I imagine that water comes out of a household faucet at some pressure, and that pressure must exceed 1 atmosphere (15 lbs/sq in) or it couldn't force itself past normal air pressure at sea level. So lets assume water comes out of the typical faucet at 2 atmospheres pressure. (Actually, I have no idea, and it probably varies a great deal from faucet to faucet, but 2 sounds like a reasonable guess.)

As it turns out, water pressure increases at a rate of roughly 1 atmosphere for every 30 feet or so of water depth. (It is already 15 lb/sq in at the surface due to the weight of earth's atmosphere.) So if you dive to the bottom of a 30 foot pool by holding your breath, the water pressure outside is double the air pressure inside your lungs.

So for 2 atmospheres of water pressure coming out of your faucet, going down 30 feet will just counteract it. Any deeper and water will flow IN your faucet.

It helps doing this kind of problem to keep in mind that a column of water 1 inch square and 30 feet high weighs about 15 lbs.

And a column of air 1 inch square reaching all the way to the top of our atmosphere will also way weigh about 15 lbs.