Equation average concentration

Eor a food container, the amount of sorption could be estimated in the following way. Eor simple diffusion the concentration in the polymer at the food surface could be estimated with equation 3. This would require a knowledge of the partial pressure of the flavor in the food. This is not always available, but methods exist for estimating this when the food matrix is water-dorninated. The concentration in the polymer at the depth of penetration is zero. Hence the average concentration C is as from equation 9. 

The puff model describes near-instantaneous releases of material. The solution depends on the total quantity of material released, the atmospheric conditions, the height of the release above ground, and the distance from the release. The equation for the average concentration for this case is (Growl and Louvar, 1990, p, 143) ... 

When there is an upwind background concentration Xb and the mixing height is rising with time into a layer aloft having an average concentration of Xa/ equation of continuity is... 

This equation, which may be used directly to predict average concentration in the liquid phase under various operating conditions, is shown graphically in Fig. 12. Combining Eq. (164) with the expression for the total average rate of gas absorption in the vessel,... 

Equation (8.4) defines the average concentration, Ugut, of material flowing from the reactor. Omit the V ir) term inside the integral and normalize by the cross-sectional area, Ac = ttR, rather than the volumetric flow rate, Q. The result is the spatial average concentration a patiai, and is what you would measure if the contents of the tube were frozen and a small disk of the material was cut out and analyzed. In-line devices for measuring concentration may measure a panai rather than Uout- Is the difference important ... 

Kinetic analysis of the data obtained in differential reactors is straightforward. One may assume that rates arc directly measured for average concentrations between the inlet and the outlet composition. Kinetic analysis of the data produced in integral reactors is more difficult, as balance equations can rarely be solved analytically. The kinetic analysis requires numerical integration of balance equations in combination with non-linear regression techniques and thus it requires the use of computers. 

Several boundary conditions have been used to prescribe the outer limit of an individual rhizosphere, (/ = / /,). For low root densities, it has been assumed that each rhizosphere extends over an infinite volume of. soil in the model //, is. set sufficiently large that the soil concentration at r, is never altered by the activity in the rhizosphere. The majority of models assume that the outer limit is approximated by a fixed value that is calculated as a function of the maximum root density found in the simulation, under the assumption that the roots are uniformly distributed in the soil volume. Each root can then extract nutrients only from this finite. soil cylinder. Hoffland (31) recognized that the outer limit would vary as more roots were formed within the simulated soil volume and periodically recalculated / /, from the current root density. This recalculation thus resulted in existing roots having a reduced //,. New roots were assumed to be formed in soil with an initial solute concentration equal to the average concentration present in the cylindrical shells stripped away from the existing roots. The effective boundary equation for all such assumptions is the same ... 

The MDL and practical quantitation limit (PQL) should be appropriate for the objectives of the analysis. MDL refers to the minimum concentration of the compound of interest that can be measured and reported with a specified confidence (99% probability) that the concentration is above zero. The registrants must provide or develop an analytical method for water for the parent pesticide and its degradates that has an MDL of 0.01% of the label application rate (calculated as the average concentration in the top six inches of soil), or 0.05 pgL , whichever is lower. PQL refers to the lowest concentration at which the laboratory can confidently quantify the concentration of the compound of interest. The study authors must report all samples with concentrations above the MDL as detections, including those below the PQL in which the concentration cannot be quantified. In addition, the study authors must provide sample equations to demonstrate how the PQL was calculated. 

Maximum selectivity requires a minimum ratio r2/ri in Equation 5.65. A batch or plug-flow reactor maintains higher average concentrations of feed (CFeed) than a mixed-flow reactor, in which the incoming feed is instantly diluted by the PRODUCT and BYPRODUCT. If ax > a2 in Equations 5.64 and 5.65 the primary reaction to PRODUCT is favored by a high concentration of FEED. If ax < a2 the primary reaction to PRODUCT is favored by a low concentration of FEED. Thus, if... 

For the above-described model, the average concentration of cations and anions in the intermolecular spaces can be calculated using equations derived in [51] ... 

A direct method for determining worker exposures is by continuously monitoring the air concentrations of toxicants on-line in a work environment. For continuous concentration data C t) the TWA (time-weighted average) concentration is computed using the equation... 

Equation 5-23 is solved together with boundary conditions expressed by Equations 5-12 and 5-13. The solution for the average concentration at any point3 is... 

