Dimensionless quantities, such as p, e, and f are used in mathematics, engineering, physics, and chemistry. In recent years the dimensionless groups, as demonstrated in detail here, have grown in significance and importance in contemporary mathematical and computer modeling as well as the traditional fields of physical modeling. This book offers the most comprehensive and up to date resource for dimensionless quantities, providing not only a summary of the quantities, but also a clarification of their physical principles, areas of use, and other specific properties across multiple relevant fields. Presenting the most complete and clearly explained single resource for dimensionless groups, this book will be essential for students and researchers working across the sciences. - Includes approximately 1,200 dimensionless quantities - Features both classic and newly developing fields - Easy to use with clear organization and citations to relevant works

Dimensionless quantities, such as p, e, and f are used in mathematics, engineering, physics, and chemistry. In recent years the dimensionless groups, as demonstrated in detail here, have grown in significance and importance in contemporary mathematical and computer modeling as well as the traditional fields of physical modeling. This book offers the most comprehensive and up to date resource for dimensionless quantities, providing not only a summary of the quantities, but also a clarification of their physical principles, areas of use, and other specific properties across multiple relevant fields. Presenting the most complete and clearly explained single resource for dimensionless groups, this book will be essential for students and researchers working across the sciences. Includes approximately 1,200 dimensionless quantities Features both classic and newly developing fields Easy to use with clear organization and citations to relevant works

Prepared by the IUPAC Physical Chemistry Division this definitive manual, now in its third edition, is designed to improve the exchange of scientific information among the readers in different disciplines and across different nations. This book has been systematically brought up to date and new sections added to reflect the increasing volume of scientific literature and terminology and expressions being used. The Third Edition reflects the experience of the contributors with the previous editions and the comments and feedback have been integrated into this essential resource. This edition has been compiled in machine-readable form and will be available online.

The present text sets itself in relief to other titles on the subject in that it addresses the means and methodologies versus a narrow specific-task oriented approach. Concepts and their developments which evolved to meet the changing needs of applications are addressed. This approach provides the reader with a general tool-box to apply to their specific needs. Two important tools are presented: dimensional analysis and the similarity analysis methods. The fundamental point of view, enabling one to sort all models, is that of information flux between a model and an original expressed by the similarity and abstraction Each chapter includes original examples and applications. In this respect, the models can be divided into several groups. The following models are dealt with separately by chapter; mathematical and physical models, physical analogues, deterministic, stochastic, and cybernetic computer models. The mathematical models are divided into asymptotic and phenomenological models. The phenomenological models, which can also be called experimental, are usually the result of an experiment on an complex object or process. The variable dimensionless quantities contain information about the real state of boundary conditions, parameter (non-linearity) changes, and other factors. With satisfactory measurement accuracy and experimental strategy, such models are highly credible and can be used, for example in control systems.

The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.

Reality as we know it is bound by a set of constants—numbers and values that dictate the strengths of forces like gravity, the speed of light, and the masses of elementary particles. In The Constants of Nature, Cambridge Professor and bestselling author John D.Barrow takes us on an exploration of these governing principles. Drawing on physicists such as Einstein and Planck, Barrow illustrates with stunning clarity our dependence on the steadfastness of these principles. But he also suggests that the basic forces may have been radically different during the universe’s infancy, and suggests that they may continue a deeply hidden evolution. Perhaps most tantalizingly, Barrow theorizes about the realities that might one day be found in a universe with different parameters than our own.

Overview White's Fluid Mechanics offers students a clear and comprehensive presentation of the material that demonstrates the progression from physical concepts to engineering applications and helps students quickly see the practical importance of fluid mechanics fundamentals. The wide variety of topics gives instructors many options for their course and is a useful resource to students long after graduation. The book’s unique problem-solving approach is presented at the start of the book and carefully integrated in all examples. Students can progress from general ones to those involving design, multiple steps and computer usage. McGraw-Hill Education's Connect, is also available as an optional, add on item. Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, how they need it, so that class time is more effective. Connect allows the professor to assign homework, quizzes, and tests easily and automatically grades and records the scores of the student's work. Problems are randomized to prevent sharing of answers an may also have a "multi-step solution" which helps move the students' learning along if they experience difficulty. The eighth edition of Fluid Mechanics offers students a clear and comprehensive presentation of the material that demonstrates the progression from physical concepts to engineering applications. The book helps students to see the practical importance of fluid mechanics fundamentals. The wide variety of topics gives instructors many options for their course and is a useful resource to students long after graduation. The problem-solving approach is presented at the start of the book and carefully integrated in all examples. Students can progress from general examples to those involving design, multiple steps, and computer usage.