In my previous articles, I gave an introduction to Otto cycle and derived the airstandard efficiency of Otto cycle. In this article, I will derive the mean effective pressure (m.e.p) of Otto cycle.
What is Mean Effective Pressure?
Mean effective pressure is the ratio of work done (W) during the working stroke(s) of a cycle to the stroke volume or swept volume (V_{s}) of the cylinder. It is denoted by ‘p_{m}‘ and its unit is N/m^{2}.
In order to derive an expression for mean effective pressure of Otto cycle, we have to find out an expression for work done and stroke volume of Otto cycle.
From my previous article, pV and Ts diagrams of Otto cycle are as follows:
pV Diagram  Ts Diagram 

From my previous article,
Compression ratio,
Pressure ratio,
In process 12 (isentropic compression),
In process 34 (isentropic expansion),
Also from the pV diagram above,
V_{1} = V_{4} and V_{2} = V_{3}
Let V_{c} = V_{2} = V_{3} = 1
Work done during Otto cycle,
W = Work done during isentropic expansion (process 34) – Work done during isentropic compression (process 12)
This is the expression for work done (W) in terms of r, k, γ and p_{1}.
Now, let us derive an expression for stroke volume V_{s} in terms of r.
We know that in Otto cycle,
V_{s} = V_{1} – V_{2} (See pV diagram above)
Now, Mean effective pressure,
The above expression can be written as
which is the required expression for mean effective pressure of otto cycle
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