lesson opener : how does a plane fly? how does a perfume spray work? why does a cricket ball curve?
TRANSCRIPT
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Lesson Opener:
How does a plane fly?How does a perfume spray work?Why does a cricket ball curve?
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Daniel Bernoulli (1700 – 1782)
Derivation and Applications of the
Bernoulli PrincipalNIS TaldykorganGrade 11 Physics
Lesson Objective:1.To apply Bernoulli’s equation to solve problems
2.To describe Bernoulli’s principle and to derive his formula in terms of conservation of energy
3.To present applications of the Bernoulli principle
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Bernoulli’s PrincipleBernoulli’s PrincipleAs the speed of a fluid goes up, its
pressure goes down!
The pressure in a fast moving stream of fluid is less than the pressure in a slower stream
Fast stream = low air pressureFast stream = low air pressure
Slow stream = High air pressureSlow stream = High air pressure
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v small v smallv large
p large p large
p small
A1 A2
v1v2
A1
v1Low speedLow KEHigh pressure
high speedhigh KElow pressure
Low speedLow KEHigh pressure
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Equation of Continuity
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Bernoulli’s Equation in terms of Fluid Energy“for any point along a flow tube or streamline”
P + ½ v2 + g h = constant
Each term has the dimensions of energy / volume or energy density.
½ v 2 KE of bulk motion of fluid
g h GPE for location of fluid
P pressure energy density arising from internal forces within moving fluid (similar to energy stored in a spring) Transformation of SI Units to Joule/meter3= energy/volume:
P [Pa] = [N m-2] = [N m m-3] = [J m-3]
½ v2 [kg m-3 m2 s-2] = [kg m-1 s-2] = [N m m-3] = [J m-3]
g h [kg m-3 m s-2 m] = [kg m s-2 m m-3] = [N m m-3] = [J m-3]
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Deriving Bernoulli’s starting with the law of continuity
2211
2211
2211
21
fluid of massgiven aConsider
(constant)
:fluid ible"incompress"an For
vAvA
tvAtvAM
xAxAM
VVM
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Bernoulli’s EquationFor steady flow, the velocity, pressure, and elevation of an incompressible and nonviscous fluid are related by an equation discovered by Daniel Bernoulli (1700–1782).
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Deriving Bernoulli’s equation as Conservation of Energy
22
222
111
212
1
2222
1121
212
1
2222
1
121212
1
222111
fluid of piece""
on iprelationshwork -Energy
PgyvPgyv
gyvPPgyv
VM
MgyMv
VPPMgyMv
UKWUK
UKWUK
M
fffiii
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Bernoulli’s equation:
22222
111
212
1 PgyvPgyv
21
2
1
2222
1
2222
11
212
1
221121
1
PPA
Av
PvPv
vAvAyy
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BERNOULLI’S EQUATION
2
222
21
1
22
2
Vp
Vp
Vp
• In a moving fluid p+½V2 = constant everywhere• An increase in velocity of the fluid results in a decrease in
pressure• Bernoulli’s equation is an extension of F=ma for fluid
flows and aerodynamics
Constant
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HOW DOES A WING GENERATE LIFT?
• An imbalance of pressure over the top and bottom surfaces of the wing.– If the pressure above is lower than the pressure on
bottom surface, lift is generated
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Airplane Wing is curved on top
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HOW DOES A CURVED WING GENERATE LIFT?
Flow velocity over the top of wing is faster than over bottom surface– Air over wing is squashed to smaller cross-
sectional area– Mass continuity AV=constant, velocity must
increase
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high speedlow pressure
force
force
What happens when two ships or trucks pass alongside each other?
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velocity increasedpressure decreased
low pressurehigh pressure
(patm)
VENTURI EFFECT
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artery
External forces causes artery to collapse
Flow speeds up at constrictionPressure is lowerInternal force acting on artery wall is reduced
Arteriosclerosis and vascular flutter
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References and links:• Bernoulli Activity:• http://mitchellscience.com/
bernoulli_principle_discussion_nomath• Steve Spangler and Hydrogen Hexafluoride: • http://www.youtube.com/watch?v=GRLOgmmz_EU• Phet Colorado Fluid Pressure and Flow simulation:• http://phet.colorado.edu/en/simulation/fluid-pressure-and-flow • Types of Fluids:
http://mechteacher.com/fluid/#ixzz2fcgGwLbq• Flowing Fluids,Laminar Flow and stream lines:• http://www.youtube.com/watch?v=_aWdeXby7CA