With Scotty shouting underwater in the clear tubing at the beginning of this sequence, we have what would seems to be a "life threatening situation", especially if you've spent your teen summers as a lifeguard and swimming instructor. The fact that Scott survived the untested transwarp beaming onto a ship far out of sensor range, much less transporters is bad enough, but in this throwaway scene we have another example of this Trek turning the chief engineer character into a complete clown.
Also, in most cases of submersion, people trying to survive have an instinct to move upward, the same direction as buoyancy and air. Perhaps he was in the tank and saw light coming in from the exhaust, so I'll give the film that mulligan.
In addition, Scotty the Clown has superhuman abilities. Here's one illustration we might try: sitting down without exertion, we might exhale normally, and hold our breath as if we were underwater. Without much of an oxygen exchange reservior in our lungs, the blood going through our alveoli has little opportunity exchange its CO2 for O2, and discomfort based on CO2 buildup begins within 10 seconds, after about 15 seconds, lightheadedness, panic, and loss of consciousness follows shortly thereafter if we are able to suppress our breathing reflex this long which is, for most people, past the "breath-hold breakpoint". It is extremely unpleasant, as our bodies are conditioned to regard this as imminent death. This is similar to electicity and other means of fooling the body into discomfort evolutionarily linked to death, and why it is so good for torture. These methods allow for extended, repeated simulated death experiences that can go on for years, whereas actual situations that cause these reactions would cause so much physical trauma that keeping the victim alive becomes a real bother. Once again we see science and technology as making life easier and providing greater capabilities, yet the additional responsibility that comes with such power remains tragically unknown to those who just want the latest gadget.
Let's go back to Chekov's unforgetable order "Hold on!" for some insight into why Kirk says "Hold on a second!" to Scott, who is being washed through the pipes of a turbine system in engineering. What do Chekov and Kirk's lines have in common, are they pointless? Yes. Can either intended recipient hear the instruction to "Hold on"? No. Could either follow the directions even if they heard them? No.
As if to indicate he senses his dialog is slipping into some of Chekov's silliest, Chris Pine says "Oh no," but is unable to stop from another "Hold on!" as he chases Scott around the plumbing. "No! No!" he cries, dashing back and forth after Scotty.
Finally coming to a stop, standing and dumbly watching what now would certainly be an unconscious officer, Kirk gawks in horror at the giant salad slasher turbine (also conveniently in a transparent housing) toward which Scott is being drawn. Miraculously, a a Scotty-sized "release valve" just happens to be upstream of the monster blades. Kirk dashes over to a computer panel and in less than 3 seconds has them open, saving the ships future engineer, assuming of course, his violation of an unknown number of regs in addition to dereliction of duty by abandoning his post, unauthorized transport aboard the Enterprise and interfering with operations during a state of emergency or war, and any upcoming failure to obey direct orders issued under penalty of court-martial by the ship's Captain.
Miraculously, opening the release valve does not bleed the lines as one might expect, so presumably no damage to the ship occurred. Also miraculous is that although Scotty goes into the valve head first, he falls feet first. Also miraculous is that he falls an easy 10 meters onto a rock solid deck without dying or even breaking a pinkie! Also miraculous is that he has not, as we indicated before, asphyxiated dispite plenty of time. A silly and stupid way to insert a stunt scene in the film.
Kirk yells "Are you alright?" and for good measure "Are you alright?" again.
Spitting water, Scotty shouts back "Mah head's buzzin' and ahm sooked, but otherwise I'm fine!"
In a cut to the bridge, Chekov reports "Captain Spock, detecting unauthorized access to water turbine control board."
No women speak in this segment although a background appearance on the bridge is tolerated for a split second.
Kirk is back on the Bridge in our next installment of Star Trek by the Minute 089: Engineering Run