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Torque and Speed Equations of dc motor

Before analysing the various characteristics of motors, let us revise the torque and speed equations are applied to various types of motors.
...              T α Φ Ia from torque equation.
       This is because, 0.159(PZ)/A is a constant for a given motor.
       Now  Φ is the flux produced by the field winding and is proportional to the current passing through the field winding.
                   Φ α Ifield
       But for various types of motors, current through the field winding is different. Accordingly torque equation must be modified.
       For a d.c. shunt motor,  Ish is constant as long as supply voltage is constant. Hence Φ flux is also constant.
...              T α  Ia                 for shunt motors
       For a d.c. series motor,   Ise  is same as  Ia. Hence flux Φ is proportional to the armature current Ia.
...               T  α  Ia   α  Ia2                   for series motors.
Similarly as Eb   = (ΦPNZ)(60A), we can write the speed equation as,
                   Eb  α    Φ N 
...                 N  α  Eb/Φ
       But   V =  Eb   +  Ia  Ra          neglecting brush drop
...             Eb   = V -  Ia  Ra
...     Speed equation becomes,
                N   α (V-Ia  Ra)/Φ
       So for shunt motor as flux is constant,
...              N   α   V - Ia  Ra
       While for series motor, flux Φ is proportional to Ia.
       These relations play an important role in understanding the various characteristics of different types of motors.
1.1 Speed Regulation
       The speed regulation for a d.c. motor is defined as the ratio of change in speed corresponding to no load and full load condition to speed corresponding to full load.
       Mathematically it is expressed as,  
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