In
mechanical engineering
Mechanical engineering is the study of physical machines and mechanism (engineering), mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principl ...
, the Beale number is a parameter that characterizes the performance of
Stirling engine
A Stirling engine is a heat engine that is operated by the cyclic expansion and contraction of air or other gas (the ''working fluid'') by exposing it to different temperatures, resulting in a net conversion of heat energy to mechanical Work (ph ...
s.
It is often used to estimate the power output of a Stirling engine design. For engines operating with a high temperature differential, typical values for the Beale number are in the range 0.11−0.15; where a larger number indicates higher performance.
Definition
The Beale number can be defined in terms of a Stirling engine's operating parameters:
:
where:
* ''B
n'' is the Beale number
* ''Wo'' is the power output of the engine (
watt
The watt (symbol: W) is the unit of Power (physics), power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantification (science), quantify the rate of Work ...
s)
* ''P'' is the
mean average
In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results fr ...
gas
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
(
Pa) or (
MPa
MPA or mPa may refer to:
Academia
Academic degrees
* Master of Performing Arts
* Master of Professional Accountancy
* Master of Public Administration
* Master of Public Affairs
Schools
* Mesa Preparatory Academy
* Morgan Park Academy
* M ...
, if volume is in
cm3)
* ''V'' is swept
volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
of the power piston (
m3, or
cm3, if pressure is in
MPa
MPA or mPa may refer to:
Academia
Academic degrees
* Master of Performing Arts
* Master of Professional Accountancy
* Master of Public Administration
* Master of Public Affairs
Schools
* Mesa Preparatory Academy
* Morgan Park Academy
* M ...
)
* ''F'' is the engine cycle frequency (
Hz)
Estimating Stirling power
To estimate the power output of an engine, nominal values are assumed for the Beale number, pressure, swept volume and frequency, then the power is calculated as the product of these parameters, as follows:
:
See also
*
West number
References
External links
Stirling Engine Performance CalculatorBeale number calculator
Dimensionless numbers of thermodynamics
Piston engines
Mechanical engineering
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