Otto Cycle - calculate the net work per cycle in Btu

[jdawg]

Homework Statement

A four cylinder, four stroke internal combustion engine has a bore of 3.7 in and a stroke of 3.4 in. The clearance volume is 16% of the cylinder volume at bottom dead center and the crankshaft rotates at 2400 RPM. The processes within each cylinder are modeled as an air standard Otto cycle with a pressure of 14.5 lbf/in² and a temperature of 60 °F at the beginning of compression. The maximum temperature in the cycle is 5200 °R. Based on this model, calculate the net work per cycle in Btu and the power developed by the engine in horse power.

Homework Equations

The Attempt at a Solution

So p1=14.5 lbf/in² and T1=520°R. The max temperature is at T3 so T3=5200°R. V3=V2. V4=V1.

And they tell you in the problem that the clearance volume ( V2) is 16% of the volume at bottom dead center (V1). I would think that meant V2=(0.16)*(V1), but the solution I'm looking at says V2=(0.16)*(V1+V2).

What exactly is the stroke? All my book says about it is that its the distance the piston moves in one direction, which kind of makes me think its the total volume? The solution I have kind of treats it as a height because they multiply the stroke by the area they calculated with the bore:
ΔV_1-2=(π(3.7/2)²)(3.4)=0.02116 ft³

I feel like the terminology is the main thing that's tripping me up. If someone could clarify I would really appreciate it! :)

 

[SteamKing]

Homework Statement

A four cylinder, four stroke internal combustion engine has a bore of 3.7 in and a stroke of 3.4 in. The clearance volume is 16% of the cylinder volume at bottom dead center and the crankshaft rotates at 2400 RPM. The processes within each cylinder are modeled as an air standard Otto cycle with a pressure of 14.5 lbf/in² and a temperature of 60 °F at the beginning of compression. The maximum temperature in the cycle is 5200 °R. Based on this model, calculate the net work per cycle in Btu and the power developed by the engine in horse power.

Homework Equations

The Attempt at a Solution

So p1=14.5 lbf/in² and T1=520°R. The max temperature is at T3 so T3=5200°R. V3=V2. V4=V1.

And they tell you in the problem that the clearance volume ( V2) is 16% of the volume at bottom dead center (V1). I would think that meant V2=(0.16)*(V1), but the solution I'm looking at says V2=(0.16)*(V1+V2).

What exactly is the stroke? All my book says about it is that its the distance the piston moves in one direction, which kind of makes me think its the total volume? The solution I have kind of treats it as a height because they multiply the stroke by the area they calculated with the bore:
ΔV_1-2=(π(3.7/2)²)(3.4)=0.02116 ft³

I feel like the terminology is the main thing that's tripping me up. If someone could clarify I would really appreciate it! :)

The stroke is the distance the piston moves up or down during one revolution of the crankshaft. The clearance volume is that small space which remains when the piston is at the top of its stroke. The swept volume is the product of the area of the cylinder and the piston stroke.

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[jdawg]

Ok thanks! Now I'm trying to find v_r2 and its coming out wrong. I looked up the value for v_r1 to be 158.58 and calculated V1=0.026 ft³ and V2=0.004716 ft³.

So now using (v_r2/v_r1)=(V2/V1) and found v_r2=28.76... But it should be 25.373.

They did (1/6.25)*(158.58)=v_r2
How did they find the compression ratio to be 6.25? It seems like they found the compression ratio without using V1 and V2. I know 1/6.25=0.16, is it a coincidence that the inverse of the compression ratio is the percentage of the clearance volume at bottom dead center?

 

[SteamKing]

Ok thanks! Now I'm trying to find v_r2 and its coming out wrong. I looked up the value for v_r1 to be 158.58 and calculated V1=0.026 ft³ and V2=0.004716 ft³.

So now using (v_r2/v_r1)=(V2/V1) and found v_r2=28.76... But it should be 25.373.

They did (1/6.25)*(158.58)=v_r2
How did they find the compression ratio to be 6.25? It seems like they found the compression ratio without using V1 and V2. I know 1/6.25=0.16, is it a coincidence that the inverse of the compression ratio is the percentage of the clearance volume at bottom dead center?

The compression ratio is defined using the geometric properties of the cylinder:

$CR = \frac{SV+CV}{CV}$

 

[jdawg]

I don't understand why it doesn't work when I just plug in my values to (vr2)=(V2/V1)*(vr1)

Are the values for V1 and V2 incorrect?

 

[SteamKing]

I don't understand why it doesn't work when I just plug in my values to (vr2)=(V2/V1)*(vr1)

Are the values for V1 and V2 incorrect?

Your calculation for SV = 0.02116 ft³ looks OK. IDK if you have calculated the CV correctly, though.

I would work in cubic inches for these calculations and convert to cubic feet later. 1 ft³ = 1728 in³

 

[jdawg]

Thanks, I'll try that!

 

[jiasd]

Can you show the complete solution I want to compare with mine