A pipe bender uses a double$-$acting pneumatic cylinder.

Determine:

a$)$ Calculate the minimum diameter that the piston must have if the force it has to exert is $200$ kgf and the compressor pressure is $8$ bar.

b$)$ Calculate the air flow that the compressor must supply if $25$ bends are made per minute and the rod stroke is $60$ cm$.$

c$)$ The speed of the rod if the pressure drops to $5\mathrm{.}3$ bar.

d$)$ What happens to the force of the cylinder if the pressure is increased to $10$ bar.

e$)$ Determine the diameter of the rod if it is used with group $1($buckling$)$