The balanced vane pump shown to the right has a rotor diameter of $2$ in $.$ and a cam ring diameter of $3$ in $.$ The vane thickness is $0\mathrm{.}08$ in $.,$ and the vane width is $2$ in $.$ The pump delivers a flow rate of $28ga\frac{l}{m}in$ at $2400$ psi $.$

Determine:

$($a$)$ The pump speed in $[$rpm$].$

$($b$)$ The fluid power in the discharged hydraulics fluid in $[$hp$].$

$($c$)$ The pump torque in $N*m.$