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            As with solids, the bulk modulus, B, quantifies how much pressure must be applied to change the volume of a liquid:   

Here, ΔP is the change in pressure necessary to cause a fractional change in volume, ΔV is the volume change, and V is the original volume. This quantity helps us understand how liquids respond to pressure changes, and is also important as it describes how easily a pressure wave, such as sound, will travel through a liquid. 

    Liquids are typically more compressible than solids, though far less compressible than gases.  The bulk modulus for water is 1.96 x 10⁹ Pa, as compared to 160 x 10⁹ Pa for stainless steel.  However, it is within an order of magnitude of the bulk modulus for bone, which is 15 x 10⁹ Pa.  By considering how pressure and volume change with depth, we can use the bulk modulus to calculate how the density of water changes with depth.  Pressure increases with depth in a liquid because of the weight of the liquid pressing down from above.  For water, pressure increases 101,325 Pa (1atm) for every 10 m of depth.  Therefore, at a depth of 100 m, the pressure increase (ΔP) will be 1,013,250 Pa (10 times the pressure at the surface).  As a result of this pressure increase, the water volume (ΔV/V) will decrease.  Based on equation 2,  this fractional change in volume will be ΔP/B = 5.2x10^-4 which is quite small.  As a result of this decrease in volume, the water density will increase from 1000 kg m^-3 to 1000.52 kg m^-3.  Therefore, water density increases only slowly with depth in a lake or the ocean.

            As discussed above, liquids and solids are largely incompressible.  This enables animals to remain robust and survive at different altitudes and particularly different depths.  Though some animals retain a modest gas volume which can vary in size with pressure, others avoid this problem by using incompressible liquids or solids of lower density.  One of the more unusual ways of holding air in the body is found in a cuttlefish.  It is named for its cuttlebone, a foam-like, incompressible structure which holds gases at varying pressure.  Other organisms actually modify the chemical composition of their bodies to adjust their density and so avoid using a compressible volume of air for buoyancy compensation.  Some jellyfish exclude sulfate from their tissues.  Squids replace sodium ions with the lighter ammonium.  Others accumulate low density lipids or waxes.  Though these substantive changes take time to accumulate, they are more stable, and are insensitive to large pressure changes.