Free-streamlines

Two classes of classical Free-Streamlines are computed efficiently, using series expansions in conjunction with the method of Frobenius. The first class are jet free-streamlines from a nozzle with straight walls. The hodograph plane is mapped on a semidisk by an algebraic equation. The physical plane is obtained by a Schwarz-Christoffel-type integral. The second class is the plane butterfly valve. Two Schwarz-Christoffel-type integrals are necessary to obtain the flow in the the physical plane. Different regions of convergence are determined to cover the semidisk. The series expansions are computed with the aid of the convolution number. Several solutions of potential flow are plotted. Contraction coefficients of the symmetric jet in terms of nozzle angle, and for the butterfly valve in terms of closing angle, are given.