TABLE OF CONTENTS Theory of flows of ideal fluids not only provides us the basis of study of fluid flows, but also gives us fundamental physical ideas of continuous fields in Newtonian mechanics. Extending the ideas of ideal fluid flows, the physical concepts can be applied to extensive areas in physics and mathematics.
Governing equations of flows of an ideal fluid derived in Chapter 3 are summarized as follows:
Boundary condition for an ideal fluid flow is that the normal component of the velocity vanishes on a solid boundary surface at rest:
where n is the unit normal to the boundary surface. If the boundary is in motion, the normal component v n of the fluid velocity should coincide with the normal velocity component V n of the boundary
Tangential components of both of the fluid and moving boundary do not necessarily coincide with each other in an ideal fluid.
One of the basic theorems of flows of an ideal fluid is Bernoulli s theorem, which can be derived as follows. Suppose that the fluid s entropy is uniform, i.e. the entropy s per unit mass of fluid is constant everywhere, and the external force has a potential ? represented by f = ?grad ?. Then, Eq. (5.2) reduces to (3.30), which is rewritten here again:
where h is the enthalpy ( h = e + p/ ?) and e the internal energy. From this equation, one...
