# Does anyone recognise this equation (Indicated mean pressure)?

1. Dec 7, 2009

### bsodmike

Hi,

I have been reading some online papers and have been struggling with the following equation as the author seems to introduce it without much detail. Since my background is primarily in electronic engineering, it is quite possible that this could be one of the elementary equations in thermodynamics.

$$P_i=\dfrac{q_C}{\lambda_{\text{tot}}\alpha_{\text{st}}}\rho_C\epsilon_{\text{Vi}}\eta_i$$

What I know:
$$P_i$$: indicated mean pressure; This is OK!

$$\alpha_{\text{st}}$$: the ideal air-to-fuel ratio for gasoline; values vary between 14.3 and 14.8. This is also defined as the "stoichiometric air-fuel ratio"

$$\rho_C$$: compressor air density; This is OK! Standard value of 1.2 kg/m^3 is used.

$$\eta_i$$: Indicated efficiency, 0.38 is being used; This is OK!

Variables I have no idea about:
$$q_C$$: A value of $$42.5\times10^6$$ is being used; have no idea.

$$\lambda_{\text{tot}}$$: relative air ratio, it seems 1.8 is a typical value for constant-pressure (pulse factor = 1) turbochargers??!?

$$\epsilon_{\text{Vi}$$: no clue! A value of 0.97 has been used. Seems it is a percentage of sorts, an efficiency may be. The subscript "i" is typically used to indicate the word 'indicated' but "Vi" is not making much sense.

Summary: Have you seen this equation before? Please let me know what $$\epsilon_{\text{Vi}$$ and I would greatly appreciate if you can confirm the other variables and my guesses/suggestions.

Cheers
Mike!

Last edited: Dec 7, 2009
2. Dec 7, 2009

### bsodmike

I have split the variables above into two sections: (1) the variables I have figured out and are certain of and (2) the variables that continue to elude me.

The two driving me up the wall are $$q_C$$ and $$\epsilon_{\text{Vi}}$$. Really would be glad if someone could help. Thanks!

3. Dec 8, 2009

### xxChrisxx

Indicated mean effective pressure.

evi is probably volumetric efficiency (hew well the cylinder fills)
Qc is the heating value of the fuel.
lambda is the fuel equivilance ratio. its the ratio of fuel air mix to stoichiometric fuel air mix. (another way of noting how ruch or lean the engine is running)

The equation is not commonly seen looking like that (its usually in a simplified form work per cycle / volume dispaced). In this case the auther has simply expanded it to include all the basic variables.

mep is not really a pressure per se. It's a method of characterising how well an engine is performing regardless of displacement. The higher the mep the better.

This isn't general thermodynamics if its the equation im thinking of. It's to do with internal combustion engines. What book is it?

Last edited: Dec 8, 2009
4. Dec 8, 2009

### bsodmike

Is Qc the same as heat of combustion? This page lists a HHV value for diesel of 44.8 MJ/kg; considering the equation I've seen uses 42.5 MJ/kg, it explains the 10^6 factor!

You're right; I did look up some books and found equations in terms of work per cycle/volume displaced. It was an undergraduate draft report I was perusing, rather than a book. Referencing books didn't help of course for the reason you mentioned.

Thanks a lot for your explanation... I am very bad at letting things 'go' if I cannot understand something, and this would have continued to nag away at me :)

Cheers
Mike.