# Engine

 Power Brake Mean Effective Pressure Volumetric Flow Rate Indicated Mean Effective Pressure Friction Mean Effective Pressure Compression/Expansion Ratio Combustion Pumping Losses Mean Piston Speed Total Bore Area Volumetric Efficiency Gas Dynamics

There is not much to say about the volumetric flow rate except if we are in presence of an engine with a known fixed displacement, i.e. we know how much air it can theoretically displace per crankshaft angular displacement ( Vθ ).

By definition, the measured volumetric flow rate ( Qm ) is related to the theoretical volumetric flow rate ( Qth ) and the volumetric efficiency ( VE ):

 Qm = VE Qth
(1)

And the theoretical volumetric flow rate is simply defined with the volume of air displaced per angular displacement ( Vθ ) and the angular velocity of the output shaft ( ω ):

 Qth = Vθ ω
(2)

## Detailing the volumetric flow rate

For a piston engine, the theoretical volumetric flow rate can be defined as:

(more)
Qth =
vmps Ab
 θc ⁄ θs
(5)

Where:

vmps = Mean piston speed (m/s)
Ab = Total bore area (m²)
 θc ⁄ θs
= Number of stroke per cycle (2, 4, 6-stroke; hit-and-miss cycle)

Note: For some engine cycles, such as the Atkinson cycle or the Miller cycle, one could argue that the theoretical volumetric flow rate is smaller because the effective intake stroke is smaller than the engine stroke. However, we will consider the engine stroke as the potential volume of air that can be displaced and consider a lower volumetric efficiency for those cycles.

One important thing to notice about equation (5):

##### The stroke is irrelevant for evaluating the air capacity of engine.

So the true potential of a piston engine depends only on its total bore area.

### Wankel engine

The previous equation could be used with a Wankel engine as well. Although, mean piston speed is a rather meaningless value in that case. As a trial and to show that for any type of engine, the volumetric flow rate can be related to a characteristic speed and an «area», this site will consider the more meaningful mean rotor tip speed instead. So, for the Wankel engine:

(more)
Qth =
9
 √ 3
2π
NrWe vmrts
(6)

If we assume that the mean rotor tip speed ( vmrts ) is a characteristic of a Wankel engine, the rotor radius becomes irrelevant for evaluating the air capacity. The product NrWe becomes the basic dimension of the engine, which could be called the «Wankel area».