Mean beam lengths, table

TABLE 5-7 Mean Beam Lengths for Volume Radiation... 

Note that these values are specific to the subject problem in which the mean beam length is L, , with gS evaluated from basic data, such as Table 5-8. (1 — in Eq. (5-165) represents the emissivity of a gray gas, which will be called Ec,i. For later use, note that,... 

Table 9.7. Mean beam lengths for various geometries 54 ...

Using Table 8-2, we calculate the mean beam length as... 

The mean beam length for a cylinder of equal diameter and height for radiation emitted to all surfaces is, from Table 13-4,... 

In Figure 8.23, the emissivity of such a gas is represented as a function of temperature and the product PL of the partial pressures of water and carbon dioxide and the path of travel defined by the mean beam length. Item 8 of Table 8.16 is a curve fit of such data. 

In order to explain the determination of the mean beam length, we first have to look at the calculation of the spectral emissivity e G of a gas volume. We will then show how sm is determined and put together in Table 5.11 values of. sni that have been calculated for different geometries. In addition a simple approximation formula will be derived with which sm can be determined for gas spaces that are not covered in this collection. 

Table 5.11 Mean beam lengths s/, for vanishingly small optical thicknesses and sm for finite optical thickness. Further information in [5.37], [5.48] and [5.59]...

Table 10.1 Mean beam length for gas radiation (from Rohsenow and Hartnett [24]).

For a black differential receiving surface area dA located in the center of the base of a hemisphere of radius L containing a radiating gas, the mean beam length is L. The mean beam length has been evaluated for various geometries and is given in Table 4.11-1. For other shapes, L can be approximated by... 

Table 4.11-1. Mean Beam Length for Gas Radiation to Entire Enclosure Surface Ml, R2, P3)... 

The equivalent or mean beam length or a given system at low values of total gas pressure times beam length is four times the enclosure s mean hydraulic radius. Some values of the mean equivalent beam length (Le) are given in Table 9-2. 

The deflection exhibited by a beam under load is a function of material, section properties, length, means of support or attachment and loading. Engineering tables give design formulas for maximum deflections and slopes created by loads. 

The topography of the discs was measured by means of laser profilometry (UBM, type UBC 14, UBM Messtechnik GmbH, Ettlingen, Germany), in order to determine the amount of wear. A Kr Tiaser beam (beam size 1 pm, wave length 407 and 413 nm) was dynamieally focussed onto the sample and the z-value measured (aceuracy 10 nm) [36]. The sample table can be laterally moved and an area of 13 X 13 mm was measured with a resolution of 120 points/mm. The data were stored in a z-value matrix. 

Mean Length of Radiant Beam (L), This has been evaluated by HotteP as shown in Table 18-4. The mean length is defined in terms of the ratios of length, width, and height, and in terms of diameter and height. 

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