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This book starts by presenting a detailed summary of the most general equations of fluid mechanics and then shows how various approximations are made to solve problems of engineering interest. This approach shows exactly where the given approximation fits within the general framework. This is very different than the approach in many other books where the various approximations (such as ideal fluid flow, compressible gas dynamics, Stokes flow, etc.) are presented right from the outset in different chapters, so that their connection to the most general framework is not apparent. Several new theoretical results (some based on technical papers) have been added, and keeping in view the emphasis on applications, several new examples have also been added to the first chapter. Several appendices list hundreds of results related to special functions which can be of interest to applied mathematicians and academicians interested in exact solutions.