Induction Motors help

A four-pole induction motor is delta connected and operates from a 440V, 60 Hz three
phase supply with an efficiency of 96% and a power factor of 0.85. Ifthe motor shaft
speed and shaft power are determined as being 1440 rpm and 30 kW respectively and it
is driving a pump connected to the same shaft, then determine:

(a) The electrical input power to the motor.
(b) The line current demanded by the motor.
(c) The current flowing in each phase of the motor.
(d) The motor torque.
(e) The load torque.
(d) The power demanded in kW, kVA and kVAR

Pinput = Pshaft / η = 30 kW / 0.96 = 31.25 kW
Apparent power input: S = Pinput / pf = 31.25 kW / 0.85 = 36.76 kVA

line current: I_line = S/V = 36.76 /0.44 = 83.5 A
I_phase = I_line / √3 = 83.5/1.73 = 48.26 A
motor torque: T = P/ω
synchronous speed: ω_s = 2ω/p = 2*2π60/4 = 60π rad/s
angular velocity of shaft: ω_mech = 1440(2π/60) = 48π rad/s
slip: s = ω_s - ω_mech / ω_s = 60 - 48 / 60 =
load torque: T_load = Pshaft/ω_mech

angular velocity of shaft: ω_mech = 1440(2π/60) = 48π rad/s

T_load = 30x10³ / 48π = 0.2 N-m

kVAR => Q = S√( 1 - pf²) = 36.76*√( 1 - 0.85²) = 19.36 kVAR