(Photo: Frank Fox)
You can close your mouth, but your lips, however tighly sealed, are still a gap. It's a different situation for the Hydra viridissima. The hydra's mouth disappears at the cellular level when closed. Ed Yong explains at National Geographic:
In 1987, Richard Campbell from the University of California, Irvine discovered why: a hydra mouth is not a permanent opening. It constantly forms and vanishes. When it closes, a wide ring of cells around the edge of the mouth collapses into a small mound called a hypostome, with a rosette of 6 to 12 cells at its centre. These cells are stapled together by small junctions, so that not even a tiny pore remains between them. In many ways, Campbell wrote, closing the mouth is very much like healing a wound.
-via Super Punch