Is it possible to find the density or specific volume of water, by only knowing its pressure? Or we need to know its temperature as well? I can't find any relevant table, so can you advise me please? Thanks
The density of water (and other fluids) depends both on the pressure and the temperature. A graph for water is here:
You may see that at 1 bar (1 atmosphere), the density is highest around 4 °C. That's the conditions where the density reaches the nice 1,000 kilograms per cubic meter. Water contracts when it gets warmer than that, but also when it gets cooler than that. Between 4 and 25 °C, the density of water drops by 0.3% or so.
This decrease may be compensated by the increase of the pressure to 60 atmospheres (bar) or so, also by 0.3%. Because 60 atmospheres is harder to get "by hand" than 25 °C, we may say that the temperature matters more at conditions that may be prepared by "human hands".
However, the pressure deep in the ocean is much greater. 10 meters of water column is about 1 atmosphere, so deep in the sea (Marianna trench), one can get up to 1,000 atmospheres, and there are other ways to achieve high pressures, too. In the trench, the density of water is higher by a few percent.