Branched channel free-streamlines Original Research Article

Two configurations of free-streamlines in a branched channel in plane incompressible potential flow are analysed for three different branch angles. These cases were studied before by Modi et al. and Sinha et al. But their results are found to be incorrect. The hodograph method is used, producing a Schwarz-Christoffel-like integral over a semi-disk region. The integration is carried out using convolution number algebra, which produces the potential flow in analytical form. The unknown parameters in the integral are solved by iteration, using the Newton-Raphson method, with the Jacobian matrix approximated by a finite difference Quotient matrix. It is shown how a further conformal mapping of the semi-disk to the full circular disk leads to the transformation of Elcrat and Trefethen.