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
$$
D=\sqrt{\frac{4}{\pi}A} = \sqrt{\frac{4}{\pi} 0.002~\m^2}= 0.0505~\m = 50.5~\mm
$$