Equation of continuity and Bernoulli’s Principle (Ch. 10). Owen von Kugelgen Head-Royce School. Moving Fluids. Continuity Principle A 1 v 1 = A 2 v 2 Bernoulli’s Principle P 1 + Dgh 1 + (1/2)Dv 1 2 = P 2 + Dgh 2 + (1/2)Dv 2 2 (really just conservation of energy!).
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Owen von KugelgenHead-Royce School
When the diameter of a pipe decreases,
the speed of the water increases(imagine a garden hose)
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)Dv2Can we apply energy concepts to fluids?
P2 = P1 + Dgh∆Pressure = ∆PE/V = Dg∆h
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
Higher fluid speed produces lower pressure
atomizers and carburetors
Do their job
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