Fluid statics and Archimedes

The equations of fluid statics derive from the fact that in a stationary fluid only normal stress (pressure) is present and tangential stresses are absent. In this article we derive equations for variation of pressure in a static fluid or in one that is moving as a rigid body. Also, we show that surfaces of constant pressure and constant density should coincide. Various types of instabilities related to submerged bodies and multi layerd fluids are briefly discussed.