Consider a capillary tube of height $H_1$. Water raises to a height $h_1$ in this tube. Now the capillary tube is cut such that its new height is $H_2 < h_1$.
I've read in many textbooks and other online sources that water will rise to a height $H_2$ in this new capillary and NOT come out of it like a fountain, not even slowly.
However I cannot find a rigorous mathmetical proof for this claim, intuitively I feel that the water should actually come out (slowly perhaps). If anyone could help me with the proof or provide some hint or insight related to this, it would be very much appreciated.