Chapter 3, Problem 11P

If at the surface of a liquid the specific weight is γ_o, with z and p both zero, show that, if E = constant, the specific weight and pressure are given by

$\gamma =\frac{E}{(z+E/{\gamma }_o)}\text{and}p=-E\ln \left(1+\frac{{\gamma }_{o}z}{E}\right)$

Calculate specific weight and pressure at a depth of 2 km assuming γ_o = 10.0 kN/m³ and E = 2070 MPa.