# Diameter to prevent water flow into a closed-end tube?

Imagine I drill three holes of different diameter into a large block of plastic but the holes don't go all the way through. (They form three close-ended tubes, see the image.) I then submerge the block into a bucket and fill it with water. I want to know which holes/indents/tubes will fill with water.

Water will not flow through these tubes (they're closed on one end), and if the diameter is narrow enough, water will not fill it completely either. Based on this information, it seems that wettability, capillary action, and viscosity are the important factors determining water ingress. Wettability will be constant across all three holes (they're made of the same material and are submerged in the same liquid), as will viscosity. The only difference is the radius of the entrance, and I believe in the equation for calculating capillary action, the radius is in the denominator.

Is there a way to calculate the largest diameter of the hole/tube that will prevent water from flooding it? (And by flooding it, I mean removing all air from the tube.) Assume a constant, arbitrary height of water in the cup, say 1 meter.

• When do you consider the water to be flooding in? May 23, 2019 at 0:10
• You haven't mentioned the height of water above the holes, as the pressure above the holes also matters. May 23, 2019 at 0:25
• Sorry, I edited the question to address your concerns. Flooding in would be when all the air in the tube is removed and replaced with water. The height is arbitrary, so let's just say it is 1 meter. May 23, 2019 at 0:49