Also Energy conservation conservative forces

Piping systems often involve interconnected segments in various combinations of series and/or parallel arrangements. The principles required to analyze such systems are the same as those have used for other systems, e.g., the conservation of mass (continuity) and energy (Bernoulli) equations. For each pipe junction or node in the network, continuity tells us that the sum of all the flow rates into the node must equal the sum of all the flow rates out of the node. Also, the total driving force (pressure drop plus gravity head loss, plus pump head) between any two nodes is related to the flow rate and friction loss by the Bernoulli equation applied between the two nodes. 

Credit for the first recognizable statement of the principle of conservation of energy (heat plus work) apparently belongs to J. Robert Mayer (Sidebar 3.2), who published such a statement in 1842. Mayer also obtained a (slightly) improved estimate, approximately 3.56 J cal-1, for the mechanical equivalent of heat. Mayer had actually submitted his first paper on the energy-conservation principle two years earlier, but his treatment of the concepts of force, momentum, work, and energy was so confused that the paper was rejected. By 1842, Mayer had sufficiently straightened out his ideas to win publication,... 

The system evolves with the innermost orbit receding from the central body (because of the non-conservative forces acting on mi) up to the moment where the system is captured into a resonance, a2 is almost constant. When the 2/f-resonance is reached, the system is trapped by the resonance. As known since Laplace, after the capture, mi continuously transfers one fraction of the energy that it is getting from the non-conservative source to m2, so that 02 also increases. One may note from Figure 9 that, after the capture into the resonance, ai increases at a smaller pace than before the capture. The increase of the semi-major axes is such that the ratio ai/a2 remains constant. 

The second term in Eq. [3] is a charge switching force, which results from the motion of the charge among the reactant atoms. Its inclusion is vital not only in achieving energy conservation in the trajectories, but also in interpreting the results of the dynamics. 

It is the first one that will be emphasized, and can be broken into conservation of mass and energy, which are coupled with Einstein s mass-energy equivalence (E=mc ). As such, the accumulation terms of the conservation of mass are not affected. Also, we could neglect forced convection effects in the system. The resulting mass diffusion equation would be similar to that in Eq. (1.5.2), except that a so-called elastic strain energy could be added to the potential function to take into account crystal lattice differences between solid phases (De Fontaine, 1967). 

In this section we first review general modeling principles, emphasizing the importance of the mass and energy conservation laws. Force-momentum balances are employed less often. For processes with momentum effects that cannot be neglected (e.g., some fluid and solid transport systems), such balances should be considered. The process model often also includes algebraic relations that arise from thermodynamics, transport phenomena, physical properties, and chemical kinetics. Vapor-liquid equilibria, heat transfer correlations, and reaction rate expressions are typical examples of such algebraic equations. 

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