Diesel Engines - Power question

[cabellos6]

Homework Statement

Please can someone help me with this...
I have a question on a four stroke diesel engine. I have been given the stroke length of 500mm and the bore size of 300mm. The compression ratio as 18/1 and the speed of revolution of 600rpm. Also the ambient air conditions are assumed to be 20C at 1 bar. Max cylinder pressure = 100 bar and exhaust gas temperature = 480C

It asks to calculate the power developed per cylinder using the air conditions at the start of the cycle?

Homework Equations

The Attempt at a Solution

Now i have answerd the previous question which was to calculate the thermal efficiency of the cylce. So as this is a Dual Cycle i have drawn it and calculated all the temperature points and worked out the efficiency which was 67%. Correct

It says calculate the power from the initial air conditions but i have tried to do this by using Power = Work done x cycles per second

I have worked out the Work done as Qin - Qout and multiplied this by 5 cycles per second (as 600 rpm is 10 rps and there are 2 revolutions in one cycle as it is 4 stroke).

i am not getting the correct answer which is supposed to be 153KW.

Why??



Thanks

 

[KataKoniK]

for your question! It seems like you have already made some good progress on your calculations. To calculate the power developed per cylinder, you will need to use the formula Power = Work done / time. In this case, the time would be the time for one cycle, which is 1/600 seconds (since the engine is running at 600 rpm, or 10 revolutions per second).

To find the work done, you will need to use the formula Work = Pressure * Volume. In this case, the volume would be the displacement volume of the engine (pi/4 * bore size^2 * stroke length) and the pressure would be the maximum cylinder pressure of 100 bar. This will give you the total work done per cycle.

To find the power developed per cylinder, you will then divide the work done by the time for one cycle (1/600 seconds). This should give you the correct answer of 153 kW.

I hope this helps and good luck with your calculations! Let me know if you have any further questions.

 

[piercas]

for reaching out for help with this question. To calculate the power developed per cylinder, you can use the formula P = (m x n x V x eta x Pmax)/(60 x 1000), where P is power, m is mass of air in the cylinder, n is number of cycles per second, V is volume of the cylinder, eta is the thermal efficiency, and Pmax is the maximum cylinder pressure.

First, you will need to calculate the mass of air in the cylinder. This can be done by using the ideal gas law, PV = mRT, where P is pressure, V is volume, m is mass, R is the gas constant, and T is temperature. You can use the given conditions of 20C and 1 bar to find the initial mass of air in the cylinder.

Next, you will need to calculate the volume of the cylinder. This can be done by using the formula V = (pi/4) x D^2 x L, where pi is 3.14, D is the bore size, and L is the stroke length.

Then, you can use the given compression ratio of 18/1 to calculate the final pressure in the cylinder. This can be done by using the formula P2 = P1 x (V1/V2)^gamma, where P2 is the final pressure, P1 is the initial pressure (1 bar), V1 is the initial volume (calculated in the previous step), V2 is the final volume (calculated using the stroke length and bore size), and gamma is the ratio of specific heats for air (1.4).

Once you have the final pressure, you can use the given exhaust gas temperature of 480C and the ideal gas law again to calculate the final volume of the cylinder. Then, you can use the formula for work done (W = P2 x V2 - P1 x V1) to find the work done per cycle.

Finally, you can plug all of these values into the initial formula for power to find the power developed per cylinder. Repeat this process for each cylinder to find the total power developed by the engine.

I hope this helps! Please let me know if you have any further questions or if you need clarification on any of the steps. Good luck with your calculations!