Dimensional Analysis and Important Parameters
In chapter IV, we discussed the fundamental equations of magnetogasdynamics and other cases of plasma dynamics These fundamental equations are nonlinear. There is no general method of finding the solutions of these nonlinear equations. In order to bring out the essential features of the flow problem, it is desirable to find important parameters which characterize the flow problem. These parameters are very useful in the analysis of experimental results. There are two methods (4) to find these parameters: one is known as inspection analysis and the other, dimensional analysis. In the inspection analysis, we reduce the fundamental equations to non-dimensional form and obtain the non-dimensional parameters from the resultant equations as we did in chapter IV, § 4. In dimensional analysis we form non-dimensional parameters from the physical quantities occurring in the flow problem. Both methods give the same results. In this chapter we shall use dimensional analysis to find the important non-dimensional parameters of plasma dynamics.
KeywordsMach Number Free Path Froude Number Flow Problem Dimensional Analysis
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- 1.Burgers, J. M.: Applications of Transfer Equations to the Calculation of Diffusion. Heat Conduction, Viscosity and Electric Conductivity. I and II. Tech. note 124 a and b, Inst. for Fluid Dynamics and Appl. Math. Univ. of Md., May 1958.Google Scholar
- 3.Grad, H., and M. H. Rose: Dimensional Considerations. Notes of Magnetohydrodynamics, No. II. Inst. of Math. Sci., New York Univ., 1956.Google Scholar
- 4.Kantrowitz, A. R., and H. E. Petscher: An introductory discussion of magnetohydrodynamics; A Symposium of magnetohydrodynamics. Ed. by R. K. M. Landshoff, Stanford Univ. Press, pp. 3–15, 1957.Google Scholar
- 5.Pax, S. I.: Viscous Flow Theory I. Laminar Flow. D. Van Nostrand Co., Inc., Princeton, N. J., 1956.Google Scholar
- 6.pai, S. I.: Plasmadynamics from Gasdynamic Point of View. Proc. of First Intern. Symp. of rarefied gasdynamics. Pergamon Press, 1959.Google Scholar
- 7.Pai, S. I., and A. Spete: The Wave Motions of Small Amplitude in Radiation-electromagneto-gasdynamics. Proc. of 6th Midwestern Conf. of Fluid Rech. Univ. of Texas, pp. 446–466, Sept. 1959.Google Scholar
- 9.Tonks, L., and I. Langmuir: Oscillations in Ionized Gases. Phys. Rev., vol. 33, pp. 195210, Feb. 1929.Google Scholar
- 10.Tsien, H. S.: Superaerodynamics. Jour. Aero. Sci., vol. 13, No. 12, pp. 633–664, Dec. 1946.Google Scholar