To determine air velocity changes, it is proposed to measure the electric current required to maintain a platinum wire of 0.5-mm diameter at a constant temperature of 77°C in a stream of air at 27°C.

(a) Assuming Reynolds numbers in the range 40 < ReD < 1000, develop a relationship between the wire current and the velocity of the air that is in cross flow over the wire. Use this result to establish a relation between fractional changes in the current, ∆I/I, and the air velocity, ∆V/V.

(b) Calculate the current required when the air velocity is 10 m/s and the electrical resistivity of the platinum wire is 17.1 x 10^-5 n ∙ m.