Explicit physics instruction
Fluid dynamics synthesis connects continuity, energy, viscosity, and model limitations.
A strong explanation distinguishes mass/volume conservation from the additional assumptions needed for a Bernoulli model.
Faster flow does not universally mean lower pressure in every real situation; the simple Bernoulli relation has assumptions.
Core relation: A₁v₁=A₂v₂; ideal Bernoulli reasoning within stated assumptions.
Worked example
A flow moves through 4 cm² at 2 m/s and narrows to 2 cm². Continuity predicts v₂=(4×2)/2=4 m/s.
Guided question
Explain a narrowing-flow case using continuity first and energy reasoning second.
Independent work
- Solve three continuity/flow calculations.
- State Bernoulli assumptions for one case.
- Identify one viscosity/turbulence limitation.
Spiral retrieval bridge
- From Week 26: distinguish density from buoyant force.
- From Week 13: explain energy losses and efficiency.
- From Week 05: interpret residuals rather than hiding them.
Misconception check
Faster flow does not universally mean lower pressure in every real situation; the simple Bernoulli relation has assumptions.
Formative check
If cross-sectional area halves for steady incompressible flow, what happens to average speed?
Reveal response
It doubles.
Mentor evidence conference
Ask Archaemenes to audit continuity assumptions, energy terms, and residual interpretation.
Teacher guidance
Foundation: Apply continuity.
Core: Combine continuity with bounded Bernoulli reasoning.
Extended: Analyze viscosity/turbulence residuals.