Depends on how deep the sub sits in the water. There are many kinds of subs.

The shallowest submerged draft of any modern submarine is ~ 33 feet (10 m). The navigational draft (surfaced) ranges between 18 to 61 feet depending on type. This represents the necessary clearance for the submarine to pass, like the clearance a truck needs to go under a bridge. It is preferable to travel in water much deeper than this to prevent grounding. A submarine is really not very effective in water shallower that 100 feet because in many parts of the ocean the water may not hide them and they have limited room for maneuver. Diesel-electric subs have an advantage due to their smaller size and lack of noise-generating coolant pumps (for a nuclear reactor) in shallow water <600'. In deeper water the greater speed, diving depth, and range of nuclear submarines is more decisive.

Surfaced, the depth of water limited by the draft of the submarine, which varies from class to class just like for a surface ship. Submerged, you have to take into account the diameter of the hull and the height of the sail. This also varies from ship to ship. Peace time rules for US submarines when transiting out from port do not allow them to submerge until they cross the 100 fathom curve. This is a safety precaution. Shallow water operations are limited for several reasons, not the least important of which is the hydrodynamic effect of operating a moving vessel near the ocean bottom. Here's an experiment for you to try: Place two books, about an inch apart thick and three or four inches apart. Lay a sheet of paper across the gap. Now, get down and close and blow a gentle breath of air under the paper and see what happens. The paper will flex downward as the air passes between the paper and the table top. This same effect is felt with submarines operating close to the ocean floor, and is why they do not do it if at all possible. Submarines do not operate in shallow waters routinely because of this...among other things. Some of those other things are inherent in the design of the ship itself. For example, placement of sea water suctions for various sea water cooled systems is important. Suctions along the bottom of the ship are more limiting in shallow waters than suctions along the side of the ship, for obviosu reasons. Sea water systems don't work too well when you suck mud into them off the ocean floor. Also, there are the tactical and strategic limitations inherent in operating in shallow waters. It's much easier to detect a submarine during shallow water operations because they are easier to see. Also, ship's speed is limited, as well as the ability to swiftly and silently accelerate, at shallow waters due to an effect known as "cavitation" around the screw (propeller) blades. This creates a LOT of distinctive noise, and noise is the merciless enemy of a submarine. And, of course, maneuverability is limited in shallow waters. If you google a class of submarine, you can easily find the draft of that sub. For example, the Los Angeles class submarine has a draft of 31 feet. This means when she is on the surface, the keel of the submarine is 31 feet under the water, so she cannot operate in waters shallower than 31 feet without grounding. http://en.wikipedia.org/wiki/Los_Angeles_class_submarine And take a look at the picture of the USS Key West operating at periscope depth at the above link. You can clearly see the submarine under the water at that depth.