Brake mean effective pressure (BMEP): Definition, Formula

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.

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 Vd is the sum of the swept volume of all the cylinders and it is given by,
Vd = Number of cylinders (n) x Swept volume of one cylinder (Vs)

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 a higher BMEP can generate higher brake power than the engine of the same size having a lower BMEP.

The BMEP depends on 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,

`\text{BMEP}=\frac{2\pi T.n}{V_{d}}`

T = Torque at the crankshaft
n = Number of crankshaft revolutions during one power cycle
Vd = Engine displacement

For two-stroke engines the value of n =1, therefore the brake mean effective pressure is given by,

`P_{bm}=\frac{2\pi T}{V_{d}} \cdots \text{(For 2 stroke engine)}`

For four-stroke engines, the value of n = 2, thus the brake mean effective pressure becomes,

`P_{bm}=\frac{4\pi T}{V_{d}} \cdots \text{(For 4 stroke engine)}`

Brake mean effective pressure derivation:

The four-stroke engine performs 2 complete revolutions of the crankshaft for one power stroke and the two-stroke engine performs a single complete revolution of the 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,

`\text{Rate of power stroke}=\frac{N}{n}`

N = Engine speed (RPS)
n = 2 for four-stroke engine
n = 1 for a two-stroke engine

Now the power generated by the engine is given by,

P = Work done by single power stroke x Rate of power stroke

`P=\text{Work done by single power stroke} \times \frac{N}{n} \cdots \text{Equation [1]}`

By the definition of BMEP,

`P_{bm}=\frac{\text{Work per power stroke}}{V_{d}}`

`\text{Work per power stroke}=V_{d} \times P_{bm}`

Vd is engine displcement
Pbm is brake mean effective pressure

By putting this value in Equation [1],

`P=(V_{d} \times P_{bm}) \times \frac{N}{n} \cdots \text{Equation [2]}`

The brake power at the crankshaft is given by,

P = 2πNT

T = Torque at crankshaft
N = Crankshaft speed (rps)

Put this value of P in an equation [2],

`\text{2πNT}=(V_{d} \times P_{bm}) \times \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:-

Step-1: Find the total displacement volume (Vd) of the engine.

Step-2: Find the torque at the crankshaft (T) of the engine.

Step-3: Check the type of the engine (two-stroke/ four-stroke).
If the engine is two-stroke, then use n = 1
If the engine is four-stroke, then use n = 2

Step-4: 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 the engine.

BMEP numerical:

The four-stroke engine with a displacement volume of 1 Litre produces a torque of 84 N.m. Find the brake mean effective pressure for the engine.

Vd = 1 Litre = 10-3 m3
T = 84 N.m

The brake mean effective pressure is given by,


For the four-stroke engine, n=2

`\therefore P_{bm}=\frac{4\piT}{V_{d}}`

Put the value of Vd and T in the equation of BMEP

`P_{bm}=\frac{4\pi \times 84}{10^{-3}}`

`\mathbf{P_{bm}}=\mathbf{10.55 \times 10^{5}} \text{N/m}^2`

This is the brake mean effective pressure produced by the engine.

Pratik is a Graduated Mechanical engineer. He enjoys sharing the engineering knowledge learned by him with people.

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