I’m 100m underwater and I exhale. I know the air will expand as it travels upwards, but does it change speed? What is that acceleration and speed?
-Tcat
WAG, as the bubble rises, it expands, thereby lowering the density of the air inside, causing the bubble to rise faster, until it reaches some sort of terminal velocity caused by the friction of the water.
Too, I would think the pressure of the water pushing against the bubble would decrease as it rose, allowing it to gain speed.
I would think the front (technically top) surface area of the bubble increasing would have some effect as well. This sounds like a calculus problem to me, what with the changing rates.
This is part WAG, speculation, and observation, but I remember from my scuba diving days that it seemed the air bubbles rose at a constant rate. The bubble has a tendency to flatten out as the ambeint pressure decreases, and that extended surface area would certainly come in to play.
My guess would be that it doesn’t change speed.
Approximating a constant-size bubble, you’d have a constant buoyant force upward, and some sort of frictional force downward which would probably increase with increasing speed. So the bubble would start off accelerating, but approach a terminal velocity, much like an object falling down through air. Based on what I’ve seen of bubbles, I would estimate that this terminal velocity is reached fairly quickly.
If the bubble is allowed to expand, then both the buoyant force and the frictional force would both increase. However, the buoyant force should be proportional to the volume of the bubble, while the frictional force would probably be approximately proportional to the cross-sectional area, so the terminal velocity would increase. Given that it seems to reach terminal so quickly, it’s probably a decent approximation to say that the velocity at any point on the rise is always equal to the terminal velocity at that point.
The pressure of the water on the bubble would change, but that shouldn’t have a significant effect on the speed. All that should really matter is the pressure difference over the size of the bubble, which is what’s responsible for the buoyant force.
This is based purely on observation when scuba diving:
First, larger bubbles travel upwards faster than the smaller bubbles.
Second, the bubbles become larger as they rise (and sometimes the bubbles become large enough -or are moving fast enough- that they break apart into smaller bubbles).
I would therefore assume that the bubbbles speed up as they rise and expand, with the caveat that they may slow down again if the larger bubble breaks apart). I would also guess this is primarily due to friction/surface areas, but I’ll wait for the expertrs to chime in.
There must be some old submarine sailors out there who can answer the question.
Or maybe a few tunnelmen who’ve “rode the bubble”.
And scuba guys too!
C’mon guys—sound off!
Well, the bouyant force is equal to the weight of the water displaced. As the bubble gets bigger because of decreased water pressure, it should rise faster since the same weight of air is pulling downward and the upward bouyant force is increasing.