i Have a dc shunt motor rated at 240v and 60A at 1500rpm, The armature resistance is 0.4 ohms and the field resistance is 180 ohms....... how would i estimate

the mechanical power output
the torque
and the no-load speed????

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consider a ckt
where your dc motor is in series with a armature resistance.
there is a field resistance in parallel to the series combination of motor and arm resistance.
consider the supply applied across this combination,
some current will flow as field current,
there will be voltagedrop across armature resistance.
thus using network analysis,
calculate the voltage across motor and current thru the motor,
then any book u use will have a formula which is something like this

e=flux per pole*no of conductors*rpm*no of poles/2

i dont remember it exactly and the denominator changes from 2 to some other value depending on the type of winding (wave or lap)

once u get speed (rpm)
there is also some formula for torque(i dont recall it)
and power = torque*rps

i think for power
after calc current thru field winding and armature,
power = supply votagex supply current - arm current^2xarm resistance - field current^2xfield resistance.