![]() For keeping two terms of Taylor expansion of object in low speed motion, we have : The mass-energy equivalence, proposed by Albert Einstein in 1905 and has been studied widely and deeply in the world. Therefore, we do not use the ideal gas law while prefer to use the combination of Boyle’s la and Chares’ law. If one tries to use a micro-level law with random motion assumption to a problem of macro-level, then, even if one got a result, the result must belong to uncertain type. The element of the ideal gas law is moles or atom, its size belongs to micro-level. Equation (2.3-2) can be derived empirically or by kinetic theory under some assumptions including moles random motion, etc. R g is gas constant, equal to the product of Bolzmann constant and Avogadro constant. ![]() The ideal gas law was first stated by Clapeyrong, E in 1834, as a combination of Bole’s law, Chares/ law, and Avogadro’s law. The dimensions on both sides of (2.3-1) must be the same, then, the dimension of constant R is (J/˚C), where J is Joule. Where p is the pressure, acting normal to the boundary of “container” (“bloom”), inside the boundary V is the volume of the container, inside the boundary. In the following, only major scientific laws are mentioned and they can be used in combination.ġ) The combination of Boyles law and Chares law (2.3-1), which has advantage over the ideal gas law (2.3-2). have scientific laws related to their properties. For example, for cloud droplet, for PM 2.5, etc. Different substance has different properties relating to different scientific laws. The scientific laws related to substances involving in mushroom cloud. The membrane can be viewed as the boundary between the hot air and cold air. can be used to form an equation of air motion. The design of air wrapped by a zero-weighted membrane is to give the air with shape and volume so that the scientific laws, e.g., Boyle’s law and Chares law etc. The reason for why the weight of membrane is designed to be approached to zero, as stated by the author in that in fact the air is not wrapped by anything. In this paper, only the motion of the bloom is studied. The smaller model (hot air) moves up-side-down cyclically in the bloom axis-symmetrically. The bigger model likes a hot air bloom, (in the following it is called “bloom”) surrounding by cold air. Like case-in-case in detective story, model-in-model had been used in author’s paper, where a bigger model involves smaller model. Different signed masses are rejected each other. The positive mass attracts each other The negative mass attracts each other. The remainder is considered as positive mass. The mass of buoyancy (e.g., mass of hot air, mass of medium) is considered as negative mass, with a minus sign. No overlap or vacuum exists.ģ) The gravity-buoyancy field holds in the whole atmosphere, where the forces anti-gravity or the order of equilibrium state are called “buoyancy”. For z-axis-symmetry, a pointġ) The motion of mushroom cloud is z-axis-symmetric.Ģ) The air is continuous, isotropic and incompressible. In the following, Bold face denotes vector, matrix, tensor Non-bold face represents scalars. The relation betweenĭenote the unit vectors of Cartesian and cylindrical coordinates respectively. Section §5, is Checking the obtained PDE and its solution.Īt the explosion center. Section §4, is Solution of the PDE of mushroom cloud (3-12) by method of separating variables. In Section §3, Set up PDE of mushroom cloud by modifying N-S equations. The purpose of this paper is to set up an equation of motion of mushroom cloud, to find the solution, and to use applications of PMER, etc. In Section §2, the methods of analysis include §2.1 Coordinates and basic hypotheses §2.2 Model of mushroom cloud §2.3 Scientific laws §2.4 The gravity-buoyancy field §2.5 The Principle of Minimum Energy Release (PMER) §2.6 The Principle of Reciprocal Displacement (PRD). This obtained equation and its solution have been compared with wind speed equation of a point (mass) in air and its solution. The obtained solution is solved by the method of separating variables. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. The obtained equation is a vector partial deferential equation (PDE). ![]() This paper aims to set up an equation on motion of mushroom cloud using model as, scientific laws, and modifying Navier-Stokes equations (N-S equations). However, no literatures on mushroom cloud description by analytic equation can be found. There are many studies on A-bomb and H-bomb. The Tsar Bomb is the most powerful weapon constructed. Mushroom cloud is a special cloud, created by atomic bomb or nuclear bomb.
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