# PS type ratio error

The penetration of microwaves in various materials gives active microwave imaging a large potential for subsurface radar, civil engineering etc. Several inverse-scattering theories have been proposed in the scientific literature. Among them, the simplest Bom-type approach, which does not take into account multiple reflections, is valid for weakly scattering objects [1-2]. To improve the quality of reconstruction, the method based on the successive application of the perturbative algorithm was developed [3]. However, the inherent approximations of this approach are not overcome in the iterative scheme. Another class of algorithms aims to obtain the spatial distribution of permittivity by using numerical solutions of exact equations [4-6]. Unfortunately, a rate of convergence of the solution to the global minimum of cost function depends on actual contrast values, measurement error etc. That is why an importance of a priori knowledge about the object imder investigation is usually emphasized. In general, existing inversion algorithms suffer from serious problems when discontinuous profiles of high contrast, which are often encountered in practical applications, are to be reconstructed. Moreover, the frequency-swept imaging methods utilize usually reflection coefficient data measured in a very broad frequency band starting from zero frequency [1-2, 4-5]. Such methods are inappropriate from an application point of view. [c.127]

This method of measuring level is highly desirable because it is a noncontacting technique. There are no mechanical parts and the acoustical signal is typically not affected by the physical properties of the Hquid. An adjustment must be provided in the electronic circuit to correct for the changes in temperature of the vapor space through which the signal passes. Temperature variances affect the speed (FQ of the acoustical signal so a temperature compensation circuit is used. The circuit may be internally potted in the transducer head near the crystal or a separate temperature probe can be used which provides temperature information to the electronics. Acoustical signals transmit much faster and more efftciendy at high temperatures, slower at low temperatures. This acoustical rate change caused by the varying air temperatures necessitates the need for a temperature compensation circuit. A few other considerations should be taken into account when applying this technology. Dust particles and vapors that affect the speed of sound, high temperatures, and operating pressures exceeding - 700 kPa (100 psig) affect the measurement. Since the calculation in the microprocessor is based on the speed of sound in air, vapors with higher or lower densities impede the transmission of the sound wave to a certain degree. The ultrasonic signal slows down or speeds up and therefore induces some error into the measurement. If the Hquid surface has foam or excessive turbulence, the acoustical signal may not have a good redective target (this type of level measurement should not be used in mechanically operated tanks). There are certain foams that absorb the acoustical signal and others that have a good redective surface. [c.215]

With each row of tubes there is associated (0.203)( / V2) = 0.176 m (0.577 ft) of wall height, of area [(0.203)(9)(2) -I- (7.62)(2)]0.176 - (9)(2)(7C)(0.0508)- = 3.18 m (34.2 ft"). One row of tubes has an area of ( TC)(0.102)(7.62)(9) = 22.0 m" (236 fr). If the recommended factor of 0.7 on the refractory area is used, the effective area of the tubes is [22.0 -I- (0.7)(3.18)]/22.0 = 1.10 mVm" of actual area. The exact evaluation of the outside tube temperature from the known oil temperature would involve a knowledge of the oil-film coefficient, tube-wall resistance, and rate of heat flow into the tube, the evaluation usually involving trial and error. However, for the present purpose the temperature drop through the tube wall and oil film will be assumed to be 41.7 G (75 F), making the tube surface temperatures 357 G (675 F) and 468 G (875 F) the average is 412 G (775 F). The radiating gas temperature is [c.583]

The accuracy achievable by the ratio method amounts to approximately 5-10 atom% when ionization edges of the same type are used, i. e. only K edges or only L edges, whereas the error in quantification increases to +15-20 atom% for the use of dissimilar edges. Improvement of the quantification accuracy up to approximately 1 atom% is possible if standards are used. [c.67]

