Integral equation for small perturbations of irrotational flows

An investigation is conducted concerning the validity of analytical methods which are based on deriving an integral equation, taking into account small perturbations in the case of a nonuniform but irrotational flow. The results obtained apply to a wide Mach number range, but are restricted to small amplitude motions and to nonviscous flows. It is shown that the integral equation relating the unknown velocity potential to the known normal flow velocity can be derived from the appropriate Green's identity.