Wiginton, C. Lamar2021-12-142021-12-1419742077471https://hdl.handle.net/10657/8352The purpose of this dissertation is to analyze the velocity development of laminar incompressible flow in the entrance region of a straight duct with an unchanging eccentric annular cross-section. A linearized version of the governing equations is solved under the assumptions that the velocity is zero on the duct wall and that the initial velocity profile is uniform across the cross-section. The analysis leads to a two-dimensional eigenvalue value problem which is then posed in the appropriate Hilbert space. Galerkin's method is shown to converge for, and then applied to, this eigenvalue problem.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital