A single-screw extruder is operated at $12$ $\mathrm{rpm}$ under open discharge condition (i.e., without a die).
The screw has a diameter of $10$ $\mathrm{cm}$, a distance of $2.5$ $\mathrm{cm}$ between the adjacent flights, a gap of $0.25$ $\mathrm{cm}$ between the screw and the inner wall of the barrel, and a helix angle (i.e., angle between the flights and the plane perpendicular to the screw axis) of $8^{\circ}$.
If the flow of the molten polymer in the metering zone through the extruder is assumed isothermal, Newtonian and incompressible, the volumetric flow rate of the polymer melt is $\_\_\_\_\_\_$ $\mathrm{cm}^{3} / \mathrm{min}$ (rounded off to the nearest integer).