By changing the origin from the injection point, which is appropriate for the Poisson form of the elution equation, to the position of the peak maximum, the Gaussian or Error function form of the elution equation can be derived. The Error function form of the elution equation can be useful for certain theoretical treatments and, particularly, for the computer simulation of elution curves. Due to interaction between the concentration profiles of closely eluting peaks, the apparent retention times, or retention volumes, as measured from the position of the peak maxima, may differ significantly from the true retention times or volumes. This error will become greater as the resolution is less and the column efficiency reduced. If the peaks are asymmetrical, the effect is exacerbated and will even give a false indication of the relative peak heights. The interaction between the concentration profiles of closely eluting peaks can, however, be employed usefully for the analysis of completely unresolved peaks. The positions of the peak maxima can be related to the relative proportions of the two unresolved components. Thus, the composition of the mixed peak can be determined from the retention time of the composite peak. Peak asymmetry normally results from the separation being carried out under conditions where the adsorption isotherm is nonlinear. There can be a number of causes for this to happen, such as stationary phase saturation, or solute/solute interaction. If the isotherm is Langmuir in type, large samples will produce peaks with a sharp front and a sloping tail. If the isotherm is Freundlich in type, then the peak will have a sloping front and a sharp back. By equating the second differential of the elution equation to zero and solving, the peak width at the points of inflexion can be determined. From the peak width, by simple proportion, the efficiency of the column can be calculated from measurements made on the chromatogram. In order to do this, the position of the points of inflection, relative to the peak height, must be identified. This can be achieved, again, from the elution equation, and the height of the points of inflection are found to be 0.6065 of the peak height. Once more employing the elution curve equation, an expression for the resolution of a column can be derived, and the efficiency required to separate a pair of solutes can be calculated from the capacity factor of the first peak and their separation ratio. The efficiency of a column does not reflect its resolution for solutes eluted at low capacity ratios, the effective plate number was introduced. The effective plate number and the theoretical plate [c.231]

However, it has to be considered that it is neither the content of free formaldehyde itself nor the molar ratio which eventually should be taken as the decisive and the only criterion for the classification of a resin concerning the subsequent formaldehyde emission from the finished board. In reality, the composition of the glue mix as well as the various process parameters during the board production also determine both performance and formaldehyde emission. Depending on the type of board and the manufacturing process, it is sometimes recommended to use a UF-resin with a low molar ratio F/U (e.g. F/U = 1.03), hence low content of free formaldehyde, while sometimes the use of a resin with a higher molar ratio (e.g. F/U = 1.10) and the addition of a formaldehyde catcher/depressant will give better results [17]. Which of these two, or other possible approaches, is the better one in practice can only be decided in each case by trial and error. [c.1048]

The numerator is a random normally distributed variable whose precision may be estimated as V(N) the percent of its error is f (N)/N = f (N). For example, if a certain type of component has had 100 failures, there is a 10% error in the estimated failure rate if there is no uncertainty in the denominator. Estimating the error bounds by this method has two weaknesses 1) the approximate mathematics, and the case of no failures, for which the estimated probability is zero which is absurd. A better way is to use the chi-squared estimator (equation 2,5.3.1) for failure per time or the F-number estimator (equation 2.5.3.2) for failure per demand. (See Lambda Chapter 12 ), [c.160]

In measuring the local velocity in ducts, the sensor will obstruct a part of the duct cross-section. This results in accelerated flow by the sensor and an error occurs. In a Pitot-static tube, this is called stem blockage. If the ratio of the tube diameter to the duct diameter is smaller than 0.02, stem blockage can be neglected. Otherwise a correction has to be applied. [c.1157]

A stream containing a noncondensable and vapors to be condensed must be considered so that the continually changing gas vapor physical properties (and some thermal properties), gas film heat transfer coefficient, and mass gas flow rate are adequately represented. This operation is usually a constant pressure process. The vapor condenses at its dew-point on the tubes, thereby providing a wet surface a noncondensable gas film surrounds this surface and the vapor of the stream diffusing through this film condenses into the liquid film of the condensate on the tube, see Figure 10-84. The sensible heat and latent heat of the vapor are transferred through the gas film and the liquid film to the tube surface (except when considerable subcooled condensate film exists, in which cases there may be condensation or fogging in the gas film). The rigorous method of design of Colburn and Colburn and Hougen involving trial-and-error calculations is considered the most accurate of the various alternate procedures published to date. Kern presents a very useful analysis of special design problems with examples. [c.143]

Every accelerometer has a response curve of the type shown schematically in Figure 4-222. Instead of having an ideal linear response, a nonlinear response is generally obtained with a skewed acceleration for zero current, a scale factor error and a nonlinearity error. In addition, the skew and the errors vary with temperature. If the skew and all the errors are small or compensated in the accelerometer s electronic circuits, the signal read is an ideal response and can be used directly to calculate the borehole inclination. If not, modeling must be resorted to, i.e., making a correction with a computer, generally placed at the surface, to find the ideal response. This correction takes account of the skew, [c.906]

