The mathematics behind pouring a glass of wine

Have you ever found yourself dispensing wine from a box, or beer from a standing keg, and wondered how much liquid is left in the container? If you were thinking about it like a mathematician, you might have noticed that the fuller the keg is, the faster the beer comes out.

This might seem obvious, but this is a known mathematical relationship, and it uses a versatile piece of maths that crops up in many other real-world situations. Fluid dynamics is the study of flow: how liquids…