Flow rate corrected

Some GPC analysts use totally excluded, rather than totally permeated, flow markers to make flow rate corrections. Most of the previously mentioned requirements for totally permeated flow marker selection still are requirements for a totally excluded flow marker. Coelution effects can often be avoided in this approach. It must be pointed out that species eluting at the excluded volume of a column set are not immune to adsorption problems and may even have variability issues arising from viscosity effects of these necessarily higher molecular weight species from the column. 

In Equation (35), an estimation of the mass transfer with the Weisz-Prater criterion is given. By taking always reasonable estimations or overestimated values, one obtains a good conclusion if mass transfer is present or not. For the characteristic length, 200 pm as particle diameter is used. The reaction order usually has the value of 1 to 4 a value of 4 would therefore be a worst case scenario. The catalyst density can be measured, or the common estimation of 1.3 kg/m3 can be used, which should not be too erroneous for Li-doped MgO. The observed reaction rate re is calculated from the concentration of CH4 at the inlet of the reaction cch4 0 multiplied with the highest observed conversion of 25% (the highest initial value for all tested catalysts), divided by the inverse flow rate, corrected by the reactor temperature. The calculation of re is shown in Equation (33) ... 

Note STP m /min is the volumetric flow rate corrected to standard temperature and pressure. 

Wall effects in capillary flow of suspensions such as apple sauce occur as a result of velocity gradient near the wall that in turn causes the suspended particles to move away from the wall region. The net result is slip of the fluid at the wall (23., 24.) The correct shear rate can be calculated from flow rates corrected for slip. The procedure, due to Mooney (42.), requires the use of several capillaries of different different length to diameter ratios has been applied to food suspensions by Higgs (38) and Kokini and Plutchok (22.) to show that slip effects are significant. These results also suggest caution in using... 

If the flow rate is accurate and precise, we can speak about a correct flow rate. Correctness is therefore the generic term for accuracy and precision. However, in the literature, very often the term accuracy is used as an equivalent to correctness . 

The pumps now available for liquid chromatography applications are very consistent in their flow delivery, but a very small error in the flow rate can lead to a much more significant error in the calculated average molecular masses. Consequently, the use of an internal marker for a flow rate correction plays an essential role in calibrating an SEC system and in the subsequent calculation of results. 

Note If sampling site calibration is not possible, environmental influences may affect the flow rate. The extent is dependent on the type of pump used. Consult with the pump manufacturer to determine dependence on environmental influences. If the pump is affected by temperature and pressure changes, correct the flow rate using the formula shown in the section Sampling Pump Flow Rate Corrections at the end of this appendix. 

Now assume that Well 1 is pressure constrained at 500 psi, that the six sides of the computational box are solid no-flow walls, and that the simulator is run in a purely transient compressible flow mode for an isothermal gas. The gas has a viscosity of 1 cp, a surface density of 0.003 Ibf sec2/ft4 at 14.7 psi, and a gas exponent of m = 1. Let us initialize our reservoir to 10,000 psi to provide a significant shock to the system, and let us study the initial history obtained at Well 1, as extracted from WELL 1. SIM. Recall that Well 1 is initially pressure constrained at 500 psi. Note how the flow rate correctly decreases with time and how the cumulative volume increases in time. The computed rate behavior shows no unrealistic oscillations in time. 

Panhandle A Equation. This equation is best used for pipelines with Reynolds numbers in the range of 5 x 10 to 11 x 10 . The average pipeline efficiency factor used in this equation is 92 percent. This number is based on actual empirical experience with the metered gas flow rates corrected to standard conditions. For larger diameter pipelines, the pipeline efficiency factor can be as high as 98 percent. With this equation, pipeline efficiency factors should be reduced for smaller pipe diameters. The Panhandle A Equation provides a reasonable approximation for partially turbulent flow. For fully turbulent flow, this equation does not produce accurate results, hi the fully turbulent flow region, the Panhandle B Equation is recommended. 

The column outlet flow-rate corrected to room temperature and pressure for example, the flow-rate as measured by a flow metre. can be calculated from the average carrier gas linear velocity and the column dimensions. 

From Figure 38 it is apparent that the heat flow rate was higher than the set-point during 1 h after the dilution rate increase so that there was no feed flow rate correction. Then, at t = 2.1 h, the controller activates because the heat flow rate became lower than the set-point. This is shown in Figure 38 where the feed rate decreased at this moment. Controller action confirms that the culture was forced to work at its highest specific Oj consumption rate, but at the same time ethanol production was extremely low (Figure 39). Moreover, the heat flow rate measured was almost equal to its set-point value towards the end of the experiment resulting in little modification of the flow rate. As a consequence, feed... 

The Ft correction factor is usually correlated in terms of two dimensionless ratios, the ratio of the two heat capacity flow rates R and the thermal effectiveness P of the exchanger ... 

When a solute elutes from the column, the thermal conductivity of the mobile phase decreases and the temperature of the wire filament, and thus its resistance, increases. A reference cell, through which only the mobile phase passes, corrects for any time-dependent variations in flow rate, pressure, or electrical power, ah of which may lead to a change in the filament s resistance. 

Pot flow rate in fP /min and power in brake horsepower, a correction factor of 0.157 must be appHed to each equation. 

