## Electrical Power vs Mechanical Power

written by: Suvo • edited by: Lamar Stonecypher • updated: 1/25/2010

As a mechanical design engineer you have to deal with Kw mechanical force as well as Kw of electrical power. This article will help you understand the concept of electrical power and mechanical power and related formulas.

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The unit of the mechanical and electrical power is Kw (most popular). However, different formulas and units are used for calculating power in mechanical and electrical engineering.

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### Definitions of Power

Power is the rate of work done or work done per unit time or energy converted per unit time. Now though the basic concept remains the same, the expressions of power differs in electrical and mechanical engineering because the expression of the work done or energy conversion is different in the two disciplines.

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### Mechanical Power

• Mechanical power (P) is typically expressed by the work done (W) (if expressed in Foot-pound) divided by the time (t) (if expressed in Second).

P = W/t Foot-Pound/ Sec.……………..Eqn.1

Now, as work done (W) is equals to force (F) (if expressed in Pound) multiplied by the distance travelled (d) (if expressed in Foot / sec).

W = F*d Foot-Pound …………………Eqn.2

So, the Eqn.1 becomes,

P= (F*d)/t

= F*(d/t)

= F* V Foot-Pound / Sec………………Eqn.3

As, d/t is equal to velocity (V).

• The power in hydraulic systems is expressed using the pressure (Pr) (if expressed in Pound / Square Foot) and the volumetric flow rate (Q) (if expressed in Cubic Foot / Sec) as below:

P = Pr * Q Foot-Pound / Sec………………Eqn.4

• In rotational mechanical systems power is expressed by torque (T) (if expressed in Pound-Foot) and the angular velocity (V) (if expressed in RPS) as below:

P = T * V Foot-Pound / sec……………….Eqn.5

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### Electrical Power

• The electrical power (P) is expressed by current ( I ) (in Amps) and voltage (V) (in volts) as below:

P = VI Watts ……………Eqn.6

• Few other forms of the equation (Eqn.6) are also used in industry like below:

P = I2R Watts …………...Eqn.7

V is replaced by I*R in the above equation. Where the R is resistant (in Ohms).

• Another form of the equation (Eqn.6) is:

P = V2/R Watts ……………..Eqn.8

I is replaced by V/R here.

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### So What is the Difference?

• The mechanical power is measured by the rate at which work is done. On the other hand, electrical power is measured by the rate at which electrical energy is transformed.
• In terms of the power generation, mechanical power is generated by the mechanical equipment like piston-cylinders, turbines, etc and the electrical power is generated by alternators.
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### Units of Power

• In SI method, the unit of work done is Joules, so, Joules per second or Watt is the SI unit of the power. Kilowatts (103) and megawatt (106) are used for expressing power in higher power.
• In CGS systems the unit of work is Ergs, so, Ergs per second is the unit of power in this system.
• In FPS method, the power is represented by Foot Pounds per second as the unit of work done in FPS is Foot pound.
• Horse Power is another widely used unit in industry. One horse Power equals to 550 foot pound per second and is approximately equals to 746 Watts.

Although, all the units can be used irrespective of mechanical or electrical power but, the normal industry practice is: the horse power is used for engines and motors. The power of electrical heaters, bulbs or boliers are expressed in Kilowatts.

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### Conclusion

The concept of power is same in the context of mechanical as well as electrical engineering applications. The unit Kw is an electrical as well as mechanical power unit. Though the basic concepts remain the same, the form of the governing equations in case of the mechanical power is different than that of electrical power. Moreover, in mechanical engineering application itself, different equations are used for calculating power for hydraulic, thermal, and rotational systems.