No and the reason is that water is almost incompressible. The bulk modulus of water is about 2Giga Pascal. The bulk modulus at a high level describes how much the volume of a substance changes if you apply pressure. Water you can apply a lot of pressure with almost no change in volume. Now imagine you are deep sea like several kilometers below the surface of the ocean. The pressure on the lower layers of water are very high, yet the compression of the water deep sea is only slightly higher as closer to the water surface (approximately 2% higher in deep sea vs surface).
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