AH three parameters, the cut size, sharpness index, and apparent bypass, are used to evaluate a size separation device because these are assumed to be independent of the feed size distribution. Other measures, usually termed efficiencies, are also used to evaluate the separation achieved by a size separation device. Because these measures are dependent on the feed size distribution, they are only usefiil when making comparisons for similar feeds. AH measures reduce to either recovery efficiency, classification efficiency, or quantitative efficiency. Recovery efficiency is the ratio of the amount of material less than the cut size in the fine stream to the amount of material less than the cut size in the feed stream. Classification efficiency is defined as a corrected recovery efficiency, ie, the recovery efficiency minus the ratio of the amount of material greater than the cut size in the fine stream to the amount of material greater than the cut size in the feed stream. Quantitative efficiency is the ratio of the sum of the amount of material less than the cut size in the fine stream plus the amount of material greater than the cut size in the coarse stream, to the sum of the amount of material less than the cut size in the feed stream plus the amount of material greater than the cut size in the feed stream. Thus, if the feed stream analyzes 50% less than the cut size and the fine stream analyzes 95% less than the cut size and the fine stream flow rate is one-half the feed stream flow rate, then the recovery efficiency is 95%, the classification efficiency is 90%, and the quantitative efficiency is 95%. 

The Displacement Distance theory suggests that since the stmcture of the flame is only quantitatively correct, the flame height can be obtained through the use of the displacement length or "displacement distance" (35,36) (eq. 12), where h = flame height, m V = volumetric flow rate, m /s and D = diffusion coefficient. 

The hydrauhc diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function only of the ratio of cross-sectional area to wetted perimeter. For some shapes, the Navier-Stokes equations have been integrated to yield relations between flow rate and pressure drop. These relations may be expressed in terms of equivalent diameters Dg defined to make the relations reduce to the second form of the Hagen-Poiseulle equation, Eq. (6-36) that is, Dg (l2SQ[LL/ KAPy. Equivalent diameters are not the same as hydraulie diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(tiDe/4). Equivalent diameter Dg is not to be used in the friction factor and Reynolds number ... 

The large variety of displacement-type flmd-transport devices makes it difficult to list characteristics common to each. However, for most types it is correct to state that (1) they are adaptable to high-pressure operation, (2) the flow rate through the pump is variable (auxiliary damping systems may be employed to reduce the magnitude of pressure pulsation and flow variation), (3) mechanical considerations limit maximum throughputs, and (4) the devices are capable of efficient performance at extremely low-volume throughput rates. 

Another instance in which the constant-temperature method is used involves the direc t application of experimental KcO values obtained at the desired conditions of inlet temperatures, operating pressure, flow rates, and feed-stream compositions. The assumption here is that, regardless of any temperature profiles that may exist within the actu tower, the procedure of working the problem in reverse will yield a correct result. One should be cautious about extrapolating such data veiy far from the original basis and be carebil to use compatible equilibrium data. 

When straight or serrated segmental weirs are used in a column of circiilar cross secdion, a correction may be needed for the distorted pattern of flow at the ends of the weirs, depending on liquid flow rate. The correction factor F from Fig. 14-33 is used direcdly in Eq. (14-112) or Eq. (14-119). Even when circular downcomers are utilized, they are often fed by the overflow from a segmental weir. When the weir crest over a straight segmental weir is less than 6 mm V in), it is desirable to use a serrated (notched) weir to provide good liquid distribution. Inasmuch as fabrication standards permit the tray to be 3 mm Vh in) out of level, weir crests less than 6 mm V in) can result in maldistribution of hquid flow. 

Effect of Physical Properties on Drop Size Because of the extreme variety of available geometries, no attempt to encompass this variable is made here. The suggested predictive route starts with air-water droplet size data from the manulac turer at the chosen flow rate. This drop size is then corrected by Eq. (14-195) for different viscosity and surface tension ... 

The actual mass flow rates and speeds are corrected by factor ( /0/ ) and (l/ /0) respectively, reflecting variations in inlet temperature and pressure. The surge line joins different speed lines where the compressor s operation becomes unstable. A compressor is in surge when the main flow through a compressor reverses direction for short time intervals, during which the back... 

The flow controller amplifies the transmitter signal and sends a modified signal to the final element. Rest and rate correction factors may also be required. 

An eluted solute was originally identified from its corrected retention volume which was calculated from its corrected retention time. It follows that the accuracy of the measurement depended on the measurement and constancy of the mobile phase flow rate. To eliminate the errors involved in flow rate measurement, particularly for mobile phases that were compressible, the capacity ratio of a solute (k ) was introduced. The capacity ratio of a solute is defined as the ratio of its distribution coefficient to the phase ratio (a) of the column, where... 

If the mobile phase is a liquid, and can be considered incompressible, then the volume of the mobile phase eluted from the column, between the injection and the peak maximum, can be easily obtained from the product of the flow rate and the retention time. For more precise measurements, the volume of eluent can be directly measured volumetrically by means of a burette or other suitable volume measuring vessel that is placed at the end of the column. If the mobile phase is compressible, however, the volume of mobile phase that passes through the column, measured at the exit, will no longer represent the true retention volume, as the volume flow will increase continuously along the column as the pressure falls. This problem was solved by James and Martin [3], who derived a correction factor that allowed the actual retention volume to be calculated from the retention volume measured at the column outlet at atmospheric pressure, and a function of the inlet/outlet pressure ratio. This correction factor can be derived as follows. 

Consequently, as the inlet pressure increases, the mean flow rate will be reduced according to the pressure correction function and the expected decrease in elution rate will not be realized. Consider an open tubular column. 

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