I have a balloon consisting of thin rubber and willed with helium or air under some pressure greater than 1 atmosphere. The balloon is tied off at the bottom.
Without the complication of the tie at the bottom, and neglecting minutia such as air pressure gradients, the balloon would be a sphere. But we always picture party balloons as rounder at the top and a bit more sharply curved at the bottom.
What dictates the shape (is it the additional weight of the bottom knot, or a string attached that keeps the balloon static in position?) and what is the equation of the shape.