ABSTRACT

Similarly, for potential flows, using eqn (55), eqn (51) reduces immediately to the derivative of eqn (60) with respect to t*. Thus, for potential flows, eqns (50) and (51) are not independent.

Finally, considering the component of eqn (59) in direction n,, and taking the limit as x,, approaches a point x0 on the surface 9', one obtains a boundary integral equation

00 an

f (41 aG a2 G clY (61) o x = x x.—.„, an an anon* *

which may be used to find 4), from the values of its normal derivative, prescribed from the boundary conditions.