A $30,000$ hp$,13\mathrm{.}8$ kV$,3-$phase, $60$ Hz air$-$to$-$water cooled induction motor drives

a turbo compressor in a large oxygen manufacturing plant. The motor runs at an

exact full$-$load speed of $1782\mathrm{.}6$ r$/$min and by means of a gearbox, it drives the

compressor at a speed of $5064$ r$/$min$.$ The motor has an efficiency of $85\mathrm{.}9\%$

and a power factor of $0\mathrm{.}88.$ The LR torque and the current are respectively $0\mathrm{.}7$ pu

and $4\mathrm{.}8$ pu$.$

Calculate the following:

$(15)$ The full$-$load current

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ A$.$

$(16)$ The rotor I$2$R losses if the windage and friction losses amount to $68$ kW

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ kW$.$

$(17)$ The LR current

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ A$.$

$(18)$ The torque developed at the compressor shaft

$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ kN$-$m