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# Relation between power and rpm in an electrical motor

04/23/2022 1:45 AM

How do we get this for an electric motor?

P1/P2 = (N1/N2)3

where P is the power drawn and N is the speed in rpm for the motor.

It's not explained how they obtained it here (link below). There is a graph where this is mentioned.

https://www.researchgate.net/profile/Wael-Salah-3/publication/235640818_Importance_of_Energy_Efficiency_From_the_Perspective_of_Electrical_Equipments/links/55a101c108aed84bedf55b49/Importance-of-Energy-Efficiency-From-the-Perspective-of-Electrical-Equipments.pdf?origin=publication_detail

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#1

### Re: Relation between power and rpm in an electrical motor

04/23/2022 2:53 AM

..."(P1/P2) = (N1/N2)3 where P is the power required to spin the shaft and is proportional to the cube of the shaft speed. (Q1/Q2) = (D1/D2) with the shaft speed held constant, flow is proportional to the diameter D of the impeller."...

https://novantaims.com/technology-blog/affinity-laws-and-other-considerations-fan-application/#:~:text=(P1%2FP2)%20%3D%20(,diameter%20D%20of%20the%20impeller.

https://whatispiping.com/pump-affinity-laws/

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#3
In reply to #1

### Re: Relation between power and rpm in an electrical motor

04/24/2022 2:57 PM

Exactly. It’s got a lot to do with what the motor is agitating.

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#2

### Re: Relation between power and rpm in an electrical motor

04/23/2022 11:26 AM

If your load (torque) increases with the square of RPM, power supplied by the motor (RPM x torque) will be proportional to the cube or RPM.

It's common for the torque or force to be proportional to speed or RPM squared. For example, fluid drag is proportional to the square of velocity, so the torque required to drive a pump would be proportional to RPM squared.

For the same reason, the drag on an automobile is proportional to the square of the speed and the power required is proportional to force x speed or cube of speed.

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#4

### Re: Relation between power and rpm in an electrical motor

04/24/2022 3:01 PM

The Power Number is a dimensionless number that can be used to compare the effectiveness of agitation across different configurations. If the Power Number for two configurations are the same, then the effectiveness of the agitation will be the same in each case.

Recommended Reading: Perry, “The Chemical Engineer’s Handbook”, any edition.

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#5

### Re: Relation between power and rpm in an electrical motor

04/25/2022 9:05 PM

This is all part of the ideal fan laws, or relationships between speed (rpm), power, etc. This relationship is completely different for other types of loads, such as conveyors. The ideal fan relationships are fairly reliable for modest changes in the parameters. The same relationship of power being proportional to the cube of the speed applies to wind resistance for a car moving down the road. Look up the "ideal fan laws".

--JMM

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### Re: Relation between power and rpm in an electrical motor

04/26/2022 5:45 AM

Since P1=kTq1*N1 then P1/P2=T1*N1/(T2*N2) and if P1/P2=(N1/N2)^3 then T1/T2=(N1/N2)^2. This curve may represent a load torque but not a motor torque.Attached is presented NEMA standard induction motor types' behavior.

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#7

### Re: Relation between power and rpm in an electrical motor

04/26/2022 7:28 AM

The operating point is where the load demand torque/speed curve intersects with the motor capability torque/speed curve.

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#8

### Re: Relation between power and rpm in an electrical motor

04/28/2022 12:41 PM

Thank you, PWSlack!

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