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When [H] is known, the free concentration [A] is calculated from the mass-balance equation in A. The diagram alongside, shows an example of the hydrolysis of the aluminium Lewis acid Al 3+ (aq) [ 22 ] shows the species concentrations for a 5 × 10 −6 M solution of an aluminium salt as a function of pH.
Often, constructing local balance equations is equivalent to removing the outer summations in the global balance equations for certain terms. [ 1 ] During the 1980s it was thought local balance was a requirement for a product-form equilibrium distribution , [ 10 ] [ 11 ] but Gelenbe 's G-network model showed this not to be the case.
Strictly speaking the above equation holds also for systems with chemical reactions if the terms in the balance equation are taken to refer to total mass, i.e. the sum of all the chemical species of the system. In the absence of a chemical reaction the amount of any chemical species flowing in and out will be the same; this gives rise to an ...
[2] [3] In hydrology, a water balance equation can be used to describe the flow of water in and out of a system. A system can be one of several hydrological or water domains, such as a column of soil, a drainage basin, an irrigation area or a city. The water balance is also referred to as a water budget. Developing water budgets is a ...
Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where = = = = Then the only non-trivial equation is the -equation, which now reads + = Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
The momentum equation = | |, gives us the inertial speed = | |. The inertial speed's equation only helps determine either the speed or the radius of curvature once the other is given. The trajectory resulting from this motion is also known as inertial circle. The balance-flow model gives no clue on the initial speed of an inertial circle, which ...
Fluid balance is an aspect of the homeostasis of organisms in which the amount of water in the organism needs to be controlled, via osmoregulation and behavior, such that the concentrations of electrolytes (salts in solution) in the various body fluids are kept within healthy ranges.