Explicit physics instruction
Bernoulli reasoning tracks mechanical energy per fluid volume along a streamline under ideal conditions.
When elevation is unchanged, pressure and kinetic terms can trade off; however pumps, friction, and turbulence add or remove energy.
Use the energy statement only after checking assumptions.
Core relation: A₁v₁=A₂v₂; ideal Bernoulli reasoning within stated assumptions.
Worked example
If speed increases through a constriction at the same elevation in a low-loss ideal model, static pressure can decrease as energy shifts toward kinetic form.
Guided question
What assumptions must hold before using a simple Bernoulli pressure–speed comparison?
Independent work
- Solve three continuity/flow calculations.
- State Bernoulli assumptions for one case.
- Identify one viscosity/turbulence limitation.
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.