Armature Diameter formula question

[krispots]

so, I'm taking up a course on electrical machine design and our professor gave us the equations for computing the different values required for a given specification.

here is my problem:

given these two equations:

laD^2 = (W/N)(6.079x10^8)/(Byqr) --> eq. 1

and

la = pi(D)(r)/(pK) --> eq. 2

where la = length of armature core (inches)
D = diameter of armature core (inches)
r = ratio of pole arc to pole face
By = air gap density
W = output of armature (watts)
N = speed
p = number of poles
K = some constant ranging from 0.667 to 1

equation 1 came from

W = Z*Ec*Ic

where Z = total number of armature conductors
Ec and Ic = voltage and current on the conductor

Ec = 6.45(Bg)(la)(pi)(D)(r)(N)/60x10^8

where Bg = average flux density in the air gap under each pole (gauss)

and

Ic = q(pi)(D)/Z

where q = specific loading

substituting all Ec and Ic in W you can get equation 1.

and then you can solve for D by combining the two equations.

my question is where does the second equation came from??

 

[anorlunda]

ping @jim hardy

 

[jim hardy]

hmmm dc machines ? We need a 1930's tetbook. I'm away from home right now but will see if i can find a reference.

Meantime -
it's clear the second equation is related to voltage produced in the armature(e-Blv), and the first one to power... remember product of current and flux determines force(Lorentz) , and force X radius detremines torque, and torque X RPM is power... so the terms involved all seem at first glance to make sense.

In old days when we used Gauss instead of Teslas you had a 10^4 units adjustment term and i wager that's where your 10^8 comes from - cgs vs SI units... which does our professor use ?

old jim