Source/sink balance

The third term on the left side of the equation has significance in reactive systems only. It is used with a positive sign when material is produced as a net result of all chemical reactions a negative sign must precede this term if material is consumed by chemical reactions. The former situation corresponds to a source and the latter to a sink for the material under consideration. Since the total mass of reactants always equals the total mass of products in a chemical reaction, it is clear that the reaction (source/sink) term (R should appear explicitly in the equation for component material balances only. The overall material balance, which is equivalent to the algebraic sum of all of the component balance equations, will not contain any (R term. 

Budget. A balance sheet of all sources and sinks of a reservoir. If sources and sinks balance and do not change with time, the reservoir is in... 

Before stating the main results, it will be sensible to clarify a physical sense of the function u(x), which solves problem (1) subject to the conditions [u] = 0 and [kii ] = — Qq (/ — x) kg = g at the point x =. Here q stands for the capacity of a point heat source (sink) at the point X =. Being dependent on x, the quantity q varies very widely. Specifically, q —+ 00 as X — 5 0. Thus, the physical reason for the convergence of scheme (2) is that the heat balance (the conservation law of heat) is... 

A mass balance on one compound in our box is based on the principle that whatever comes in must do one of three things (1) be accumulated in the box, (2) flux out of another side, or (3) react in the source/sink terms. If it seems simple, it is. 

A complete mix reactor is one with a high level of turbulence, such that the fluid is immediately and completely mixed into the reactor. The outflow concentration and the reactor concentration are equal, and the diffusion term is zero due to the gradient being zero. Figure 6.1 shows an illustration of the concept. If we make the entire reactor into our control volume, then a mass balance on the reactor gives Rate of = Flux rate - Flux rate - - Source — sink... 

Mason R. P. and Fitzgerald W. F. (1996) Sources, sinks and biogeochemical cycling of mercury in the ocean. In Global and Regional Mercury Cycles Sources, Fluxes and Mass Balances. NATO ASl Series 2. Environment (eds. W. Baeyens, R. Ebinghaus, and O. Vasiliev). Kluwer, Boston, vol. 21, pp. 249-272. 

Budget. A balance sheet of all somces and sinks of a reservoir. If sources and sinks balance and do not change with time, the reservoir is in steady-state, i.e. M does not change with time. It is common in many budget estimates that some fluxes are better known than others. If steady-state prevaUs, a flux that is unknown a priori can be estimated by its difference from the other fluxes. If this is done, it should be made very clear in the presentation of the budget which of the fluxes is estimated as a difference. 

Since there appears to be no He sinks in the soil or in the lower levels of the atmosphere, it is more than probable that this noble gas escapes from the upper atmosphere into outer space. It follows from the constant atmospheric level that this sink balances the effect of the sources. When the total atmospheric helium mass is taken into account, as well as the above formation mechanism, the residence time of He is estimated to be approximately 107 years. 

In equation 4, the subscripts f and t refer to flowing and trapped foam, respectively, and ni is the foam texture or bubble number density. Thus, nf and t are, respectively, the number of foam bubbles per unit volume of flowing and stationary gas. The total gas saturation is given by Sg = 1 — Sw = S + St, and Qb is a source—sink term for foam bubbles in units of number per unit volume per unit time. The first term of the time derivative is the rate at which flowing foam texture becomes finer or coarser per unit rock volume, and the second is the net rate at which foam bubbles trap. The spatial term tracks the convection of foam bubbles. The usefulness of a foam bubble population-balance, in large part, revolves around the convection of gas and aqueous phases. 

In Chap. 51 we derived Bernoulli s equation from the energy balance equation. Since the energy balance has no onc-dimensional restriction on it, the same approach must apply to two- and three-dimensional flows. However, in our derivation bf Bernoulli s equation, we restricted our attention to systems with only one flow in and out. How can we apply this idea to a two-dimensional flow field in which there is a continuously varying velocity over some region of space In Fig. 10.15 such a region is shown with no sources, sinks, or solid bodies, but with streamlines. 

Time-Averaged Properties. The unsteady-state macroscopic mass balance for mobile component A is applied to the quiescent liquid, where the rate of interphase mass transfer via equation (11-205) is interpreted as an input term due to diffusion across the gas-liquid interface. There are no output terms, sources, sinks, or contributions from convective mass transfer in the macroscopic mass balance. Hence, the accumulation rate process is balanced by the rate of interphase mass transfer across time-varying surface S t), where both terms have dimensions of moles per time ... 

Reaction rate for y-th reaction Inner tube radius Source/sink term for heat balance Source/sink term for mass balance Time... 

T), may depend on pol3nner or ion concentration, temperature etc is the dispersion of component i in the aqueous phase and q are the source/sink terms for component i through chemical reaction and injection/ production respectively. Polymer adsorption, as described by the term in equation (2), may feed back onto the mobility term in equation (1) through permeability reduction. In addition to the polymer/tracer transport equation above, a pressure equation must be solved (5-8), in order to find the velocity fields for each of the phases present ie aqueous, oleic and micellar (if there is a surfactant present). If thermal effects are also to be included, then a heat balance equation is also required. The SCORPIO simulator (26, 27), which is used in our studies allows for all of these effects. 

One cautionary note should be kept in mind when using Eqs. (42)-(45) and (71) to calculate radiative heat transfer in FFB. The bed s absolute temperature 1), is normally assumed to be uniform across the bed and is used as the source or sink temperature in Eqs. (42) and (43). This assumption may be inappropriate in those cases in which a dense aimular region of particles shields the FFB wall from the bulk bed. In sueh situations, it is the average temperature of the particles in the annular layer that should be taken as the source/ sink temperature for ealeulation of radiant heat flux to/from the wall. This requires a mass and heat balance analysis for the material flowing in the annulus, and the reader is referred to Chapter 19 for necessary hydrodynamic models. 

A mass balance expression for an indoor air pollutant may be written as Input — output -h sources — sinks = rate of change of storage... 

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