$($b$)$ In a single$-$screw extruder the dimensions of the channel are :

Diameter $(D)=5\mathrm{.}03cm,$ Width $(w)=1\mathrm{.}1,cm,$ Height $(H)=0\mathrm{.}36cm,$ Screw Angle $()=6\mathrm{.}3,$ speed of Rotation $=10$ revolution per second $($ rps $)$

Assume a flat plate model in the melt zone of a single$-$screw extruder $\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{z}}=\frac{de{l}^2{v}_z}{del{y}^2},v_z=0$ at $y=0$ and $v_z=V_{bz}$ at $y=H$

Find the expression for $v_z$ for fully developed flow in the z direction.

Find $Q,$ if in the absence of a die in a single$-$screw extruder $P=0.$