Function to describe teardrop shape If I fill a plastic ziploc-shaped bag with water, the cross section profile should be sort of teardrop shaped (assuming we ignore the edge effects of the bag being sealed on the sides as well as the top and bottom). The bag should "sag"/get wider until to get the center of gravity as low as possible. Initially, getting wider will let more water towards the bottom but eventually this is offset by the bottom of the bag moving up (because the sides are fixed length).
Is there a common function that describes the shape the cross-section of the bag makes?
I would guess the bottom is a parabola, since gravity likes to make parabolas. Then I would guess the top is linear because its under tension. But I have no idea what the transition region might look like and whether you could put those two together into a nice function.

If you want something that looks like a drop but is not physically based, try the implicit equation $ax^2-(1-y)^3(1+y)=0$. The shape varies a little with $a$. Here it is for $a=4$, courtesy of WA.

