Equation of continuity and Bernoulli’s Principle (Ch. 10)

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Equation of continuity and Bernoulli’s Principle (Ch. 10)

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Equation of continuity and Bernoulli’s Principle (Ch. 10)

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Equation of continuity and Bernoulli’s Principle(Ch. 10)

Owen von KugelgenHead-Royce School

- Continuity PrincipleA1v1 = A2v2
- Bernoulli’s PrincipleP1 + Dgh1 + (1/2)Dv12 =P2 + Dgh2 + (1/2)Dv22(really just conservation of energy!)

A1

A2

v2

v1

When the diameter of a pipe decreases,

the speed of the water increases(imagine a garden hose)

A1

A2

∆x2

∆x1

Vol1/t = Vol2/t

A1 ∆x1 / t = A2 ∆x2 / t

A1v1 = A2v2

PE = mghPE/Vol = Dgh

Pressure = F/AP = (F*d)/Vol = W/VolP = Energy/Vol

KE = (1/2)mv2KE/Vol = (1/2)Dv2

Bernoulli’sPrinciple

P2

h

P1

P2 = P1 + Dgh∆Pressure = ∆PE/V = Dg∆h

v2

P1

P2

v1

P1 + Dgh1+ (1/2)Dv12 = P2 + Dgh2 + (1/2)Dv22P1 = P2 + (1/2)Dv22 - (1/2)Dv12

P1 = P2 + (1/2)D[v22 - v12]

Due to the continuity principle: v2 > v1

so P1 > P2

Conceptual meaning:

Higher fluid speed produces lower pressure

This helps

wings lift

balls curve

atomizers and carburetors

Do their job

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 theBernoulli equation and provides a lift force

Curve Ball