continuously: if they don't then you need to consider a discrete model.