Continuity and Bernoulli's Principle
For steady incompressible flow, Av = constant, and P + ρ v2/2 + ρ g h = constant along a streamline.
What is Continuity and Bernoulli's Principle?
For steady incompressible flow, Av = constant, and P + ρ v2/2 + ρ g h = constant along a streamline.
Key formula / rule: Continuity: A1 v1 = A2 v2.
Key points
- Derive Bernoulli's equation from work-energy considerations.
- Apply continuity and Bernoulli to pipe and efflux problems.
Common exam trap
Applying Bernoulli's equation across turbulent or viscous flow.
Definitions
- Term
Continuity and Bernoulli's Principle
- Meaning
For steady incompressible flow, Av = constant, and P + ρ v2/2 + ρ g h = constant along a streamline.
- Term
Continuity and Bernoulli's Principle — explanation
- Meaning
Bernoulli's principle is energy conservation per unit volume for an ideal fluid, and explains why a faster stream has lower pressure. It applies to steady, non-viscous, incompressible, streamline flow only.
Learning objectives
Derive Bernoulli's equation from work-energy considerations.
Apply continuity and Bernoulli to pipe and efflux problems.
Formulae
- Key point
Continuity: A1 v1 = A2 v2.
- Key point
Bernoulli assumes steady, non-viscous, incompressible, streamline flow.
- Key point
Speed rises where the cross-section narrows, so pressure falls.
Prerequisites
PHY-U3-MPM-T2-S1-C1
PHY-U1-WEP-T1-S2-C2
Common mistakes
Applying Bernoulli's equation across turbulent or viscous flow.
Comparing points that do not lie on the same streamline.
Keywords
Continuity
Bernoulli
Principle
Practice preview
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