Illustrated Physics
physics, drawn
Concept

Torricellis law — where it appears

The rule that liquid leaves a hole at the speed it would reach falling freely from the surface above, the square root of twice gravity times the head. Because the outflow falls as the level drops, a straight-sided tank drains in a time proportional to the square root of its depth.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

One height inside the bottle where the pressure is the air's. Gauge pressure against height inside a sealed bottle with an open tube reaching down to 10 cm above its outlet, while it is bubbling, at three water levels: 30.0, 22.0, 13.0 cm. Each line rises at the same hydrostatic slope, ρg, from the air pocket at the top, which is below atmospheric, to the outlet at the foot. All three cross atmospheric pressure at the tube's tip — 7.4 mm below it, the extra a bubble needs to leave a 2 mm tube — and so all three reach the outlet at the same 906 Pa above atmospheric, whatever the level. Dashed: an open bottle at the same levels, whose pressure at the outlet is 2937, 2154, 1273 Pa.

The bottle that pours at one rate however full it is

Water running from a hole in the foot of an open bottle slows as the bottle empties, because the pressure at the hole is the depth of water above it. Seal the bottle and push an open tube through the stopper, down into the water, and it stops slowing: the flow holds steady from full until the level reaches the bottom of the tube. Nothing regulates it. The tube's tip is the one point inside where the pressure is the atmosphere's, the water above it hangs from an air pocket below atmospheric, and the outlet sees only the height of the tip.

fluids · Hydrostatics Three vessels emptying through the same hole. The water level against time in three vessels that each hold 25 litres to a depth of 35 cm and drain through the same 0.8 mm hole in the floor, the outflow following Torricelli's law. The cylinder empties in 16.0 hours, but its level falls fast at first and slowly at the end — a parabola in time — and it is half empty in depth after only 32% of the run. The bowl whose radius grows as the fourth root of the height lowers its level at one rate from top to bottom, a straight line, and empties in 12.9 hours. A straight-sided cone sloping outwards, the shape a potter can actually throw, comes between: half its depth goes in 49% of its run.

The vessel whose level falls evenly

Water leaves a hole in the floor of a vessel faster when the vessel is full, because the pressure at the hole is the depth of water above it. In a cylinder that makes the level fall quickly at first and slowly at the end, so hour marks on its wall crowd towards the bottom. A level that falls at one rate needs a vessel that widens as the outflow quickens: its radius must grow as the fourth root of the height. The Egyptians who made the oldest surviving water clock, about 1400 BC, gave it sloping sides, which halves the error of a cylinder. They also gave it a scale for every month, because the hours they wanted to count were not all the same length.

fluids · Hydrostatics

Named alongside it

The objects these essays reach for when they reach for this one.

Hydrostatic pressureAtmospheric pressureCapillary lengthDischarge coefficientGauge pressureIsochronismLaplace pressureMariotte bottlePoiseuilleReynolds numberTautochroneWater clock

All concepts