Potential Flow Through a Conical Pipe With An Application to Diffraction Theory

Cover Potential Flow Through a Conical Pipe With An Application to Diffraction Theory
Potential Flow Through a Conical Pipe With An Application to Diffraction Theory
Jack Bazer
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Ud) and (2. 5)3. The contour C [cf. Fig. T\ is the curve traced from the point -(-s- + ioo) to - ^ + ioo along the line Re v = -1/2 except near the point v = -1/2 which is circumvented by a small semicircle traced in a clockwise fashion. The choice of C is dictated by the requirement that U (r, ©) approach a constant at in- finity [cf. Eq. (2, Ud)J. That the present choice of c' suffices to satisfy - 17 - this requirement will become apparent later.
c; - kim V V — plane ( I H 1 Re \1 > Cp k Fig
...ure 2 Our object now is to determine the functions A(v) and B(v) from the conditions of the problem. Let us assume, subject to later verification, that the integrals of Eqs. (U. 2) and (U. 2') are convergent and that it is permissible to take the necessary limits and derivatives under the integral 1 2 signs. It follows immediately that U (r, ©) and U (r, ©j satisfy the potential equation in the regions

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