As the feed composition approaches a plait point, the rate of convergence of the calculation procedure is markedly reduced. Typically, 10 to 20 iterations are required, as shown in Cases 2 and 6 for ternary type-I systems. Very near a plait point, convergence can be extremely slow, requiring 50 iterations or more. ELIPS checks for these situations, terminates without a solution, and returns an error flag (ERR=7) to avoid unwarranted computational effort. This is not a significant disadvantage since liquid-liquid separations are not intentionally conducted near plait points. [c.127]

Another small asbestos plug is then inserted to confine the lead peroxide (it s very important that the lead peroxide is not tamped down or it will almost completely prevent passage of gas through the tube) followed by a 30 mm. roll of silver gauze, treated in the same way as the first one inserted. This is the main halogen-absorbent, the one already inserted sendng as a trap (at 180 ) to catch any halogen lost by the hot (680°) silver halide first formed. Next about 25-30 mm. of ignited asbestos is added this is known as a " choking plug" as it is this clement of filling that offers the major part of the resistance to the flow of oxygen in the apparatus. The exact dimensions and compression of the choking plug are determined by trial and error. The amount of asbestos is so adjusted that, when the combustion tube is completely packed, the apparatus assembled, the absorption tubes in place, the furnace and thermostatic mortar at their equilibrium temperatures, and also when there is a pressure of 60 mm,/water registered on the pressure gauge and a reduced head of about 20 mm. of water on the Mariotte bottle, the rate of flow of oxygen through the apparatus is about 5 ml. per min. It is essential to have the furnace and mortar on while this adjustment is being made as temperature greatly affects the rate at w hich gas will flow at a given pressure difference (hot tubes generally run noticeably faster than cold). [c.473]

Another small asbestos plug is then inserted to confine the lead peroxide (it is very important that the lead peroxide is not tamped down or it will almost completely prevent passage of gas through the tube) followed by a 30 mm. roll of silver gauze, treated in the same way as the first one inserted. This is the main halogen-absorbent, the one already inserted serving as a trap (at 180°) to catch any halogen lost by the hot (680°) silver halide first formed. Kext about 25-30 mm. of ignited asbestos is added this is known as a choking plug " as it is this element of filling that offers the major part of the resistance to the flow of oxygen in the apparatus. The exact dimensions and compression of the choking plug are determined by trial and error. The amount of asbestos is so adjusted that, when the combustion tube is completely packed, the apparatus assembled, the absorption tubes in place, the furnace and thermostatic mortar at their equilibrium temperatures, and also when there is a pressure of 60 mm./water registered on the pressure gauge and a reduced head of about 20 mm. of water on the Mariotte bottle, the rate of flow of oxygen through the apparatus is about 5 ml. per min. It is essential to have the furnace and mortar on while this adjustment is being made as temperature greatly affects the rate at which gas will flow at a given pressure difference (hot tubes generally run noticeably faster than cold). [c.473]

The effect of pulsating flow on pitot-tube accuracy is treated by Ower et al., op. cit., pp. 310-312. For sinusoidal velocity fluctuations, the ratio of indicated velocity to actual mean velocity is given by the factor /l + AV2, where X is the velocity excursion as a fraction of the mean velocity. Thus, the indicated velocity would be about 6 percent high for velocity fluctuations of 50 percent, and pulsations greater than 20 percent should be damped to avoid errors greater than 1 percent. Tne error increases as the frequency of flow oscillations approaches the natural frequency of the pitot tube and the density of the measuring fluid approaches the density of the process fluid [see Horlock and Daneshyar, y. Mech. Eng. Sci, 15, 144-152 (1973)]. [c.887]

Reversed, Mixed, or Cross-Flow if the flow pattern in the exchanger is not completely countercurrent or cocnrrent, it is neces-saiy to apply a correction factor Ff by which the LMTD is multiplied to obtain the appropriate MTD. These corrections have been mathematically derived for flow patterns of interest, still by making assumptions 1 to 5 [see Bowman, MneUer, and Nagle, Trans. Am. Soc. Mech. E/ig., 62, 283 (1940) or Hewitt, et al. op. cit7. For a common flow pattern, the 1-2 exchanger (Fig. 11-2), the correction factor Ff is given in Fig. 11-4, which is also vahd for finding Ff for a 1-2 exchanger in which the shell-side flow direc tion is reversed from that shown in Fig. 11-2. Figure ll-4<7 is also applicable with neghgible error to exchangers with one shell pass and any number of tube passes. Values of Ff less than 0.8 (0.75 at the very lowest) are generally unacceptable because the exchanger configuration chosen is inefficient the chart is difficult to read accurately and even a small violation of the first assumption underlying the MTD will invahdate the mathematical derivation and lead to a thermodynamically inoperable exchanger. [c.1035]

