Determination of density at a depth in a compressible liquid. Hi all, Let us consider a tank containing some compressible liquid with bulk modulus K and having density at its surface s. Consider some part of liquid with volume V, a depth h below the surface. Due to liquid above it there will be some extra pressure dP, acting on the volume V of the liquid considered. This pressure or volumetric stress will cause some volumetric strain(negative) dV in liquid volume V. The bulk modulus is related with the pressure and volume changes as K= -dPV/dV or 1/K= -dV/dPV. .........(1) We also know density = mass/volume.... For the sake of analysis we can assume Liquid volume V at the surface(where the liquid is negligibly compressed). If its density is s(as specified already), then we can say: s=m/V. .........(2) where m is the mass of liquid with volume V at surface. To form a similar equation for density at a depth h, let us imagine that the liquid of volume,V is now dipped below a depth h. At this depth the volume is this liquid changes by dV(a negative value) the mass of this liquid will however remains same. This accounts for a change in density say s* being the density at depth h. The equation will then be: s*= m/(V+dV). ..........(3) from equation (2), m=sV, putting this value in 3 we get s*= sV/(V+dV). or V+dV= sV/s*. or dV= sV/s* -V. or dV= V(s/s*-1). .........(4) Putting this value in equation 1,we get 1/K= -V(s/s*-1)/VdP. or 1/K= (1-s/s*)/dP.....(5) Equation (5), will give the density s* at a depth h, provided we know the pressure differenece at depth h. This is where I am finding difficulty. At one look, one may simply say the pressure at depth h will be hsg. But as a matter of fact the liquid is compressible its density is not s throught. The formula hsg will work only if the density were constant and liquid is incompressible. I have tried a lot of integration tools but in vain. Any help will be highily appreciated. Thanks a bunch.