Equation of continuity and Bernoulli

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Equation of continuity and Bernoullis
Principle(Ch. 10)

• Owen von KugelgenHead-Royce School

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Moving Fluids

• Continuity Principle A1v1 A2v2
• Bernoullis Principle P1 Dgh1 (1/2)Dv12 P2
  Dgh2 (1/2)Dv22 (really just conservation of
  energy!)

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Continuity Principle A1v1 A2v2
A1
A2
v2
v1
When the diameter of a pipe decreases, the speed
of the water increases (imagine a garden hose)
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Continuity Principle A1v1 A2v2
A1
A2
?x2
?x1
Vol1/t Vol2/t A1 ?x1 / t A2 ?x2 / t A1v1
A2v2
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Can we apply energy concepts to fluids?

• PE mghPE/Vol Dgh
• Pressure F/AP (Fd)/Vol W/VolP
  Energy/Vol

• KE (1/2)mv2 KE/Vol (1/2)Dv2

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BernoullisPrinciple
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Bernoullis Principle
P2
h
P1
P2 P1 Dgh?Pressure ?PE/V Dg?h
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Bernoullis Principle
v2
P1
P2
v1
P1 Dgh1 (1/2)Dv12 P2 Dgh2 (1/2)Dv22
P1 P2 (1/2)Dv22 - (1/2)Dv12 P1 P2
(1/2)Dv22 - v12 Due to the continuity
principle v2 gt v1 so P1 gt P2
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Bernoullis Principle
Conceptual meaning Higher fluid speed produces
lower pressure This helps wings lift balls
curve atomizers and carburetors Do their job
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Wing lift
The air across the top of a conventional airfoil
experiences constricted flow lines and
increased air speed relative to the wing. This
causes a decrease in pressure on the top
according to the Bernoulli equation and provides
a lift force
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Curve Ball