Hamilton's principle applied to fluid mechanics

Hamilton's principle is rigorously applied to fluid systems to yield initially the equations of motion of a real (compressible, viscous) fluid. The assumptions of incompressibility and inviscidity are considered within the context of the variational principle. The principle is then used directly to obtain equations of motion for various fluid systems. These equations are approximate in that only the first terms of a set of admissible functions are considered; closure of the set leads to exact solutions. The concept of added mass is generated in passing and the variational equivalent of the D'Alembert paradox is examined.