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THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES
Citation:
Frick, W E. THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES. Presented at American Geophysical Union Meeting, Fort Collins, CO, April 2-5, 2001.
Impact/Purpose:
Produce a computer model utilizing water transport estimates or real-time current-meter data to track the motion of contaminants from point and other sources, and to predict the concentration of pathogens or other pollutants at beach and other sensitive sites.
Description:
The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed to model turbulent flow. In a re-examination of the derivation, Frick (2001) shows that the Theorem of the Mean for Integrals, not the assumption of absolute incompressibility, is the underlying justification for the simplification that makes it possible to derive the Bernoulli equation from the Euler equation. In other words, the assumption of incompressibility is unnecessary and the equation actually represents a compressible relationship. While this finding supports the expansive turbulence model proposed by Frick, Emerman, and Sigleo (2001), a closer look at their derivation of flow between two disk suggests that the underlying approximations are not entirely consistent with the theory. In other words, the physics of the expansive turbulence model proposes that the divergence of the velocity is positive, which is not what their solution shows.