Since the material-balance equations, 16.2-1 and -2, derived above refer to a particular radial position, we must integrate radially to obtain an average concentration cA at any axial position x, including at the outlet, where x = L. The latter is the observed outlet concentration that corresponds to the outlet fractional conversion. We develop the expression in terms of cA,... 

From equation (12) it can be concluded that the required residence time 0 to achieve a certain value of s is inversely proportional to the average concentration of ozone present in tire reactor. The value of the required residence time and therefore the required volume V of the reactor is completely independent of the distribution of ozone over the reactor. This also holds for the conversion of component A and component B. 

It is also interesting to compare the ozone losses due to the presence of ozone in the effluent. To that aim we consider the ideal situation that in both reactors the ozone concentration is distributed equally over the reactor volume. Further we assume that both reactor systems have the same average residence time, 0. The average concentration of ozone in the CFSTR and PFR is given by equation (5) and (12) respectively. From these two equations it can be derived that the ratio of the average ozone concentration in the PFR and the CFSTR, Re is given by ... 

The plot of the loadings for each chromatographic peak (Beta 1 vs. Beta 2 and 1 2 Equation [3]) reveals information about the sources of the variance in the four samples (Figure 8). Information in Table 11 confirms these findings, as it is seen that the variability is largely the result of the failure to detect two peaks (peak 1 [variable 5], and peak 4 [variable 9]). Also, peak 63 (variable 67) in sample 20 exceeds its average concentration measured in all samples by 9%. 

If we consider a system polyelectrolyte-enzyme, the catalytic implications of the polyelectrolyte theory become evident when Eq. (39) is applied to protons, substrates, and inhibitors (as long as these are charged molecules). Equation (39) shows that the average concentration of protons in the polyelectrolytic environment is different from that of the bulk medium ... 

Fig. 10.4 Measured breakthrough curve of bromide with CTRW and advection-dispersion equation (ADE) fits. Here, the quantity j represents the normafized, flux-averaged concentration (top) Complete breakthrough curve, (bottom) Region identified by the bold-framed rectangle in the top plot. Note the difference in scale units between the plots. Pressure head h=-10cm water velocity v=2.82 cm/h. The dashed tine is the best advection-dispersion equation solution fit. The soUd line is the best CTRW fit. (Cortis and Berkowitz 2004)...

Equation (4) states that the linear deposition rate vj is a diffusion controlled boundary layer effect. The quantity Ac is the difference in foulant concentration between the film and that in the bulk flow and c is an appropriate average concentration across the diffusion layer. The last term approximately characterizes the "concentration polarization" effect for a developing concentration boundary layer in either a laminar or turbulent pipe or channel flow. Here, Vq is the permeate flux through the unfouled membrane, 6 the foulant concentration boundary layer thickness and D the diffusion coefficient. 

Katchalsky and Curran W formulated the nonequilibrium thermodynamic equations for the transport of material through a discontinuous membrane. However, there was a difficulty in their expressions, as they required the "average concentration" in the membrane. In order to overcome this difficulty of evaluating the... 

The general population can be exposed to chemical substances in indoor as well as in outdoor (ambient) air via inhalation of vapors, aerosols, and dusts in the air. The term inhalation exposure is defined as the concentration of a substance in inhaled air at the boundary of the body, and is expressed as an average concentration per unit time (e.g., mg/m per day). In order to estimate a daily dose of a substance from the exposure concentration of the substance in the air, the inhalation rate is used. According to US-EPA (1997), the average daily dose (ADD) can be estimated from the exposure concentration by using the following equation ... 

Now the behavior of the general solution of Equation 5-89b is examined. As t co, the volume-averaged concentration reaches a constant value (steady state) ... 

In addition to volume-averaged concentration in the mineral, the concentration distribution inside the mineral may also be investigated. From Equation 5-88c, the steady-state concentration profile is... 

The two equations have the same mathematical form, although they deal with different physical quantities. The initial and boundary conditions are also somewhat different. In the bulk recombination, the initial electron concentration is assumed to be uniform in the space and equal to the average concentration Cq... 

The peak area ratio of the blank is due to the endogenous BA concentration in plasma samples. In the reported paper the 95% confidence limits of the calculated average concentrations were calculated as x0 tsx0, where sx0, the standard error for both the sample and the calibration curve, was determined using equation 5.10 from Miller and Miller [39]. This calculated average concentration was then compared to the actual concentration using a f-test. 

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