Alan G. answered • 04/27/16

I love to teach and will do my best to help students learn

I'm going to do a few conversions, let me know if any of this gets too confusing!

60 Hz frequency converts to 3600 RPM in the engine as 1 rpm is equal to 1/60 Hz

60 Hz frequency converts to 3600 RPM in the engine as 1 rpm is equal to 1/60 Hz

You stated that the capacity of the engine is 550kW, so i'll use that number as it is lower than the 588.24kW you stated later:

Torque (or "T"), in Nm, is equal to Power ("P") over Angular Velocity aka Radians per Second ("w") in the equation

T = P/w

w can be found using another equation, w = (2*pi*RPM)/60 , which gives w = approx. 22619.467

Using this, T (in Nm), is equal to about 1458.92 Nm

Now, 1 Nm is equal to 100 Ncm so 1458.92 Nm is 145892 Ncm

Assuming that your initial question is asking you to find the amount in mg of each emission product per torque in Ncm produced over the course of a year, you simply take the values you found earlier, convert from metric tons to mg, and put them over the Ncm value shown above:

So:

PM:

0.0407 metric tons = 40700000 mg

40700000 / 145892 = 278.973 mg/Ncm

CO:

0.125 metric tons = 125000000 mg

0.125 metric tons = 125000000 mg

125000000 / 145892 = 856.798 mg/Ncm

NOx:

0.579 metric tons = 579000000 mg

0.579 metric tons = 579000000 mg

579000000 / 145892 = 3968.689 mg/Ncm

SOx:

0.037 metric tons = 37000000 mg

37000000 / 145892 = 253.612 mg/Ncm

VOC:

0.040 metric tons = 40000000 mg

40000000 / 145892 = 274.175 mg/Ncm

I wasn't quite sure if this was what you were asked to do, but hopefully it helps!