Problem solving Motor Q from Wildi

[t5rrr]

So the question goes:

"A 3-phase, 75hp, 440V induction motor has a full-load efficiency of 91 percent and a power factor of 83 percent. Calculate the nominal current per phase."

The steps I took are:

Convert 75hp > 100kW

Power (1-phase) = 3ph power / (3 x efficiency) = 100kW / (3 x .91)

= 36.63kW

P (1-phase) = VI pf

36.63kW = 440/1.73 x I x .83

I = 173.52A

That is wrong and I'm at wits end (scroll down for book's answer for people wanting to take a stab at it first)

answer is 97.2A

 

[pelaw]

S = sqrt 3 * V * I -> I = S / (sqrt 3 * V); also eff = P out / P in; also pf = P in / S

S = P in / pf = P out / eff / pf = P out / eff * pf = (75 hp * 746 W/hp) / 0.91 * 0.83 = 55,950 / 0.7553 = 74,076.5 VA

I = S / 440 * 1.732 = 74,076.5 VA / 1.732 * 440 V = 97.2 A

 

[GabeM]

So the question goes:"A 3-phase, 75hp, 440V induction motor has a full-load efficiency of 91 percent and a power factor of 83 percent. Calculate the nominal current per phase."

The steps I took are:

Convert 75hp > 100kW

Power (1-phase) = 3ph power / (3 x efficiency) = 100kW / (3 x .91)

= 36.63kW

P (1-phase) = VI pf

36.63kW = 440/1.73 x I x .83

I = 173.52A

That is wrong and I'm at wits end (scroll down for book's answer for people wanting to take a stab at it first)

answer is 97.2A

You just converted horsepower to kilowatts incorrectly. I was confused too because the rest of the calculation made sense.

 

[Kahrlo]

I line= (hp x 746)/ (sqrt(3)x V line-line x efficiency x pf)

 

[BamaBino]

This is exactly Question 13-18 in Wildi.

 

[knight1fox3]

This is exactly Question 13-18 in Wildi.

So I'm guessing the voltage (4400) is a typo then? Should be 440 to obtain 97.2 A.