The area of fluid dynamics/mechanics is common to several disciplines in engineering such as aerospace, mechanical, chemical, biotechnological, industrial, electrical, and civil, to mention but a few. In this book, common materials are presented and hopefully can be used by all. Also, in this book, models of fluid flow in an annulus, the cylindrical coordinate is considered. One of the differences in this book is the introduction of the semi-analytical solution to the fluid flow problems which is a two-step approach: Laplace transformation method and a numerical approach known as Riemann-sum approximation of Laplace inversion. This book is written in the motivation derived from my supervisor and mentor Professor Basant Kumar Jha, aside from his research activity, supervised a thesis turn to a book that brought an expansion in the education of fluid dynamics. This book is organized as follows: Chapter one: introduction, Chapter two: a literature review. Chapter three: mathematicalanalysis and solutions to the governing equations with their non-dimensionalization. Chapter four: Discussion of the results using graphs and tables and chapter five presents the summary and conclusion.