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HomeConcept libraryFluid and Pressure

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Follow the authored sequence, or switch to recap mode for a faster review of the same path.

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Starter track5 concepts3 checkpoints145 min

Fluid and Pressure

Not started

Start with pressure in a resting fluid, then carry that same branch through continuity, Bernoulli, buoyancy, and drag-limited motion.

Use this track when the fluids pages still feel like separate demos instead of one connected branch. The path stays bounded: Pressure and Hydrostatic Pressure fixes force per area and hydrostatic pressure, Continuity Equation keeps one stream's flow-rate bookkeeping honest, Bernoulli's Principle turns that same flow into a pressure-and-height trade, Buoyancy and Archimedes' Principle loops back to pressure differences in a resting fluid, and Drag and Terminal Velocity closes with one falling-body bench where the fluid's pushback grows until forces balance.

Pressure in fluidsContinuity and flowBernoulli tradeBuoyancyTerminal speed

Entry diagnostic

Decide where to enter this path without opening a second testing system.

Reuse the pressure quick test, the continuity quick test, and the Bernoulli compare challenge to decide whether to start from fluid statics or skip ahead to buoyancy.

Start from beginning0 / 3 probes ready

Check the pressure-to-flow bridge before you open the full fluids path

Start from beginning

No saved diagnostic checks are available yet, so the opening concept is still the best place to start.

Uses the same local-first quick tests, checkpoint challenges, and track history already saved in this browser.

Begin with Pressure and Hydrostatic Pressure
  1. Quick testNot started5 questions

    Pressure in fluids quick test

    Check whether force per area, same-depth pressure, and the hydrostatic slope are already stable.

    No saved quick-test result yet.

    Pressure in fluids
    Open Pressure and Hydrostatic Pressure quick test
  2. Quick testNot started3 questions

    Continuity quick test

    Check whether the same flow-rate story is already trustworthy before pressure trades are added.

    No saved quick-test result yet.

    Continuity
    Open Continuity Equation quick test
  3. ChallengeNot started9 checks

    Bernoulli bridge checkpoint

    Use the compare challenge to verify that widening the same throat can recover pressure without changing the entry state.

    No saved checkpoint attempt yet.

    BernoulliCompare
    Open Same entry state, wider B recovers pressure

Why this order

The sequence is authored to keep the model honest.

Pressure and Hydrostatic Pressure comes first because the rest of the fluids branch is harder to trust if pressure itself still feels like a slogan. Continuity Equation then shows where the speed change lives in one steady stream. Bernoulli's Principle adds the matching pressure and height trade without leaving that same pipe. Buoyancy and Archimedes' Principle returns to pressure differences in a resting fluid so floating comes from the same hydrostatic story instead of a separate force shelf. Drag and Terminal Velocity closes by showing a different fluid interaction where resistive force grows with speed until the motion settles into terminal balance.

Shared concept pages

Each step opens the same simulation-first framework.

Compare mode, prediction mode, quick test, worked examples, guided overlays, challenge mode, and read-next cues stay on the concept pages. The track only decides the guided order and the next recommended stop.

Guided path

Follow the concepts and checkpoint moments in order.

Checkpoint cards reuse the authored challenge entries already living on the concept pages.

  1. 1Not startedMastery: NewStart here

    Pressure and Hydrostatic Pressure

    Use one piston-and-tank bench to connect force per area, pressure acting in all directions, and the way density, gravity, and depth build hydrostatic pressure.

    Start here before moving into Continuity Equation.

    FluidsIntro30 min
    Start concept
  2. Checkpoint 1LockedNot started

    Hydrostatic checkpoint

    Lock in the pressure-depth story by hitting a target with depth alone before the track turns static pressure into moving-fluid bookkeeping.

    Finish Pressure and Hydrostatic Pressure first. This checkpoint ties together Pressure in fluids through Hit 24 kPa by depth alone.

    Pause here after Pressure and Hydrostatic Pressure before moving into Continuity Equation.

    Pressure in fluids8 checksCoreGraph-linkedGuided start
    Return to Pressure in fluidsOpen concept
  3. 2Not startedMastery: New

    Continuity Equation

    Keep one steady stream tube on screen and use Q = Av to connect cross-sectional area, flow speed, and the same volume flow rate through narrow and wide sections.

    Builds on Pressure and Hydrostatic Pressure before setting up Bernoulli's Principle.

    FluidsIntro25 min
    Open concept
  4. 3Not startedMastery: New

    Bernoulli's Principle

    Follow one steady ideal-flow pipe and see how pressure, speed, and height trade within the same Bernoulli budget while continuity keeps the flow-rate story honest.

    Builds on Continuity Equation before setting up Buoyancy and Archimedes' Principle.

    FluidsIntro30 min
    Open concept
  5. Checkpoint 2LockedNot started

    Flow-pressure checkpoint

    Keep the same entry state, then widen the throat to recover pressure so continuity and Bernoulli stay tied to one bounded stream.

    Finish Bernoulli's Principle first. This checkpoint ties together Pressure in fluids, Continuity, and Bernoulli through Same entry state, wider B recovers pressure.

    Pause here after Bernoulli's Principle before moving into Buoyancy and Archimedes' Principle.

    Pressure in fluidsContinuityBernoulli9 checksStretchCompareGraph-linkedGuided start
    Return to BernoulliOpen concept
  6. 4Not startedMastery: New

    Buoyancy and Archimedes' Principle

    Use one immersed-block bench to connect pressure difference, displaced fluid, and the density balance behind floating, sinking, and neutral buoyancy.

    Builds on Bernoulli's Principle before setting up Drag and Terminal Velocity.

    FluidsIntro30 min
    Open concept
  7. 5Not startedMastery: New

    Drag and Terminal Velocity

    Drop one body through a fluid and use mass, area, and drag strength to see drag grow with speed until force balance settles into terminal velocity.

    Capstone step after Buoyancy and Archimedes' Principle.

    FluidsIntro30 min
    Open concept
  8. Checkpoint 3LockedNot started

    Terminal-speed checkpoint

    Finish by pausing near terminal speed so the fluid branch closes on force balance instead of a memorized speed cap.

    Finish Drag and Terminal Velocity first. This checkpoint ties together Buoyancy and Terminal speed through Freeze the near-terminal moment.

    Final checkpoint that closes the authored track after Drag and Terminal Velocity.

    BuoyancyTerminal speed6 checksStretchInspect timeGraph-linkedGuided start
    Return to Terminal speedOpen concept