The brake mean effective pressure is used to compare different engines with varying engine capacity and it is also used to determine how effectively the engine is functioning. in this article, we are going to talk about the topic brake mean effective pressure.
Contents:
What is Brake mean effective pressure?
Brake mean effective pressure (BMEP) is an average value of the pressure inside the cylinder and if it is applied uniformly from TDC to BDC instead of the power stroke then the engine will produce the same amount of brake power as an actual engine.
The brake mean effective pressure is the ratio of work done by the engine during power stroke to the engine displacement.
`P_{bm}` = `\frac{\text{Work per power stroke}}{V_{d}}`
The brake mean effective pressure shows the ability of the engine to generate the maximum brake power based on the engine displacement volume.
Note: Engine displacement `V_{d}` is the sum of the swept volume of all the cylinders and it is given by,
`V_{d}` = Number of cylinders (n) x Swept volume of one cylinder (`V_{s}`)
The BMEP says the amount of brake power generated per unit volume of engine displacement thus it becomes criteria to compare the different engines irrespective of the size and number of cylinders.
Example: Among the two engines of the same size, the engine with higher BMEP can generate higher brake power than the engine of the same size having lower BMEP.
The BMEP depends on the factors like engine volumetric efficiency, the density of intake charge, compression ratio, etc.
Brake mean effective pressure equation:
The brake mean effective pressure of the engine is given by,
BMEP = `\frac{2\pi T.n}{V_{d}}`
Where,
T = Torque at the crankshaft
n = Number of crankshaft revolutions during one power cycle
`V_{d}` = Engine displacement
For twostroke engines the value of n =1, therefore the brake mean effective pressure is given by,
`P_{bm}` = `\frac{2\pi T}{V_{d}}` ——(For 2 stroke engine)
For fourstroke engines, the value of n = 2, thus the brake mean effective pressure becomes,
`P_{bm}` = `\frac{4\pi T}{V_{d}}` ——–(For 4 stroke engine)
Brake mean effective pressure derivation:
The fourstroke engine performs 2 complete revolutions of crankshaft for one power stroke and the twostroke engine performs a single complete revolution of crankshaft for one power stroke.
Thus for the engine running at N (revolutions per second), the numbers of power strokes completed by the engine per second are given by,
Rate of power stroke = `\frac{N}{n}`
Where,
N = Engine speed (RPS)
n = 2 for fourstroke engine
n = 1 for twostroke engine
Now the power generated by the engine is given by,
P = Work done by single power stroke x Rate of power stroke
P = Work done by single power stroke x `\frac{N}{n}` ——Equation [1] 
By the definition of BMEP,
`P_{bm}` = `\frac{\text{Work per power stroke}}{V_{d}}`
`\text{Work per power stroke}` = `V_{d}` x `P_{bm}`
Where,
`V_{d}` is engine displcement
`P_{bm}` is brake mean effective pressure
By putting this value in Equation [1],
P = (`V_{d}` x `P_{bm}`) x `\frac{N}{n}` —Equation [2] 
The brake power at the crankshaft is given by,
P = 2πNT
Where,
T = Torque at crankshaft
N = Crankshaft speed (rps)
Put this value of P in an equation [2],
2πNT = (`V_{d}` x `P_{bm}`) x `\frac{N}{n}`
`P_{bm}` = `\frac{2\pi T.n}{V_{d}}`
This is the equation to find the brake mean effective pressure of the engine.
How to calculate brake mean effective pressure?
The brake mean effective pressure can be calculated by following the given steps:
Step1: Find the total displacement volume (`V_{d}`) of the engine.
Step2: Find the torque at the crankshaft (T) of the engine.
Step3: Check the type of the engine (twostroke/ fourstroke).
If the engine is twostroke, then use n = 1
If the engine is fourstroke, then use n = 2
Step4: Find the mean effective pressure using the following formula.
`\mathbf{P_{bm}}` = `\mathbf{\frac{2\pi T.n}{V_{d}}}`
Significance of brake mean effective pressure:
The significances of the break mean effective pressure are as follows:
1] The brake mean effective pressure is the method to compare the different engines with different engine specifications.
2] The BMEP also relates the temperature of the gases in the engine cylinder.
3] The brake mean effective pressure gives the average pressure inside the cylinder during the power stroke.
4] The BMEP shows the compactness of the engine to produce a certain amount of brake power. The engines that have higher BMEP are more compact. It means that the engine can produce high power with the smaller size of engine.
Brake mean effective pressure example:
The fourstroke engine with a displacement volume of 1 Litre produces a torque of 84 N.m. Find the brake mean effective pressure for the engine. 
Given:
`V_{d}` = 1 Litre = `10^{3}` m³
T = 84 N.m
The brake mean effective pressure is given by,
`P_{bm}` = `\frac{2\piT.n}{V_{d}}`
For the fourstroke engine, n=2
∴ `P_{bm}` = `\frac{4\piT}{V_{d}}`
Put the value of `V_{d}` and T in equation of BMEP
`P_{bm}` = `\frac{4\pi \times 84}{10^{3}}`
`\mathbf{P_{bm}}` = `\mathbf{10.55 \times 10^{5}}` N/m²
This is the brake mean effective pressure produced by the engine.
FAQs:

What is the brake mean effective pressure?
The mean value of the pressure inside the cylinder during the power stroke that gives the same amount of brake power as like normal engine is known as brake mean effective pressure.

Why is brake mean effective pressure important?
The brake mean effective pressure shows the brake power produced by the engine per unit displacement volume thus it shows the capacity of the engine to produce brake power that can be used as criteria to compare different engines.
Above formulae are fine and Thank you.