How are flying and scuba diving related?

Answer 1

If you fly before you dive, then not much (except sometimes you are a bit dehydrated after flying).

However, if you dive before you fly, then bad things can happen. When you dive, your body absorbs nitrogen into your tissues. When you are on the surface after the dive, those gases slowly leave your tissues. However, if you go in an aircraft (especially an unpressurised one), or otherwise ascend to high altitude, the air pressure is much lower, so that gas wants to leave your tissues more quickly, which can form bubbles that lead to decompression sickness.

The risk varies with how deep you have gone, how long you stayed at depth, and how soon afterwards you fly. Most dive agencies recommend that you do not fly for 12 - 24 hours after your last dive. The US Navy recommends a minimum of 4 hours before flying on the assumption that the dive was not a dive involving mandatory decompression stops.
At sea level we all have roughly 15 lbs per square inch of pressure on our bodies (14.7 for the hair-splitters out there). The amount of gas (nitrogen for this explanation) that can and will dissolve in the bodily fluids is related to the amount of pressure applied to the body. For every 33 feet a body is submerged, the atmospheric pressure is doubled. So, for a depth of 33 feet, a diver's body is under 2 atm. 66 feet (often the limit of "Sport diving") that pressure equals to 3 atm. As Boyle's law states, the volume of gas dissolved in solution will double with the square of the pressure. What this means in English is that the more pressure applied to a body, the more gas will dissolve into the liquid. Imagine examining a fresh bottle of Sprite- one sees a clear, colorless liquid with no bubbles. Now crack open that same bottle quickly, and thousands of bubbles form; this is because the pressure on the liquid was released quickly. A diver that goes to a depth absorbs more of the gasses from his or her mix than someone at sea-level. Send that same diver up in a plane soon after diving and his or her blood and lymph behaves like that Sprite; gas bubbles form and cause debilitation pain (the Bends), neurologic or pulmonogic accidents or even death.

Answer 2

They both involve surrounding ambient pressure as well as movement through fluid and plenty of other things that could be added.