Molten plastic at a temperature of \(510^{\circ} \mathrm{F}\) is augered through an extruder barrel by a screw occupying \(\frac{3}{5}\) of the barrel's volume (Fig. P5.16). The extruder is \(16 \mathrm{ft}\) long and has an inner diameter of 8 in. The barrel is connected to an adapter having a volume of \(0.48 \mathrm{ft}^{3}\). The adapter is then connected to a die of equal volume. The plastic exiting the die is immediately rolled into sheets. The line is producing 4 - \(\mathrm{ft}\) widths of material at a rate of \(30 \mathrm{ft} / \mathrm{min}\) and a gauge thickness of \(187 \mathrm{mil}\). What is the axial velocity, \(V_{1}\), of the plastic in the barrel? Assume that the plastic density is constant as it solidifies from a liquid (in the extruder) into a solid sheet.

Figure P5.16

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V2= 30 ft/min Thin sheet Rolls Die Adapter Extruder Screw barrel