ABSTRACT
This chapter may be used as a text for tutorial or for refresher purposes. Algebra is highest level of mathematics needed. There are 14 tutorial-type examples of fully solved problems.
6.2 DIMENSIONLESS PARAMETERS Modern fluid mechanics is based on a combination of theoretical analysis and experimental data. Very often, the engineer is faced with the necessity of obtaining dependable, practical results in situations where for various reasons the flow phenomena cannot be described mathematically and ex perimental data must be considered. The generation and use of dimen sionless parameters provide a powerful and useful tool in (1) reducing the number of variables required for an experimental program, (2) establishing
All physical equations should be dimensionally correct, so that a di mensionless parameter may be generated by simply dividing one side of the equation by the other, as will be illustrated. The principles of similarity are used to develop dimensionless parameters for model-prototype re lations to insure geometric, kinematic, and dynamic similarity by con sideration of dimensions, velocities, and forces involved between the two. D im e n s io n a l a n a ly s is is the mathematics of dimensions and quantities. Two formal methods are used, the Lord Rayleigh’s and the Buckingham n theorem. Lord Rayleigh (1842-1919), who was born John William Strut in Essex, England, popularized the principle of dynamic similarity by introducing in 1899 a generalization of the principle. Edgar Buckingham (1867-1940) was a physicist at the National Bureau of Standards. In a series of papers published in 1914 and 1915 he brought to American notice the uses of dimensional analysis and presented his II theorem.
