Pressure
Squeeze a balloon: the fluid inside pushes back. Dive ten feet down: your ears feel the squeeze. Both are pressure, the perpendicular push of a fluid on a surface, $P = F_\perp / A$. In a still fluid, pressure rises with depth as $P = P_0 + \rho g h$. The trap: at a given depth, pressure depends on the fluid and the depth. Not the container shape. Not how much fluid sits above.
Three places students lose this. Wider container, more pressure: the natural feeling that a wide reservoir hits harder at the bottom than a narrow pipe. It does not. Same depth, same pressure. Bigger force, bigger pressure: force and pressure are not the same thing. A small force on a tiny area can be enormous pressure, and a huge force spread wide can be tiny pressure. Gauge equals absolute: a tire gauge reading 30 psi means 30 psi above atmospheric, not 30 psi total.
The work
3 ways in · any order
Lesson
Pressure
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A ten-scenario applet that walks you through pressure as force per area, the depth-density law in a fluid, and the gauge vs absolute distinction. Each scenario rotates between focus-and-choice, symbolic, and numeric prompts; first-try accuracy and progress save to your browser.
Diagnostic
10-item topic check
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Ten multiple-choice items, each tied to a specific misconception. About fifteen minutes. Your score and the misconception traps that caught you both save as you go and feed the targeted practice card below.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.