Imagine I have a vertical straw, and that it is partially filled with water. If I were to decrease the radius of the straw at the bottom end, eventually surface tension would allow the water to remain in the straw (i.e. the force of gravity would not be enough to overcome the surface tension and for water to flow out of the straw).
What I'm curious to understand is for a certain (small) radius at the bottom, how much force/pressure would be required at the top of the straw to overcome surface tension and force the water out of the bottom of the straw at a certain (volume flow) rate.
Any help would be greatly appreciated!