Beta ratio

An outstanding advantage of common differential pressure meters is the existence of extensive tables of discharge coefficients ia terms of beta ratio and Reynolds numbers (1,4). These tables, based on historic data, are generally regarded as accurate to within 1—5% depending on the meter type, the beta ratio, the Reynolds number, and the care taken ia manufacture. Improved accuracy can be obtained by miming an actual flow caUbration on the device. 

P = beta ratio orifice diameter to pipe diameter (or nozzle inlet diameter) e = (epsilon) emissivity value... 

Complementary to the passage, one can also consider the retention of a component as R = 1 - S (also called rejection). Retention can also be either an observed or an intrinsic measurement. Retention is useful in considering retained products during concentration mode operation. Other component separation characterizations include the log reduction value LRV =- logS which is used to characterize high-efficiency separations with permeate products (sterilization). The beta ratio P = I/S is sometimes used in NFF for clarification applications. 

Primary device Nominal pipe diameter D, in (mm) Beta ratio p Pipe Reynolds number NReD range Coefficient accuracy, %a... 

It is evident that the orifice coefficient incorporates the effects of both friction loss and velocity changes and must therefore depend upon the Reynolds number and beta ratio. This is reflected in Fig. 10-8, in which the orifice (discharge) coefficient is shown as a function of the orifice Reynolds number (NR d) and... 

The effect of the H-Beta ratio (y in wt%) in the dual-bed Pt/Z12(x) HB(y) catalyst system on the benzene purity at a reaction temperature (Tr) of 623 K is shown in Fig. 1. It is evident that the benzene purity gradually increased with increasing H-Beta ratio (Fig. la), eventually reaching a plateau value which meets the industrial specification of 99.85% at y 40 wt%. The effects of catalyst bed ratio on product yields are shown in Fig. lb. Comparing to the single-bed catalyst Pt/Z 12 (i.e., y = 0), the overall premium product yields of benzene and xylene (A68 yield) over the dual-bed catalyst Pt/Z12(x) HB(y) system reached an maximum at y 10 wt%. That the A68 yield dwindled and tetramethylbenzene (TEMB) increased with further increase in the H-Beta ratio may be attributed to the larger pore opening possessed by the bottom (H-beta) catalyst, which may provoke disproportionation of TMB to form tetramethylbenzene (TEMB) [8],... 

Figure 1. Effects of H-Beta ratio (y) in the dual-bed catalyst Pt/Z12(x) HB(y) on (a) benzene purity and (b) product yields during transalkylation reaction (see text) at 623 K.

P-parinaric acid, physical properties, 5 33t P-pentenoic acid, physical properties, 5 3 It P-peroxylactones, 18 484 Beta phase titanium, 24 838 in alloys, 24 854-856 properties of, 24 840, 941 P-phellandrene, 24 493 P-picoline, 21 110 from acrolein, 1 276 uses for, 21 120 P-pinene, 3 230 24 496-497 major products from, 24 478 /-menthol from, 24 522 as natural precursor for aroma chemicals, 3 232 terpenoids from, 24 478-479 P-propiolactone, polymerization of, 14 259 P-quartz solid solution, 12 637—638 Beta ratio, in filtration, 11 329—330 Beta (P) rays, 21 285 P-scission reactions, 14 280-281 P-skytanthine, 2 101 P-spodumene solid solution, 12 638-639 P-sulfur trioxide, 23 756 P-sultones, 23 527 P-tocopherol, 25 793 P-tocotrienol, 25 793 P-vinylacrylic acid, physical properties, 5 33t... 

In order to compare the performance of various adsorbent and desorbent systems for the same feedstock on must use the selectivity beta ratio. Equation (8.1) depicts the selectivity beta ratio of an adsorbent/desorbent pair is defined as the ratio of the two components in the adsorbed phase divided by the ratio of the same two components in the unabsorbed phase at equilibrium conditions. 

Venturi, Flow Tube, and Flow Nozzle Inaccuracies (Errors) in Percentage of Actual Flow for Various Ranges of Beta Ratios and Reynolds Numbers... 

Flow Sensor Line Size, Inches (1 in. = 25.4 mm) Beta Ratio Pipe Reynolds Number Range for Stated Accuracy Inaccuracy, Percentage of Actual Flow... 

