Abstract—In this paper an integral formula will be derived that will compute the velocity of a non-cylindrical flow variation in swan neck ducts with prescribed flow characteristics. The flow can be characterized by the total head,  H (ψ) a function of only the stream function,    ψ   ( x , r) a nd by the function  C (ψ) which is a functio n of the azimuthal (circumferential) component of velocity vector, u in cylindrical polar coordinates ( x , r, ). The solution to the problem is given in terms of an integral formula based on Green’s first identit y. 

Index Terms—Stokes stream function, cylindrical flow, non-cylindrical flow, singular integral formula.

Vasos Pavlika is with SOAS, University of London, UK (e-mail: vp4@soas.ac.uk).

Cite: Vasos Pavlika, "The Construction of an Integral Formula for Computing Cylindrical and Non-Cylindrical Flow in the Region Bounded by Two Coaxial Cylinders of Varying Radii," International Journal of Applied Physics and Mathematics vol. 3, no. 5, pp. 316-323, 2013.