Root-mean-square radial distance

A much more satisfactory random network model has been discussed by Alben and Boutron 82h They used a model, proposed by Polk 78> for Ge(as), scaled to fit the observed nearest neighbor 00 distance of H20(as), and with H atoms added to the OO bonds according to the Pauling ice rule that guarantees the presence of only H20 molecules 65>. In the Polk model the bond length is everywhere the same and the 000 angles are distributed with root mean square deviation of 7° about 109°. For the case of Ge(as), the observed and model radial distribution functions are in excellent agreement. 

Figure 2.14 shows the axial mean velocity on the centerline of the bath, Ua, and the root-mean-square values of the axial and radial turbulence components, M ms,ci and J.J, against the axial distance, z. The measured d value remains almost unchanged in the axial direction and approaches the following empirical correlations originally proposed for a water-air system [9] ... 

The root-mean-square values of the axial and radial turbulence components, n m and i/nns, are normalized by the axial mean velocity on the centerline of the singlephase water jet, Mm,sw, and plotted in Figs. 8.7 and 8.8, respectively. The vertical distance y is nondimensionalized in the same manner as in Fig. 8.6. The measured values of M mis/Mm,sw and v nns/ttm.sw for the single-phase water jet are close to the data of Wygnanski and Fiedler [19]. Below the x axis (y < 0) both M rms/ m,sw and v rms/Mm.sw are nearly independent of the gas flow rate while above the x axis (y > 0) they increase slightly with an increase in Qg. This is because turbulence is generated in the wake of the bubbles [20], and the number of bubbles increases as 2g increases. 

Figure 2.10 (a) The normalized end-to-end distance probability distribution function for a Gaussian chain. The radius of gyration Rg and the hydrodynamic radius R are shown in units of the root mean square end-to-end distance R. (b) Sketch of the long-ranged segment density profile falling inversely with the radial distance from the center of the chain. 

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