I recently wondered: Even when diving to just 2-3 meters without any modern equipment one can feel the change in pressure. Do we have any evidence how this was perceived and explained back in ancient times throughout middle ages, besides ascribing deeper water any religious or mythical property? (Archimedes came to my mind, but I wouldn't know how to research this question in detail).
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One has to distinguish static pressure from the dynamic pressure in a flow. Static pressure was understood to some extent by Archimedes and later Hellenistic writers like Hero and Ctesibius. At least their texts that we know do not contain mistakes: all that they wrote was essentially correct.
Dynamic pressure was very poorly understood before the modern times (that is before Bernoulli). Of course one cannot be sure what Archimedes really knew, besides what he wrote in the texts that survived, but a survived Roman engineering work on hydraulics shows very poor understanding of the matter. There is a modern commentary analysing this work.
A translation of the original book is on the same site. The author (Frontinus) was the official responsible for the water supply of Rome, so he probably used the best available knowledge.
Of course, the ancients actually did many complicated hydraulic works and they must have known a lot from experience, but this knowledge is not reflected in the surviving books.
EDIT. In connection with this question I started to investigate when was the diving bell used for the first time. Many sources refer to Aristotle who described how Alexander the Great used the diving bell in the siege of Tyre. Same story is contained in some 12 century book on Alexander. I did not find the reference on diving bell in Aristotle.
Aristotle also wrote this (in his book on animals):
Just as divers are sometimes provided with instruments for respiration, through which they can draw air from above the water, and thus may remain a long time under the sea, so also have elephants been furnished by nature with their lengthened nostril; and, whenever they have to traverse water, they lift this up above the surface and breathe through it.
On my opinion, this passage shows that Aristotle completely misunderstood the problem related to water pressure: what he describes is just non-realistic, neither for a human nor for an elephant:-)
answered Dec 8, 2015 at 14:30
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$\begingroup$ Thank you for your answer. It is every time interesting to distinguish what we actually know by books that were handed down and what we have to deduct from other sources. $\endgroup$ Dec 9, 2015 at 0:07
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$\begingroup$ There is an ample evidence that the ancients constructed canal locks and possibly caissons. So they must have been familiar with water pressure in practice. $\endgroup$ Dec 9, 2015 at 21:33
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$\begingroup$ The "diving bell" Wikipedia article mentions that one was described by Aristotle:-) $\endgroup$ Dec 9, 2015 at 21:36