Water flow through a ventilated orifice

Before I begin, please excuse the rushed and poor schematic made in haste.
I am not very knowledgeable in fluid dynamics and was curious when I observed the scenario below.

A water droplet of mass M falls upon a surface with an orifice of diameter D_O with depth h_O into the material. It is then connected to a passage way with vents of diameter h. Initially, it is observed that the water does not flow through the orifice. However, if the orifice diameter D_O is big enough then the water droplet will flow down it. So the question is, At what D_O value will this occur? Also, will this be any different if the vents on the side of the surface were sealed off.