Power output/input, energy input, efficiency of engine & generator

In summary, the equations indicate that a diesel engine produces 3100.78 watts when running for four hours.
  • #1
DevonZA
181
6

Homework Statement


upload_2016-5-3_20-46-16.png


Homework Equations


P=2piNT/60
P=I^2R
Pin=Pout/efficieny
E=P/t

The Attempt at a Solution



2.1 P=I^2R
= (5)^2x48
= 1200W

2.2 Pin=Pout/efficiency
= 1200/0.86
= 1395.35W

2.3 P=2piNT/60
*3100.78=2pi(500)T/60
T=0.016Nm.

2.4 Total efficiency = (45/100x86/100)x100% = 38.7%

2.5 Pin=Pout/efficiency
= 1395.35/0.45
= 3100.78W*

2.6 E=P/t
= 3100.78/4x60x60
= 0.215J

2.7 3.1kWx4hoursxR4.75/kWh = R58.90

I don't feel satisfied that these answers are correct, probably because they are not.
The answer to 2.6 concerns me most.
When can I use the equations P=I^2R and E=I^Rt?
 
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  • #2
DevonZA said:

Homework Statement


View attachment 100189

Homework Equations


P=2piNT/60
P=I^2R
Pin=Pout/efficieny
E=P/t

The Attempt at a Solution



2.1 P=I^2R
= (5)^2x48
= 1200W

2.2 Pin=Pout/efficiency
= 1200/0.86
= 1395.35W

2.3 P=2piNT/60
*3100.78=2pi(500)T/60
T=0.016Nm.
Extremely small torque output for a diesel engine. You would do much better turning a hand crank.

However, you overlooked the fact that the power output of the diesel engine = power input of the generator.

The efficiency for the diesel engine comes from how much energy in the fuel is converted to useful work at the shaft.
2.4 Total efficiency = (45/100x86/100)x100% = 38.7%

2.5 Pin=Pout/efficiency
= 1395.35/0.45
= 3100.78W*

2.6 E=P/t
= 3100.78/4x60x60
= 0.215J
What are the derived units for watts? Why have you used hours?
2.7 3.1kWx4hoursxR4.75/kWh = R58.90

I don't feel satisfied that these answers are correct, probably because they are not.
The answer to 2.6 concerns me most.
When can I use the equations P=I^2R and E=I^Rt?
 
  • #3
SteamKing said:
Extremely small torque output for a diesel engine. You would do much better turning a hand crank.

However, you overlooked the fact that the power output of the diesel engine = power input of the generator.

The efficiency for the diesel engine comes from how much energy in the fuel is converted to useful work at the shaft.

What are the derived units for watts? Why have you used hours?

Hi Steamking

Power input of gen = 1395.35W = power output of engine

P=2pi(N)(T)/60
1395.35=2pi(500)T/60
T=1850.64Nm
That's better :)

The efficiency for the diesel engine comes from how much energy in the fuel is converted to useful work at the shaft.

I'm lost here. Isn't the efficiency the output power/input power x 100%?

Derived unit for watts..power? I have used hours because I need to calculate kw/h?
 
  • #4
DevonZA said:
Hi Steamking

Power input of gen = 1395.35W = power output of engine

P=2pi(N)(T)/60
1395.35=2pi(500)T/60
T=1850.64Nm
That's better :)

The efficiency for the diesel engine comes from how much energy in the fuel is converted to useful work at the shaft.

I'm lost here. Isn't the efficiency the output power/input power x 100%?
You can only measure the output power of the diesel engine.

The amount of heat input theoretically furnished by the fuel can be estimated if you know the fuel consumption of the engine, which in this case you don't. :frown:

However, given the efficiency of the engine, you can work back and estimate how much fuel the engine burns in a given amount of time.
Derived unit for watts..power? I have used hours because I need to calculate kw/h?
Kilowatt-hours is a unit of energy, not kilowatts per hour. The definition of the watt is the same as it always was - the amount of work performed in joules per second.

https://en.wikipedia.org/wiki/Kilowatt_hour
 
  • #5
I will look at this again in the morning, it is almost midnight here.
Thanks for your help.
 

FAQ: Power output/input, energy input, efficiency of engine & generator

1. What is power output/input?

Power output/input refers to the amount of energy that is produced or consumed by a system. In the case of an engine or generator, power output is the amount of work that is done by the system, while power input is the amount of energy that is supplied to the system.

2. What is energy input?

Energy input is the amount of energy that is required to operate a system. In the case of an engine or generator, energy input is the amount of energy that is needed to produce the desired power output. This can include things like fuel, electricity, or other sources of energy.

3. How is the efficiency of an engine or generator calculated?

The efficiency of an engine or generator is calculated by dividing the power output by the power input and multiplying by 100 to get a percentage. This measures the effectiveness of the system in converting energy input into useful work output.

4. What factors can affect the efficiency of an engine or generator?

There are several factors that can affect the efficiency of an engine or generator, including the design and quality of the components, the type of fuel used, the operating conditions, and the maintenance and upkeep of the system.

5. Why is it important to have a high efficiency in engines and generators?

A high efficiency in engines and generators is important because it means that less energy is wasted and more of it is being used to produce useful work. This can lead to cost savings, reduced environmental impact, and improved performance of the system.

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