Q$6(6-31$E$)$

A pump delivers oil at a rate of $20$ gpm to the cap end of a $2$ in diameter hydraulic cylinder as shown. The piston contains a $\frac{3}{4}$ in diameter cushion plunger that is $1$ in long. The cylinder drives a $1000$ lb weight, which slides on a flat, horizontal surface having a coefficient of friction equal to $0\mathrm{.}15.$ The pressure relief valve setting equals $500$ psi $.$ Find the maximum pressure developed by the cushion.

Ans: $815$ psi