On the axiomatic foundations of dimensional analysis

This paper reformulates the basic axioms of dimensional analysis so as to clear up some deeply entrenched misconceptions relating to the nature of physical dimensions and generalized units. Certain novel relations are thereby discovered which although unorthodox are nevertheless useful and correct. It is shown how various systems or natural units can be constructed so as to embody the same logical structure that characterizes some given system of fixed units. The important fact is brought out that every physical equation which is valid in some given system of units remains valid if all quantities be converted into any other system which embodies the same logical structure. The paper also show that the dimensionless pi's of Buckingham's Pi Theorem simply represent various physical parameters as expressed in some appropriate system of consistent natural units. The fundamental dimensional principles considered in this paper apply in some form to every quantitative analytical and experimental problem in the entire realm of physical science and engineering. (Author)http://archive.org/details/onaxiomaticfound00gawaApproved for public release; distribution is unlimited

Analysis of a two-fluid EHD power generator including effects of compressibility

A detailed analysis and method of calculation is presented for determining the complete thermodynamic cycle of either a one-fluid or a two-fluid electrohydrodynamic (EHD) power generator. The analysis takes fully into account the compressibility of the media. Parameters are included which express the thermodynamic losses in the various components of the overall system. The severe restriction on output created by the electrical breakdown limit of the medium is clearly shown. The method for computing the net-electrical work output per unit mass of primary fluid and the net overall thermal efficiency of the system is carefully developed. The calculation procedure is illustrated by a completely worked out numerical example. The techniques presented here may be used to determine the performance possibilities and limitations of various one-fluid and two-fluid EHD power generators. (Author)Prepared for: U.S. Department of Energyhttp://archive.org/details/analysisoftwoflu00gawaInteragency Agreement No ER-78-A-03-2122N

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Author(s) key words: Dimensional analysis, dimensions, fundamental dimensions, dimensionless numbers, dimensionless coefficients, dimensionless parameters, dimensionless pi's, Pi Theorem, English units, metric units, MKS units, CGS units, consistent units, inertial units, gravitational units, fixed units, standard units, natural units, intrinsic units, generalized units, unit and measure, dynamic similarity, thermodynamic similarity, theory of models, momentum theory, propeller parameters, physical equations, mathematical invariancehttp://archive.org/details/introductiontodi00gawaNAN

Optimally loaded electrohydrodynamic power generator

By requiring that the local electrical field strength in an electrohydrodynamic (EHD) power generator be everywhere uniformly close to the critical limit, an optimum channel shape can be established. This shape is based on the one-dimensional flow of a compressible fluid into which are injected unipolar charged particles of negligible mobility. The maximum electrical work output per unit mass of fluid that can be attained in this way is shown to be greater by a factor of two than that of the best comparable channel of uniform areaPrepared for: Department of Energy, Washington, DC.http://archive.org/details/optimallyloadede00biblInter Agency Agreement No. ER-78-A-03-212

Performance analysis of a type of electrohydrodynamic power generator

This report develops a detailed analysis of a type of electrohydrodynamic power generator which employs an ejector and a so-called 'fluid flywheel' as essential components. The medium is steam containing electrically charged water droplets. The analysis takes into account the experimentally established facts that the maximum strength of the electrical field that can be sustained at incipient breakdown at the most critical location is proportional to the fluid density at that location. It is shown that as a consequence of this fact, the electrical output can be maxmized by designing the primary jet for an exit Mach number of 0.71. Estimates are made of the pump work required, of mixing losses in the ejector and of friction and secondary flow losses. The mathematical analysis is reduced to a fully non-dimensional form and the key dimensionless parameters that govern performance are clearly identified. A preliminary estimate is made of the numerical values of these parameters and the overall performance of the system is esitmated on this basis. (Author)Prepared for: U.S. Department of Energyhttp://archive.org/details/performanceanaly00gawaInter Agency Agreement No. ER-78-A-03-212

