Dimensional analysis is the basis for the determination of laws that allow the experimental results obtained on a model to be transposed to the fluid system at full scale (a prototype). The similarity in fluid mechanics then allows for better redefinition of the analysis by removing dimensionless elements. This book deals with these two tools, with a focus on the Rayleigh method and the Vaschy-Buckingham method. It deals with the homogeneity of the equations and the conversion between the systems of units SI and CGS, and presents the dimensional analysis approach, before addressing the similarity of flows. Dimensional Analysis and Similarity in Fluid Mechanics proposes a scale model and presents numerous exercises combining these two methods. It is accessible to students from their first year of a bachelors degree.

This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.

Dimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author’s research group over the past forty years at the Chinese Academy of Sciences. The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields. Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.

Introduction to Fluid Mechanics, Sixth Edition, is intended to be used in a first course in Fluid Mechanics, taken by a range of engineering majors. The text begins with dimensions, units, and fluid properties, and continues with derivations of key equations used in the control-volume approach. Step-by-step examples focus on everyday situations, and applications. These include flow with friction through pipes and tubes, flow past various two and three dimensional objects, open channel flow, compressible flow, turbomachinery and experimental methods. Design projects give readers a sense of what they will encounter in industry. A solutions manual and figure slides are available for instructors.

Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.

Dimensional analysis is the basis for the determination of laws that allow the experimental results obtained on a model to be transposed to the fluid system at full scale (a prototype). The similarity in fluid mechanics then allows for better redefinition of the analysis by removing dimensionless elements. This book deals with these two tools, with a focus on the Rayleigh method and the Vaschy-Buckingham method. It deals with the homogeneity of the equations and the conversion between the systems of units SI and CGS, and presents the dimensional analysis approach, before addressing the similarity of flows. Dimensional Analysis and Similarity in Fluid Mechanics proposes a scale model and presents numerous exercises combining these two methods. It is accessible to students from their first year of a bachelors degree.

Derived from a course in fluid mechanics, this text for advanced undergraduates and beginning graduate students employs symmetry arguments to demonstrate the principles of dimensional analysis. The examples provided illustrate the effectiveness of symmetry arguments in obtaining the mathematical form of the functions yielded by dimensional analysis. Students will find these methods applicable to a wide field of interests. After discussing several examples of method, the text examines pipe flow, material properties, gasdynamical examples, body in nonuniform flow, and turbulent flow. Additional topics include waves on a free liquid surface, examples with other fluid properties, and ideal gas equations of state. Figures appear throughout the text, which concludes with a bibliography.

This introduction to dimensional analysis covers the methods, history and formalisation of the field. Utilising topics including mechanics, hydro- and electrodynamics, and thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis, making it perfect for students on introductory courses in physics, engineering and mathematics.

One of the bestselling books in the field, Introduction to Fluid Mechanics continues to provide readers with a balanced and comprehensive approach to mastering critical concepts. The new seventh edition once again incorporates a proven problem-solving methodology that will help them develop an orderly plan to finding the right solution. It starts with basic equations, then clearly states assumptions, and finally, relates results to expected physical behavior. Many of the steps involved in analysis are simplified by using Excel.