Trace residue analysis of compounds in various matrices is an essential process for evaluation of different exposures to such toxicants, in which, preparation of samples is one of the most time-consuming and error-prone aspects prior to chromatographic analyses. A comparative study of sample preparation was performed to preconcentrate urinary 1-hydroxypyrene (1-OFIP) as a major metabolite and biological indicator of the overall exposure to polycyclic aromatic hydrocarbons (PAFIs) generated by various industrial and environmental processes. To perform this study, solid phase extraction (SPE) was optimized with regard to sample pFI, sample concentration, loading flow rate, elution solvent, washing solvent, sample volume, elution volume, and sorbent mass. The present approach proved that, 1-OFIP could be efficiently retained on CIS sorbent based on specific interaction. Further study employed methanol to extract the analyte from spiked urine. Along with, a nonclassic form of liquid-liquid extraction (LEE) also was optimized with regard to solvent type, solvent volume, extraction temperature, mixing type, and mixing duration. The results showed that, 1-OFIP could be relatively well extracted by methanol at optimum time of 2 minutes based on moderate specific interaction. At the developed conditions, obtained recovery of SPE was 99.96%, while, the EEE extraction recovery did not exceed 87.3% and also, based on applied sample volume, the limit of detection (EOD) achieved by SPE was 0.02 p.g/1 showing at least ten times less than that of EEE. The procedures were validated with three different pools of spiked urine samples showed a good reproducibility over six consecutive days as well as six within-day experiments for both developed methods as suitable results were obtained for CV% (less than 3.1% for SPE and between 2.8% and 5.05% for EEE). In this study, a high performance liquid chromatography (HPEC), using reverse-phase column was used. The mobile phase was methanol/water am at constant flow rate of 0.8 ml/min and a fluorescence detector was used, setting at 242 nm and 388 nm. Although the recovery and EOD were obtained for SPE method shows more efficiency, such results for EEE is also relatively efficient and can be applied for majority of similar studies. However, there is a significant difference between the obtained recoveries of SPE and EEE (P<0.05), showing that, SPE is superior. [c.378]

The relationships among tubular, differential and recycle reactors are shown in Figure 3.1.1. On the left side, the ideal, isothermal, tubular reactor is illustrated with m segments of equal catalyst volume. After each segmert, a sample can be taken out (not shown) for analysis to generate a curve of concentration vs. either tube length or catalyst volume. Differentiation of these curves would give the local rate of reaction at points where the concentrations are also known. Correlation of rates with the corresponding concentrations provides the rate functions. The process of differentiation increases the error of the original data. To avoid this, various curve-smoothing techniques were used. This is why statisticians prefer fitting different integrated rate equations to the original data and selecting the best fitting one. [c.53]

Since dependency analysis is not needed, we can go on to the BUILD program. Go to FTAPSUIT and select 5 "Run Build." It asks you for the input file name including extender. Type "pv.pch," It asks you for name and extender of the input file for IMPORTANCE. Type, for examle, "pv.ii . It next asks for the input option. Type "5" for ba.sic event failure probabilities. This means that any failure rates must be multiplied by their mission times as shown in Table 7.4-1. (FTAPlus was written only for option 5 which uses probabilities and error factors. Other options will require hand editing of the pvn.ii file. The switch 1 is for failure rate and repair time, switch 2 is failure rate, 0 repair time, switch 3 is proportional hazard rate and 0 repair time, and switch 4 is mean time to failure and repair time.) [c.306]

The majordata areas addressed are initiating events, sequence data, top event data components, and human error data. An alphabetical presentation of component types (mechanical, then electrical), subtypes where deemed necessary, and failure rate data in terms of mean, median, range factor, and variance values are logged in Table 7-2. Special consideration was given in the PRA to piping and tube failure rates therefore, mean and variance values are cited for small, intermediate, and large LOCAs and secondary system piping failures in Table 7-7. [c.123]

See pages that mention the term

**PS type ratio error**:

**[c.177] [c.808] [c.1344] [c.357] [c.1166] [c.52] [c.394] [c.289]**

Industrial power engineering and applications handbook (2001) -- [ c.474 ]