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LOW-VELOCITY COMPRESSIBLE FLOW THEORY
Citation:
Frick, W E. LOW-VELOCITY COMPRESSIBLE FLOW THEORY. Presented at Seminar at University of Hong Kong, Kowloon, Hong Kong, December 12, 2002.
Impact/Purpose:
A main objective of this task is to combine empirical and physical mechanisms in a model, known as Visual Beach, that
â— is user-friendly
â— includes point and non-point sources of contamination
â— includes the latest bacterial decay mechanisms
â— incorporates real-time and web-based ambient and atmospheric and aquatic conditions
â— and has a predictive capability of up to three days to help avert potential beach closures.
The suite of predictive capabilities for this software application can enhance the utility of new methodology for analysis of indicator pathogens by identifying times that represent the highest probability of bacterial contamination. Successful use of this model will provide a means to direct timely collection of monitoring samples, strengthening the value of the short turnaround time for sampling. Additionally, in some cases of known point sources of bacteria, such as waste water treatment plant discharges, the model can be applied to help guide operational controls to help prevent resulting beach closures.
Description:
The widespread application of incompressible flow theory dominates low-velocity fluid dynamics, virtually preventing research into compressible low-velocity flow dynamics. Yet, compressible solutions to simple and well-defined flow problems and a series of contradictions in incompressible flow theoretical arguments suggest that incompressible flow theory is not inevitable, robust, or powerful. As examples, it can be shown that the "incompressible" Bernoulli equation can be derived from the more general Euler equation without assuming constant density. Analytical compressible-flow solutions of simple laminar radial flow shows that compressible isothermal and compressible adiabatic solutions, as well as the corresponding incompressible solution, converge on the same relationship in the limit as velocity approaches zero, proving that the incompressible flow solution is but a special case of the more general compressible flow solution. More radically, it can be shown that adiabatic flow, the flow most often approximated in nature, cannot be accelerated without compressibility, that the pressure gradient must be supported by a density gradient, and, consequently, even low-velocity laminar flow is significantly divergent and compressible. The comparison of the linearized equation of state for an ideal gas to Einstein's famous energy-mass relationship underscores the absurdity of the notion that small density fluctuations are unimportant in low-velocity flow. Contradictions aside, low-velocity compressible flow theory explains otherwise theoretically unexplainable phenomena. For example, many insect and bird species appear to use compressible flow effects to fly efficiently. The development or suppression of turbulence in flow into and out of constrictions can be understood by applying compressible flow theory. Some low velocity geophysical flows and wave phenomena depend on compressible effects. And, finally, the basic properties of turbulent boundary layers are better explained and understood using compressible flow theory, promising to help fluid dynamicists better understand and exploit fluid-solids interactions.