We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form-valued 2-forms, and their divergence as a covariant exterior derivative. We review the necessary tools of differential geometry and obtain the ...
there is nofrictional forcein the direction of flow. Friction will operate in all directions at right angles to the flow but the net sum of all these (vector) forces must be zero. In contrast, thenet fluxof heat or mass, which arescalar quantities, must be finite in the plane of the...
Total force exerted on a fixed part of a material instantaneously in a control volumeVc =time rate of change of total linear momentum inside the control volume + net outflux of linear momentum through the control surfaceSc. Equation (7.6.2) is very useful for obtaining approximate results in...
作者: G Ruocco 摘要: Transfer of momentum is the second physical mechanism we encounter, through which the mechanics of fluidscan be examined, including their interaction with the solid structures that may contain, and... DOI: 10.1007/978-3-319-66822-2_3 年份: 2018 收藏...
(MN), Einstein-Laub (EL), Chu, and Amperian (AMP). Each of these have been shown to obey the conservations of energy and momentum21,41. Using these formulations, the dynamic interaction between matter and the electromagnetic field can be described using the momentum continuity equation, ...
• For angular momentum equation, B =H O the angular momentum vector about point O which moments are desired. • Where β is • The Reynolds transport equation can be written as follows: • For one‐dimensional inlets and outlets, the flux terms become: ...
Equation (1) means that the momentum imparted locally onto the moving object upon scattering is related to the expectation value of Qα for the specific input state |Ψin⟩ in the far field. A direct consequence of equation (1) is that if the input state |Ψin⟩ is chosen to be ...
This last step is the applicationof the divergence theorem.7Finally we have the form of themomentum equation that we want.=+8Sum of forces actingon control volumeChange inmomentum of masscontained in controlvolume over timeChange inmomentum fluxacross surface ofcontrol volume4One of the most ...
where T is the stress tensor, Γ is the momentum density, Q is the energy flux density, and E is the total energy density. When external fields are present, the kinetic potential Λ contains explicitly some of coordinates χj. Then the balance equations are satisfied rather than conservation...
(4.30) The magnetic pressure term 1 2 g(b, b) emerges naturally in the derivation, and its origin may traced back to the term b div u in the transport equation (4.24) for b. In a com- pressible fluid, whereas the fundamental magnetic flux β is simply Lie transported by the flow ...