Question

The formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74 + 0.6215T - 35.75v^0.16 + 0.4275Tv^0.16 where v is the wind speed in miles per hour and T is the temperature in degrees Fahrenheit. The wind speed is 23 ± 3 miles per hour and the temperature is 8° ± 1°. Use dC to estimate the maximum possible propagated error and relative error in calculating the wind chill.

Answer 1

Answer:

dC = 2.44

Relative error = 19%

Step-by-step explanation:

$C = 35.74 + 0.6215*T - 35.75*v^(0.16) + 0.4275*T*v^(0.16)$

Δv = 3 ; ΔT = 1 , v = 23, T = 8

Use differential Calculus

$dC = Cv.dv + Ct.dt$

$Cv = dC/dv = -5.72*v^(-0.84) + 0.0684*T*v^(-0.84)\\Ct = dC/dT = 0.6215 + 0.4275*v^(0.16)\\dC = modulus (Cv.dv) + modulus (CT.dT)\\dC = (-5.72*v^(-0.84) + 0.0684*T*v^(-0.84))* 3 + (0.6215 + 0.4275*v^(0.16))*1\\dC = 2.44$

Relative Error

dC / C @(T = 8, v=23)  * 100 = 19 %