A university laboratory that generates \(15 \mathrm{~m}^{3} / \mathrm{s}\) of air flow at design condition wishes to build a wind tunnel with variable speeds. It is proposed to build the tunnel with a sequence of three circular test sections: section 1 will have a diameter of \(1.5 \mathrm{~m}\), section \(2 \mathrm{a}\) diameter of \(1 \mathrm{~m}\), and section 3 a diameter such that the average speed is \(75 \mathrm{~m} / \mathrm{s}\).

(a) What will be the speeds in sections 1 and 2?

(b) What must the diameter of section 3 be to attain the desired speed at design condition?