A smooth orange ball weighs \(\frac{1}{64} \mathrm{lb}\) (at sea level) and has a diameter of \(1.5 \mathrm{in}\). The discharge of a vacuum cleaner is directed upward and supports the ball \(\frac{1}{2}\) in. If the hose inside diameter is 4.0 in., estimate the volume flow rate through the vacuum cleaner. The air temperature is \(100^{\circ} \mathrm{F}\).