Chapter 3, Problem 13P

Assuming the bulk modulus is constant for sea water, derive an expression for the density variation with depth, h, below the surface. Show that the result may be written ρ ≈ ρ₀ + bh where ρ₀ is the density at the surface. Evaluate the constant b. Then, using the approximation, obtain an equation for the variation of pressure with depth below the surface. Determine the depth in feet at which the error in pressure predicted by the approximate solution is 0.01 percent.