From: owner-ammf-digest@smoe.org (alt.music.moxy-fruvous digest) To: ammf-digest@smoe.org Subject: alt.music.moxy-fruvous digest V14 #4938 Reply-To: ammf@fruvous.com Sender: owner-ammf-digest@smoe.org Errors-To: owner-ammf-digest@smoe.org Precedence: bulk alt.music.moxy-fruvous digest Thursday, September 10 2020 Volume 14 : Number 4938 Today's Subjects: ----------------- The Butterfly Effect? ["Archangel Michael Message" Subject: The Butterfly Effect? The Butterfly Effect? http://sqrible.buzz/o-SAAWP-iLaqm64MaudiO5cf1pq2tfr64M1c3kK48aBGoAhm http://sqrible.buzz/41kfY0iLtQIG_0-Pmavphv7C760uXQ9HHQ2xCQwvYgefBNCb Relativistic fluid dynamics studies the macroscopic and microscopic fluid motion at large velocities comparable to the velocity of light. This branch of fluid dynamics accounts for the relativistic effects both from the special theory of relativity and the general theory of relativity. The governing equations are derived in Riemannian geometry for Minkowski spacetime. Other approximations There are a large number of other possible approximations to fluid dynamic problems. Some of the more commonly used are listed below. The Boussinesq approximation neglects variations in density except to calculate buoyancy forces. It is often used in free convection problems where density changes are small. Lubrication theory and HelebShaw flow exploits the large aspect ratio of the domain to show that certain terms in the equations are small and so can be neglected. Slender-body theory is a methodology used in Stokes flow problems to estimate the force on, or flow field around, a long slender object in a viscous fluid. The shallow-water equations can be used to describe a layer of relatively inviscid fluid with a free surface, in which surface gradients are small. Darcy's law is used for flow in porous media, and works with variables averaged over several pore-widths. In rotating systems, the quasi-geostrophic equations assume an almost perfect balance between pressure gradients and the Coriolis force. It is useful in the study of atmospheric dynamics. Terminology The concept of pressure is central to the study of both fluid statics and fluid dynamics. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods. Some of the terminology that is necessary in the study of fluid dynamics is not found in other similar areas of study. In particular, some of the terminology used in fluid dynamics is not used in fluid statics. Terminology in incompressible fluid dynamics The concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sensebthey cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure. Static pressure is identical to pressure and can be identified for every point in a fluid flow field. A point in a fluid flow where the flow has come to rest (i.e. speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it is given a special nameba stagnation point. The static pressure at the stagnation point is of special significance and is given its own namebstagnation pressure. In incompressible flows, the stagnation pressure at a stagnation point is equal to the total pressure throughout the flow field. ------------------------------ End of alt.music.moxy-fruvous digest V14 #4938 **********************************************