An air ventilating system must be designed to deliver air at $20^{\circ} \mathrm{F}$ and atmospheric pressure at a rate of $150 \mathrm{ft}^{3} / \mathrm{s}$ through $4000 \mathrm{ft}$ of square duct. If the air blower is $60 %$ efficient and is driven by a $30 \mathrm{hp}$ motor, what size duct is required if it is made of sheet metal? Under these conditions, air may be considered as an incompressible fluid.