Connected vessels
Vessels joined at the bottom are communicating vessels (a kettle and its spout, a U-shaped tube). The law: if the same liquid is poured into communicating vessels of any shape and is at rest, the liquid stands at the same level in all of them. The reason is that pressure at the same depth must be equal. The vessels must be open at the top, under the same air pressure. If different liquids are used (water and oil) the levels differ: the denser liquid stands lower: ρ1 × h1 = ρ2 × h2. The law is used in building to mark level points (the “water-level” hose), in water supply and water towers, in canal locks, in fountains (water brought by pipe from a higher level rises almost to that level) and in kettles and teapots. Hero’s fountain from ancient Greece is also based on it. In very narrow tubes surface tension can cause small level differences.
Water-level hose: fit two clear cups or tubes to the ends of a 2 m clear hose and fill it with water (no air bubbles). Place one end by a marked point on a wall and take the other to another wall 3–4 m away and mark the water level: both marks are at the same height. Safety: do not spill water; do not drink from or suck on the hose; ask an adult for help if standing on a chair.