Develop the energy balance
Connect pressure work with kinetic and gravitational energy per volume along an ideal streamline.
AP Physics 1 · Unit 8 · Fluids
Bernoulli’s Principle
Observe pressure, speed and height in flowing water, develop Bernoulli’s equation from energy, and test the speed of a tank’s emerging jet.
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Learn by doing
Three ideas you’ll put into motion
Compare pipe conditions
Change flow or height, combine continuity with Bernoulli, and interpret paired energy bars.
Predict and test an outlet
Derive Torricelli’s theorem, investigate water head and design a water level for a target exit speed.
The big idea
The key ideas, at a glance.
Include all three energy terms
Along a steady ideal streamline, P + ½ρv² + ρgy is constant. Pressure, speed and height can change while this energy balance per volume stays fixed.
Use the conditions of the comparison
Higher speed accompanies lower pressure at equal height on the same ideal streamline. When height changes, include its contribution too. For a small hole in an open reservoir, v = √(2gh).
A quick comparison
Compare two points at the same height in a narrowing pipe with steady, ideal flow.
The narrow section has higher speed and lower pressure, while the energy sum per volume stays fixed.
Teaching this topic?Classroom fit, AP connections, and support
- Classroom fit
- Use for a concept introduction, guided independent practice, or a projected class discussion.
- Before students begin
- Pressure, density, continuity, work, kinetic energy and gravitational potential energy. Short reminders develop pressure work and the common height reference.
- Built-in support
- Prepared scenes, guided prompts, and feedback on lesson questions.
- AP Physics 1 connections
- Unit 8, Topic 8.4.B: conservation of mechanical energy in fluid flow, Bernoulli’s equation and Torricelli’s theorem. Combine mathematical reasoning with controlled comparisons and evidence from the model.
- Check for understanding
- Ask students to distinguish continuity from energy conservation, explain the competing effects in a widening uphill pipe, and choose the surface-to-hole head for a tank outlet.
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The first scene is set up. Start the lesson and explore.