Is it true that fluids under pressure always rotate in a counterclockwise direction?

 

http://youtube.com/watch?v=JEVvQeamJFk

umm no. the way fluids rotate has more to do withthe geometry of the vessel and/or the direction of a stirrer than if it is under pressure. if direction of rotation were pressure dependant we should find examples of the the direction of flow varying with depth in a vessel or even ocean where no extraneous factors(like ocean currents, or pumped streams) can be responsible.

"Is it true that fluids under pressure always rotate in a counterclockwise direction?"

Well, if they rotate then yes. Anything that rotates goes clockwise and anti clockwise depending on how you look at it.

 

However, there's no real requirement for them to rotate (noticably) even on the rotating earth.

Anything that rotates goes clockwise and anti clockwise depending on how you look at it.

Absolutely! It all depends how you look at it! If you look a clock from behind then you'll see it moves counter-clockwise!, but you can't have an absolute frame of reference to decide about either one!