Air enters a 4-cm-square galvanized steel duct with \(p_{0}=\) \(150 \mathrm{kPa}, T_{0}=400 \mathrm{~K}\), and \(V_{1}=120 \mathrm{~m} / \mathrm{s}\). \(\mu=2.2 \times 10^{-5}\) \(\mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}\).

(a) Compute the maximum possible duct length for these conditions.

(b) If the actual duct length is 0.75 times the maximum value, calculate the mass flow rate, the exit pressure, and the stagnation pressure.

(c) If the actual duct length is 1.3 times the maximum value for the stated conditions, compute the new mass flow rate and inlet velocity. Assume a low back pressure and use the same value of \(f\) as used in the maximum possible duct length case.