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Influid dynamics,Bernoulli's principle states that for
aninviscid flow, an increase in the speed of the fluid
occurs simultaneously with a decrease inpressureor a decrease in
thefluid'spotential
energy.[1][2]
Bernoulli's principle is named after the Swiss scientist Daniel
Bernoulliwho published his
principle in his book Hydrodynamica in 1738.[3]
Bernoulli's principle can be applied to various types of fluid
flow, resulting in what is loosely denoted
as Bernoulli's equation. In fact, there are different forms of
the Bernoulli equation for different types of
flow. The simple form of Bernoulli's principle is valid
forincompressible flows(e.g. mostliquidflows) and
also forcompressible flows(e.g.gases) moving at lowMach
numbers(usually less than 0.3). More
advanced forms may in some cases be applied to compressible
flows at higherMach numbers(seethe
derivations of the Bernoulli equation).
An inviscid flow is the flow of anideal fluidthat is assumed to
have noviscosityIn most flows of liquids, and of gases at lowMach
number, thedensityof a fluid parcel can be
considered to be constant, regardless of pressure variations in
the flow. Therefore, the fluid can be
considered to be incompressible and these flows are called
incompressible flow. Bernoulli performed
his experiments on liquids, so his equation in its original form
is valid only for incompressible flow. A
common form of Bernoulli's equation, valid at anyarbitrarypoint
along astreamline, is:
(
A
)
where:
is the fluid flowspeedat a point on a streamline,
is theacceleration due to gravity,
is theelevationof the point above a reference plane, with the
positive z-direction pointing
upward so in the direction opposite to the gravitational
acceleration,
is thepressureat the chosen point, and
is thedensityof the fluid at all points in the fluid.
Forconservative forcefields, Bernoulli's equation can be
generalized as:[8]
where is theforce potentialat the point considered on the
streamline. E.g. for the Earth's gravity = gz.
The following two assumptions must be met for this Bernoulli
equation
to apply:[8]
the flow must be incompressible even though pressure varies,the
density must remain constant along a streamline;
http://en.wikipedia.org/w/index.php?title=Template:Continuum_mechanics&action=edithttp://en.wikipedia.org/w/index.php?title=Template:Continuum_mechanics&action=edithttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Inviscid_flowhttp://en.wikipedia.org/wiki/Inviscid_flowhttp://en.wikipedia.org/wiki/Inviscid_flowhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Potential_energyhttp://en.wikipedia.org/wiki/Potential_energyhttp://en.wikipedia.org/wiki/Potential_energyhttp://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-1http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-1http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-1http://en.wikipedia.org/wiki/Daniel_Bernoullihttp://en.wikipedia.org/wiki/Daniel_Bernoullihttp://en.wikipedia.org/wiki/Daniel_Bernoullihttp://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-3http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-3http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-3http://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Liquidhttp://en.wikipedia.org/wiki/Liquidhttp://en.wikipedia.org/wiki/Liquidhttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Gashttp://en.wikipedia.org/wiki/Gashttp://en.wikipedia.org/wiki/Gashttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equationhttp://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equationhttp://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equationhttp://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equationhttp://en.wikipedia.org/wiki/Ideal_fluidhttp://en.wikipedia.org/wiki/Ideal_fluidhttp://en.wikipedia.org/wiki/Ideal_fluidhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Arbitraryhttp://en.wikipedia.org/wiki/Arbitraryhttp://en.wikipedia.org/wiki/Arbitraryhttp://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlineshttp://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlineshttp://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlineshttp://en.wikipedia.org/wiki/Bernoulli's_principle#equation_Ahttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Earth%27s_gravityhttp://en.wikipedia.org/wiki/Earth%27s_gravityhttp://en.wikipedia.org/wiki/Earth%27s_gravityhttp://en.wikipedia.org/wiki/Elevationhttp://en.wikipedia.org/wiki/Elevationhttp://en.wikipedia.org/wiki/Elevationhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-Batchelor_265-8http://en.wikipedia.org/wiki/Conservative_forcehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Elevationhttp://en.wikipedia.org/wiki/Earth%27s_gravityhttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Bernoulli's_principle#equation_Ahttp://en.wikipedia.org/wiki/Streamlines,_streaklines,_and_pathlineshttp://en.wikipedia.org/wiki/Arbitraryhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Ideal_fluidhttp://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equationhttp://en.wikipedia.org/wiki/Bernoulli's_principle#Derivations_of_Bernoulli_equationhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Gashttp://en.wikipedia.org/wiki/Compressible_flowhttp://en.wikipedia.org/wiki/Liquidhttp://en.wikipedia.org/wiki/Incompressible_flowhttp://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-3http://en.wikipedia.org/wiki/Daniel_Bernoullihttp://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-1http://en.wikipedia.org/wiki/Bernoulli's_principle#cite_note-1http://en.wikipedia.org/wiki/Potential_energyhttp://en.wikipedia.org/wiki/Potential_energyhttp://en.wikipedia.org/wiki/Fluidhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Inviscid_flowhttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/w/index.php?title=Template:Continuum_mechanics&action=edit
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friction by viscous forces has to be negligible.
By multiplying with the fluid density , equation (A) can be
rewritten as:
or:
where:
isdynamic pressure,
is thepiezometric headorhydraulic head(the sum of the elevation
zand
thepressure head)[9][10]
and
is thetotal pressure(the sum of the static pressurep and
dynamic
pressure q).[11]
The constant in the Bernoulli equation can be
normalised. A common approach is in terms
oftotal head orenergy headH:
Bernoulli Equation
The Bernoulli Equation can be considered to be a statement of
theconservation ofenergyprinciple appropriate for flowing fluids.
The qualitative behavior that isusually labeled with the term
"Bernoulli effect" is the lowering of fluid pressure inregions
where the flow velocity is increased. This lowering of pressure in
a
constriction of a flow path may seem counterintuitive, but seems
less so when youconsider pressure to beenergy density. In the high
velocity flow through the
constriction, kinetic energy must increase at the expense of
pressure energy.
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