How Do I Calculate Thermal Efficiency with the Brake Equation?

[recreated]

Can you please help me? I am trying to calculate this equation but can't get correct answer:

Thermal Efficiency, Brake = 1/(bSPC x QHV)

bSPC (brake Specific fuel consumption) = 0.396 kg/KWh

QHV (Heating Value for fuel) = 44 MJ/Kg

The correct answer is meant to be: Thermal Efficiency, Brake = 0.207 = 20.7%.

I do not know the correct SI units for bSPC or QHV, hopefully I am not using the right ones because I can't get that answer.

Look forward to any help or advise, Thanks

 

[rock.freak667]

Your equation is correct, but I think what is confusing you are the prefixed units. What you can do is reduce everything to the same set of units.

kWh is a unit of energy so 1kWh = 1 kW * 1 hr = 1kJ/s * 3600 s = 3600 kJ = 3.6 MJ

So your bSPC = .396 kg/kWh = 0.396/3.6 kg/MJ

 

[recreated]

Wow solved perfectly, and can get correct answer,, must have been <30mins. You don't know how stupid I felt not being able to do that equation. Thank you very much

 

[SteamKing]

Your units are at fault. The bSPC is given in units of kg/kWh while the HV is given in MJ/kg.

You need to find the heat equivalent of kWh and convert the value of bSPC before plugging it nto the efficiency formula.

 

[rock.freak667]

Wow solved perfectly, and can get correct answer,, must have been <30mins. You don't know how stupid I felt not being able to do that equation. Thank you very much

Another thing that I found helpful to do is to write out your units so that you know if you are missing out a factor.

So for efficiency, it would be output power/input power which means that you units would cancel.

Just multiplying the numbers would have left you with something like MJ/kWh and you would have neglected a factor.

 

[recreated]

Thank you both soo much. I am going to learn today about manipulating units, it will help me soo much with Mechanical Engineering.