Question

Stop me if i'm wrong but displacement is, for example, when you enter a bathtub the water level rises around you.

What happens when displacement isnt possible?

I'll give an example. I have two blocks off steel, one at the top of a chamber and one at the bottom. there is a gap between the two blocks that is filled with water. There is NO gap between the two blocks and the side of the chamber (the water cannot escape)

What happens when the two block come together, in effect squashing the water? where does the water go?

Answer 1

The blocks of steel and layer of water will just sit there like a sandwich.

If there is nowhere for the water to go, the blocks of steel will not come together. Instead, the water will compress slightly, increasing its pressure. This induced pressure will support the top block of steel.

If you make the top block of steel heavier and heavier, the pressure in the water will continually increase. Eventually you'll see the layer of water shrinking. The water isn't going anywhere; its density is increasing. You'll see a significant effect when the pressure on the water (the weight of the steel block divided by its area) becomes on the order of the bulk modulus of water, about 2*10^9 Pascal or 20,000 atmospheres.

The pressure at the bottom of a deep ocean trench is about 5% of this, so your slab of steel will need to be on the order of thousands of meters tall just to see a few percent change in the size of the water layer.

Eventually, you'll burst the sides of the container you're using, or a tiny gap will form. Then water will come shooting out in a jet.