If at the surface of a liquid the specific weight is \(\gamma_{o}\), with \(z\) and \(p\) both zero, show that, if \(E=\) constant, the specific weight and pressure are given by

\[\gamma=\frac{E}{\left(z+E / \gamma_{o}\right)} \quad \text { and } \quad p=-E \ln \left(1+\frac{\gamma_{o} z}{E}\right)\]

Calculate specific weight and pressure at a depth of \(2 \mathrm{~km}\) assuming \(\gamma_{o}=10.0 \mathrm{kN} / \mathrm{m}^{3}\) and \(E=2070 \mathrm{MPa}\).