Performance of an EHD power generator with a two-fluid ejector

A detailed analysis and method of calculation is presented for determining the complete thermodynamic cycle of a two-fluid electrohydrodynamic (EHD) power generator. The analysis takes fully into account the compressibility of the media. Parameters are included which express the thermodynamic losses in the various components of the overall system. The severe restriction on output created by the electrical breakdown limit of the medium is clearly shown. The method for computing the net-electrical work output per unit mass of primary fluid and the net overall thermal efficiency of the system is carefully developed. A sample output together with the FORTRAN program are included. (Author)The work reported herein was supported by the U.S. Department of Energy, Washington, D.C.http://archive.org/details/performanceofehd00gawaInteragency Agreement No. ER-78-A-0 3-212

An alternative formulation of the lifting line wing equation and its solution

In the report, the standard wing equation, as normally derived from lifting line theory, is further refined and a solution procedure more basic than the usual collocation technique is developed. The calculation method adopted avoids the necessity of performing an explicit matrix inversion; all equations can be solved sequentially, one at a time. On the other hand this technique involves the evaluation of numerous integrals over the span. The calculations are cumulative, and can be carried as far as necessary to achieve any required degree of accuracy. The analysis is interesting not only for purposes of practical calculation but also for the light it sheds on the essential mathematical structure of the basic aerodynamic phenomena involved. This same general method of calculation can also be readily adapted to the solution of other common types of engineering problems. (Author)http://archive.org/details/alternativeformu00gawaNAN

A numerical investigation of the non-linear mechanics of wave disturbances in plane Poiseuille flows

The response of a plane Poiseuille flow to disturbances of various initial wavenumbers and amplitudes is investigated by numerically integrating the equation of motion. It is shown that for very low amplitude disturbances the numerical integration scheme yields results that are consistent with those predictable from linear theory. It is also shown that because of non-linear interactions a growing unstable disturbance excites higher wavenumber modes which have the sam frequency, or phase velocity, as the primary mode. For very low amplitude disturbances these spontaneously generated higher wavenumber modes have a strong resemblance to certain modes computed from the linear Orr-Sommerfeld equation. In general it is found that the disturbance is dominated for a long time by the primary mode and that there is little alteration of the original parabolic mean velocity profile. There is evidence of the existence of an energy equilibrium state which is common to all finite-amplitude disturbances despite their initial wavenumbers. This equilibrium energy level is roughly 3-5% of the energy in the mean flow which is an order of magnitude higher than the equilibrium value predicted by existing non-linear theories. (Author)http://archive.org/details/numericalinvesti00gaw

Dimensional analysis and the concept of natural units in engineering

Author(s) key words: Dimensional analysis, dimensions, fundamental dimensions, dimensionless parameters, dimensionless Pi's, Pi theorem, English units, metric units, consistent units, inertial units, gravitational units, fixed units, natural units, generalized units, unit and measure, dynamic similarity, thermodynamic similarity, theory of models, Reynolds number, momentum theory of propellers, propeller parameters, turbine parameters, rotorcraft parameters, pump parameters, compressor parameters, performance limits of: propellers, axial turbines, lifting rotors, mathematical invariance of physical equationshttp://archive.org/details/dimensionalanaly2031gawaNAN

Dimensional analysis and the theory of natural units

Author(s) key words: Dimensional analysis, dimensional parameters, dimensions, fundamental dimensions, dimensionless numbers, dimensionless coefficients, dimensionless parameters, dimensionless pi's, Pi Theorem, English units, metric units MKS units, consistent units, inertial units, gravitational units, fixed units, standard units, natural units, intrinsic units, generalized units, unit and measure, dynamic similarity, thermodynamic similarity, theory of models Reynolds number Mach number Froude number drag coefficient, skin friction coefficient, momentum theory, propeller parameters, turbine parameters, rotorcraft parameters, pump parameters, compressor parameters, incompressible flow parameters, viscous flow parameters, physical equations, mathematical invariancehttp://archive.org/details/dimensionalanaly00gawaN