Imagine a spaceship constructed for merfolk and it is completely filled with oxygenated water instead of air.
Since they can swim around effortlessly in the water, do they even need artificial gravity similar to their natural habitat on Earth?
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Lack of gravity means lack of convection. Lower density gasses or fluids just sit where there are. That's a reason why fires in space are spherical and automatically extinguish themselves - since there is no "up", smoke does not raise high and away from fire, and doesn't cause currents drawing in fresh air with unspent oxygen.
Similarly, if you want to oxygenate water, you won't be able to simply make air bubbles pass through water from bottom to top, increasing diffusion by increasing contact surface, like those devices used in aquariums do. Pumping oxygen in will create one large bubble next to exhaust forcing a lot of creativity in making it work - first you need to stir water next to oxygen source to make it mix with water, later you need to stir entire room to spread oxygenated water and yet later you need to somehow extract carbon dioxide out of water. Easiest way I can imagine would be to use exhausts, intakes and pumps to create artificial current in entire room, filtering and oxygenating outside of room, before returning it to internal cycle (you still need similar system to filter water anyway, but not as much as for oxygenation).
Compare this to ease of lining floor with tiny oxygen exhaust, ceiling with oxygen/carbon-dioxide intakes and letting artificial gravity do the work.
Obviously, you need pumps and filters to close the cycle - unabsorbed oxygen gathered by ceiling intakes is pumped back into floor exhausts while carbon dioxide is recycled before returning to loop. However, if you already posses artificial gravity, then this is at least one of the reasons to use it: oxygenating water without artificial gravity will require much more plumbing and with much higher throughput.
If a mermaid has a swim bladder, a lack of gravity will make it harder to move up and down.
This article has more info on how it works, but basically by increasing and decreasing the internal pressure of this bladder, a fish can easily change vertical elevation and maintain its current depth without expending a lot of energy.
If there's no gravity, there is no downward pull to make going down work. Buyoancy is defined as the upward force opposing the weight of the immersed object. With no gravity acting on you, you're weightless and have no buyoancy. That means that going up wouldn't work either.
If a mermaid had this trait, she could not change her position in vertical space with her swim bladder. She could be disoriented and need special training to learn how to travel differently. Handrails could be installed to make changing elevation easier.
Mermaid astronauts coming home might experience something akin to a swim bladder disorder, and have trouble staying level or moving vertically once they get back to their planet.
They would need it for the same reason, we thin-atmosphere-breathers need gravity. Yes, it is very nice that gravity helps us keep our boots on the ground so that we have an easier time stopping once we are in motion; but the real value of gravity is that it makes our equilibrium work.
Ask anyone who has ever suffered from chronic vertigo or sea sickness. Knowing which way is down is vital to having a happy life and journey!
Artificial gravity is expensive (you need a really long tether (which will hit space junk and dust, and will create disorienting Coriolis forces on-board) or magic), and a pump moving oxygenated water is cheap, so I'd laugh if I read that merfolk needed artificial gravity do deal with respiration.
As far as controlling one's location with a ballast goes, that's a much smaller adjustment than humans made to zero-gravity. Unless your merfolk are less physically adept than humans or bats or dogs or monkeys, that shouldn't be an issue.
I see no convincing reason to use artificial gravity for merfolk except the same reason we always see humans with artificial gravity in movies - it's prohibitively expensive to make TV and feature films in zero gravity situations.