Abstract
Analytical expressions for the complex potentials associated with irrotational incompressible flows due to a finite collection of point sources and sinks in a circular fluid region, of arbitrary finite connectivity, are derived. By the conformal invariance of the boundary value problem, the flows due to point sources and sinks in arbitrary multiply connected fluid domains are then determined up to conformal mapping. As an application of the theory, it is combined with recent results on conformal slit mappings to derive explicit formulae for the effective size of an array of holes in a screen, or grating, following considerations presented by Tuck (Adv Appl Mech 15:89–158, 1975).
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Crowdy, D. Analytical formulae for source and sink flows in multiply connected domains. Theor. Comput. Fluid Dyn. 27, 1–19 (2013). https://doi.org/10.1007/s00162-012-0258-x
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DOI: https://doi.org/10.1007/s00162-012-0258-x