In a hurricane, the wind pressure varies directly as the square of the wind velocity. If wind pressure is a measure of a hurricane’s destructive capacity, what happens to this destructive power when the wind speed doubles?

Question

In a hurricane, the wind pressure varies directly as the square of the wind velocity. If wind pressure is a measure of a hurricane’s destructive capacity, what happens to this destructive power when the wind speed doubles?
Do you have an equation to prove if this makes sense of not?

Steve · Accepted Answer

p = kv^2 so, if v is replaced by 2v, then p becomes k(2v)^2 = k*4v^2 = 4kv^2 = 4p So, p grows by a factor of 4. Makes sense, since p grows as v^2.