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# Member Dr. Donald G. Carpenter
local time: 2023-06-10 11:41 (-06:00 DST)
Dr. Donald G. Carpenter (Abstracts)
Titles
• [Updated 6 years ago]
• [Updated 6 years ago]
Abstracts Details
• [Updated 6 years ago]

The Euler fluid equations, which can be expressed as the vector equation (-?pr)-g=(v??)v+?v ?t, are shown to be missing three important terms and to contain a simplistic version of a fourth. Whenever the fluid is significantly affected by an external thrust and by either a gravitational field or a set of gravitational fields, the Euler fluid equations must be replaced by ( ) ( ) ( 2 ) ( ) ( ) e e e e e -?p r +??2 f-3 p3rr??R- M G r R-Fr= v??v+(?v ?t, where two of the three missing terms are combined into the first term times the unit vector e R (which points radially away from the effective center of gravity), ? f ? is numerically the degrees of freedom of the fluid, and ? e r ? is the distance from the effective center of gravity to the differential volume. The third missing term, F, is the non-gravitational force. The simplistic gravitational acceleration term, g, is replaced by a more general expression that takes into account the ubiquitous nature of gravity. The Euler fluid equations are used in the derivation of the Navier-Stokes equations, so the foregoing developments cause these equations to change.

• [Updated 6 years ago]

The derivation of the barometric equation concerns central forces in three dimensions. It has recently been shown that the sum of the incremental volume's side force components in the direction of the center of gravity (the ??(-2p z)(Dx)(Dy)(Dz)?? force) must be included in the Cartesian  rivation.That results in the side force component term (-2p z) being added to the differential equation, or dp dz=-??(NmMGz2 )+(2p z)??. Meteorological data does not, though, conform unambiguously to the corrected barometric equation.  This implies that an approximately compensating term might exist. Such a term results from consideration of the central force due to atmospheric particle random motion perpendicular to the radial from the center of gravity in a central force field (the ??+(2(f )p 3z)(Dx)(Dy)(Dz)?? force, where ?f? represents the degrees of freedom). The more-complete barometric equation is: dp dz= -(NmMG z2 )+??2(f-3)p3z??. .