1. Equation of continuity and Bernoulli’s Principle (Ch. 10)
Owen von Kugelgen Head-Royce School

2. Moving Fluids Continuity Principle A1v1 = A2v2
Bernoulli’s Principle P1 + Dgh1 + (1/2)Dv12 = P2 + Dgh2 + (1/2)Dv22 (really just conservation of energy!)

3. Continuity Principle A1v1 = A2v2
When the diameter of a pipe decreases,
the speed of the water increases (imagine a garden hose)

4. Continuity Principle A1v1 = A2v2
∆x2
∆x1
Vol1/t = Vol2/t
A1 ∆x1 / t = A2 ∆x2 / t
A1v1 = A2v2

5. Can we apply energy concepts to fluids?
PE = mgh PE/Vol = Dgh
Pressure = F/A P = (F*d)/Vol = W/Vol P = Energy/Vol
KE = (1/2)mv2 KE/Vol = (1/2)Dv2

6. Bernoulli’sPrinciple

7. Bernoulli’s Principleh P1
P2 = P1 + Dgh ∆Pressure = ∆PE/V = Dg∆h

8. Bernoulli’s Principlev2 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)D[v22 - v12]
Due to the continuity principle: v2 > v1
so P1 > P2

9. Bernoulli’s Principle
Conceptual meaning:
Higher fluid speed produces lower pressure
This helps
wings lift
balls curve
atomizers and carburetors
Do their job

12. 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

13. Curve Ball