The maximum pressure that can be developed for a certain fluid power cylinder is 15.0 MPa. Compute the required diameter for the piston if the cylinder must exert a force of 30 kN.

The pressure in the piston is defined as $$ p=\frac{F}{A} $$ We can rearrange this to solve for the area of the piston $$ A=\frac{F}{p}=\frac{30,000~\N}{15\times 10^6~\Pa}=0.002~\m^2 $$ The area of the piston is related to its diameter through $$ A=\frac{\pi}{4}D^2 $$ We can rearrange this to solve for the diameter of the piston $$ D=\sqrt{\frac{4}{\pi}A} = \sqrt{\frac{4}{\pi} 0.002~\m^2}= 0.0505~\m = 50.5~\mm $$