Pressure in Liquids: p = ρgh
A 2.0 m tank with a draggable pressure probe: every measurement lands as a coloured dot on a live p–h chart, so tracing water and then mercury leaves two straight lines whose slopes differ by exactly the density ratio. Five liquids, three gravities (the same tank on the Moon reads 6× less), an atmospheric-pressure toggle for gauge vs total, and three Torricelli wall spouts whose jets leave at v = √(2gh) and follow true projectile paths — the deepest hole fires fastest, which is why dam walls thicken toward the base. The technical panel holds a lovely subtlety: spout speed is independent of the liquid, because a denser liquid pushes harder and resists acceleration harder in exact proportion.
Drag the probe and its measurements land as dots on the p–h chart — trace one liquid, switch, and trace again to compare slopes. The wall spouts obey Torricelli's theorem: deeper holes fire faster jets, which is why dam walls grow thicker toward the base.
In water on Earth, every metre of depth adds about 9.8 kPa — so 10 m of water adds roughly one whole atmosphere. That is why divers feel double the surface pressure at just 10 m down.
1. Drag the probe slowly from surface to bottom: the dots on the chart form a straight line through the origin. Pressure grows in exact proportion to depth.
2. Trace water, then switch to mercury and trace again without clearing. Two lines, and the mercury one is 13.6× steeper — the density ratio, drawn by your own hand.
3. Same depth, Moon gravity: about 6× less pressure. The formula has three dials, and g is one of them.
4. Watch the three spouts: the deepest fires fastest. More depth, more pressure, more speed — the reason a dam is a wedge, thick at the bottom.
5. Open the technical panel and look at the spout speeds when you switch liquids: they do not change. Pressure pushes harder on denser liquid, but denser liquid is harder to push — a beautiful exact cancellation.
What Each Variable Means
Pressure. In pascal (Pa): the force the liquid exerts per square metre — in every direction, which is why the probe shows arrows all around.
Density. Of the liquid, in kg/m³. Mercury is 13.6× denser than water, so its pressure line is 13.6× steeper.
Gravitational field strength. In N/kg. The same tank on the Moon (g = 1.6) reads about 6× less pressure at every depth.
Depth. Below the SURFACE — not the height above the bottom. Only depth matters: the shape and width of the container are irrelevant.