Expansion incompressible body

Here we have rearranged the constants into a more compact notation. The application of the method becomes even more simple, when the Taylor expansion ends after some terms, as is the case for the incompressible body, where V = % +a T—To)) and Vp = 0. 

We discuss finally the case of a thermal expansion coefficient of zero. In this case, a pressure change does not effect a temperature change of the material and also no change in volume. So no input of compression energy is achieved. In contrary to the adiabatic application of pressure in the isothermal case in fact no change in volume will occur. Therefore, the incompressible body should be more accurately addressed as the isothermal incompressible body. 

Tuck established a mathematical expression for squat with a slender body theory. The slender body theory assumes that the beam, draft, and water depth are very small relative to ship length. This theory uses potential flow where the continuity equation becomes Laplace s equation. The flow is taken to be inviscid and incompressible and is steady and irrotational. In restricted water, the problem is divided into the inner and the outer problems, following a technique of matched asymptotic expansions to construct an approximate solution. The inner problem deals with flow very close to the ship. The potential is only a function of y and 2 in the Cartesian coordinate system. In the cross-flow sections, the potential function... 

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