Slab, equivalent

A problem obviously exists in trying to characterise anomalies in concrete due to the limitations of the individual techniques. Even a simple problem such as measurement of concrete thickness can result in misleading data if complementary measurements are not made In Fig. 7 and 8 the results of Impact Echo and SASW on concrete slabs are shown. The lE-result indicates a reflecting boundary at a depth corresponding to a frequency of transient stress wave reflection of 5.2 KHz. This is equivalent to a depth of 530 mm for a compression wave speed (Cp) of 3000 m/s, or 706 mm if Cp = 4000 m/s. Does the reflection come from a crack, void or back-side of a wall, and what is the true Cp ... 

In Fig. 3 we saw that the process A is to be regarded as equivalent to the processes B and 0 taking place simultaneously. In Sec. 4 we obtained in (3) an expression for the amount of work required to set up charges g on the plates of a condenser, when there is a vacuum between the plates. We can now find the work required to set up the same charges q, where there is a slab of dielectric between the plates clearly this will be obtained per unit volume by subtracting (7) from (2), thus... 

Several important assumptions have been implicitly incorporated in Eqs. (15) and (16). First, these equations describe the release of a drug from a carrier of a thin planar geometry, equivalent equations for release from thick slabs, cylinders, and spheres have been derived (Crank and Park, 1968). It should also be emphasized that in the above written form of Fick s law, the diffusion coefficient is assumed to be independent of concentration. This assumption, while not conceptually correct, has been... 

The same derivation as that used for the accumulation of radiogenic isotope in a slab would lead to the solution but we will take advantage of this case to fully develop an application of Duhamel s principle (Appendix 8C). The assumption of zero initial and surface concentration of the radiogenic isotope is equivalent to... 

Equivalent mass, stiffness and loading arc obtained through the use of transformation factors. Several widely used texts on blast design such as /yny, (Chapter 5) and TM 5-1300 (Chapter 3) contain tabulated transformation factors for typical structural elements such as beams and slabs. The derivations of the equations for these transformation factors are also given by these references. Transformation factors used to obtain appropriate properties for the equivalent SDOF system are as follows ... 

The fetal head or whole body is sectioned on a slab of dental wax or equivalent, using a sharp razor blade. The specimen is placed onto the wax block and the razor blade inserted between the upper and lower jaws and, with firm even pressure, the upper part of the head is cut in a plane (along the rostro-occipital axis) just below the ears. 

Personal monitors are irradiated to a known value of dose equivalent while mounted on a 30 cm X 30 cm X 15 cm slab of polymethylmethacrylate (PMMA). PMMA is an inexpensive and widely available material, but has a somewhat different density and yields somewhat different amounts of backscatter than a tissue equivalent material (Selbach et al., 1989). 

GROSSWENDT, B. (1991). The angular dependence and irradiation geometry factor for the dose equivalent for photons in slab phantoms of tissue-equivalent material and PMMA, Radiat. Prot. Dosim. 35, 221-235. 

Up to about 600°F, 85% magnesia has been the most popular material. It is a mixture of magnesia and asbestos fibers so constructed that about 90% of the total volume is dead air space. Equivalents are available for situations where asbestos is undesirable. Such insulants are applied to the equipment in the form of slabs or blankets which are held in place with supports and clips spotwelded to the equipment. They are covered with cement to seal gaps and finished off with a canvas cover that is treated for resistance to the weather. A galvanized metal outer cover may be preferred because of its resistance to mechanical damage of the insulation. 

Kempter50 studied the thermal decomposition of 88% dense NbC cylinders from 2273 to 3473 K in 1 atm of He. Data at 3273 K will be used to test our diffusion-coupled vaporization mass loss model. We transposed the cylindrical geometry into an equivalent slab by dividing the volume by the average vaporizing area. One face of the cylinder was not included in the calculation because it rested on a NbC pedestal in the furnace. Table 3.13. summarizes analytical X-ray data for average C/Nb compositions. 

The characteristic length is the thickness of the equivalent slab used in the single catalyst pellet equation and it is defined as the thickness lc of the catalyst slab that gives the same external surface to volume ratio as the original pellet. For Raschig16 rings this is given by... 

The catalyst packing of the reactor consists of an iron oxide Fe20s, promoted with potassium carbonate K COo, and chromium oxide Cr O-s,. The catalyst pellets are extrudates of a cylindrical shape. Since at steady state the problem of simultaneous diffusion and reaction are independent of the particle shape, an equivalent slab geometry is used for the catalyst pellet, with a characteristic length making the surface to volume ratio of the slab equal to that of the original shape of the pellet. 

Fig. 11.9 Types of linear continuous-flow reactors (LCFRs). (a) Continuous plug flow reactor (CPFR) resembling a batch reactor (BR) with the axial distance z being equivalent to time spent in a BR. (b) A tabular flow reactor (TFR) with (tq) miscible thin disk of reactive component deformed and distributed (somewhat) by the shear field over the volume, and (b2) immiscible thin disk is deformed and stretched and broken up into droplets in a region of sufficiently high shear stresses, (c) SSE reactor with (cj) showing laminar distributive mixing of a miscible reactive component initially placed at z = 0 as a thin slab, stretched into a flat coiled strip at z L, and (c2) showing dispersive mixing of an immiscible reactive component initially placed at z — 0 as a thin slab, stretched and broken up into droplets at z — L.

From Figure 7, for a slab the equivalent Fourier number Fo at this dimensionless temperature is 1.22. 

For the interaction of planar slabs, the Hamaker approach entails integration over finite ranges of zA or zB. For the interaction between a half-space A and a parallel slab of B of finite thickness b, this procedure is equivalent to subtracting from E(l) = — (AHam/12 /2) an amount — [AHam/12 (Z +b)2] (see Fig. L2.10). This subtraction yields a form equivalent to the equation of Table P.2.b.3 (see Fig. L2.ll) ... 

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