Q$1.$ Figure $1$ illustrates a wire$-$extrusion operation for a strain$-$hardening material. A cylindrical rod is extruded at room temperature from a diameter of $14$ mm to $9$ mm at a speed of $\backslash (3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Neglect friction and redundant work.

Figure $1$ Wire$-$extrusion operation

$(1)$ Calculate the force $\backslash ([\backslash$mathrm$\{$N$\}]\backslash )$ and the power $\backslash ([\backslash$mathrm$\{$W$\}]\backslash )$ required for this operation.

$(2)$ Calculate the pressure between work and die $\backslash ($ P$\_\{$o$\}[\backslash$mathrm$\{$MPa$\}]\backslash )$ at the entry A $.$

$(3)$ Calculate the pressure between work and die $\backslash ($ P$\_\{$l$\}[\backslash$mathrm$\{$MPa$\}]\backslash )$ at the exit B $.$