Question

The formula for wind chill C (in degrees Fahrenheit) is given by C = 35.74 + 0.6215T − 35.75v0.16 + 0.4275Tv0.16 where v is the wind speed in miles per hour and T is the temperature in degrees Fahrenheit. The wind speed is 19 ± 3 miles per hour and the temperature is 8° ± 1°. Use dC to estimate the maximum possible propagated error (round your answer to four decimal places) and relative error in calculating the wind chill (round your answer to two decimal places).†

Answer 1

The maximum propagated error in the wind chill calculation = dC = -0.0020°F

Relative error = (dC/C) = 0.000177 = 0.00 to 2 d.p

Explanation:

C, the wind chill in degree Fahrenheit is a multi-variable function with independent variables v and T

The maximum error in C, dC is given mathematically as

dC = ΔT (∂C/∂T) + Δv (∂C/∂v)

The calculations to obtain each of these partial derivatives at the given conditions is presented in the attached image to this answer.

dc is then also computed.

dC = - 0.00196°F = - 0.0020°F to 4 d.p.

b) Relative error = (dC/C)

C = 35.74 + 0.6215T - 35.75v⁻⁰•¹⁶ + 0.4275Tv⁻⁰•¹⁶

At v = 19 mph and T = 8°F

C = 35.74 + (0.6215×8) - 35.75(19⁻⁰•¹⁶) + 0.4275(8)(19⁻⁰•¹⁶) = -11.07°C

Relative error = (dC/C) = (0.00196/11.07) = 0.000177

Hope this Helps!!!