The two-dimensional free surface potential flow of a liquid poured from a container is calculated when the liquid runs along the underside of the spout and then separates or detaches. The point of separation S can be anywhere on a straight underside, but on a curved underside it must lie between the lip and a certain point S*. When S=S*, the free surface has finite curvature at S, so the Brillouin–Villat condition is satisfied. This suggests that S* is the actual point of detachment. The calculation is done analytically for a straight underside and numerically for a curved one, with gravity omitted in both cases.