Dimensional Analysis (Google eBook)
For experiments, dimensional analysis enables the design, checks the validity, orders the procedure and synthesises the data. Additionally it can provide relationships between variables where standard analysis is not available. This widely valuable analysis for engineers and scientists is here presented to the student, the teacher and the researcher. It is the first complete modern text that covers developments over the last three decades while closing all outstanding logical gaps. Dimensional Analysis also lists the logical stages of the analysis, so showing clearly the care to be taken in its use while revealing the very few limitations of application. As the conclusion of that logic, it gives the author's original proof of the fundamental and only theorem. Unlike past texts, Dimensional Analysis includes examples for which the answer does not already exist from standard analysis. It also corrects the many errors present in the existing literature by including accurate solutions. Dimensional Analysis is written for all branches of engineering and science as a teaching book covering both undergraduate and postgraduate courses, as a guide for the lecturer and as a reference volume for the researcher.
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2 Concepts Dimensions and Units
3 The PiTheorem
4 The Development of Dimensional Analysis
5 The Choice of Dimensions
6 Supplementation of Derivations
7 Systematic Experiment
8 Analytical Results
acceleration aerodynamic angle application Boltzmann constant boundary layer Bridgman cancellation Chapter Compact Solution complete equation constant convection correlation curve D f Ä D’Arcy Thompson defined definition deflexion density derived diameter diffusion dimensional analysis discussion drag elastic electrical electrode electrostatic Equa example excluded experiment experimental f Ä fluid force full-scale function given governing equations gravity group in Equation illustrated in Figure incompressible flow independent variables J C Gibbings J.C. Gibbings laminar length linear liquid logic mass model test motion non-dimensional groups notation numerical value obtained oscillation P.W. Bridgman partial modelling particle phenomenon physical pi-theorem pi-theorem solution pipe plot Prandtl pressure primary concept quantity ratio Rayleigh relation result Reynolds number scale shows stress Table temperature thermal conductivity Thermodynamics tion turbulent flow Tw T0 unit measure units-conversion factor valid velocity vertical viscosity whilst zero