There are two types of flow nozzles. The common nozzle used in the United States is the so-called long-radius, or ASME flow nozzle. This nozzle comes in two versions, known as low-beta-ratio and high-beta-ratio designs. Flow nozzles represent a transition between orifices and flow tubes. At the same pressure drop, they pass about 60% more flow than an orifice. They are more compact and less expensive, but they also produce more head loss than do flow tubes. 

D and 8 ) taps n 4 91.71P 0.5959 4- 0.46ip i -t 0.4SP -t 0.039 Detailed Reynolds number, line size, beta ratio, and other limitations are given in Table 5.13. From BIF CALC-440/441 the manufacturer should be consulted for exact coefficient information. 0.75... 

Nominal Pipe Diameter D, Beta Ratio Pipe Reynolds Number Coefficient... 

Pressure taps are required on each side of the orifice plate to allow the measurement of the pressure drop across the plate when the fluid is flowing. Knowing the differential pressure, the ratio of the orifice plate bore to pipe inside diameter (beta ratio) and fluid density, the flow rate can be calculated. 

Since the main function of any filter is the removal and separation of impurities, and the filters are rated in many different ways, it is inevitable that many tests are available to substantiate these ratings. The tests include the bubble point test used to establish the mean filter rating and the multi-pass test which provides the beta ratio of the hydraulic and lubrication filters. 

Williams MV, Denekamp J, Fowler JF (1985) A review of al-pha/beta ratios for experimental tumors implications for clinical studies of altered fractionation. Int J Radiat Oncol Biol Phys li(I) 87-96... 

Williams SG et al. (2007) Use of individual fraction size data from 3756 patients to directly determine the alpha/beta ratio of prostate cancer. Int J Radiat Oncol Biol Phys 68(l) 24-33... 

In 1972, Lakshmana Rao and his co-workers obtained the pressure loss coefficients for laminar flow in five sharp square-edged long orifices with a constant p ratio of 0.2 whilst varying the thickness to diameter ratios from 0.48 to 10.11. Pressure loss coefficients in turbulent flow for orifices with P ratios of 0.36, 0.4, 0.5 and 0.7 with aspect ratios of 4, 4, 5 and 5 respectively are compared with those of Ward-Smith (1971) and Idel chik et al. (1994). Excellent agreement was found between experimental work and turbulent flow correlations from Ward-Smith (1971) and Idel chik et al. (1994), with maximum difference between the experimental data models were 9.87% and 12% respectively for the maximum beta ratio of 0.7. This difference was well within the experimental error obtained. The comparison shows clearly that correlations published by Ward-Smith (1971) and Idel chik et al. (1994) can be used from Re > 1000, although the two models has an applicability range from Re > ICh. 

The beta ratio is a rating system introduced with the object of giving both filter manufacturer and filter user an accurate and representative comparison among various filter media. It is the ratio between the number of particles per unit volume above a specific size in the suspension upstream of the filter to the same parameter in the flow downstream of the filter, and it is determined in a test rig that enables accurate particle counting in the two flow regions. The beta ratio is then ... 

It follows that the higher the value of the beta ratio, the more particles of the specified size, or greater, are retained on the filter. The filter efficiency at this particle size can then be determined from the beta ratio ... 

The beta ratio and the corresponding efficiency are illustrated in Table 1.5 in a test where the filter was challenged with 1 million particles per unit volume (the numbers in Table 1.5 refer, of course, to the same particle size). 

The nominal rating of a filter can be expressed by means of this efficiency fignre. Given as a percentage, it can be calculated from the beta ratio, or directly from the particle number count ... 

The classic method of determining filter efficiency is by the bead challenge test, with a rating expressed as a beta ratio, thus a beta ratio > 75 specifies a filter efficiency of 98.6% or better relative to a particle size of x pm. 

From the counted samples, the cumulative particle size distribution in unit volume of the fluid is then determined, over a range of sizes to match the fed dust (such as 5,10, 20, 30 and 40 pm). The beta ratio can then be calculated for each of the selected particle sizes (as in Section ID) from ... 

The multi-pass test simulates well the behaviour of clarifying filters in hydraulic or lubricating fluid systems, because the recycle of the filtrate carries with it the undersized particles, so that the proportion of fine particles increases continuously during the test. It was the first filter test to become an ANSI standard, and is now incorporated into an international standard (see BS ISO 16889 1999). It should be noted that the beta ratio will be different from that determined by this test if it is used in a system that contains particle distributions that differ from the distribution used in the test. 

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