Square rotation effects

Kelly. Because of its greater seal effectiveness within the rotating head, a hexagonal rather than a square kelly should be used in air (or gas) drilling operations. 

A disadvantage of this technique is that isotopic labeling can cause unwanted perturbations to the competition between pathways through kinetic isotope effects. Whereas the Born-Oppenheimer potential energy surfaces are not affected by isotopic substitution, rotational and vibrational levels become more closely spaced with substitution of heavier isotopes. Consequently, the rate of reaction in competing pathways will be modified somewhat compared to the unlabeled reaction. This effect scales approximately as the square root of the ratio of the isotopic masses, and will be most pronounced for deuterium or... 

The diffusivities thus obtained are necessarily effective diffusivities since (1) they reflect a migration contribution that is not always negligible and (2) they contain the effect of variable properties in the diffusion layer that are neglected in the well-known solutions to constant-property equations. It has been shown, however, that the limiting current at a rotating disk in the laminar range is still proportional to the square root of the rotation rate if the variation of physical properties in the diffusion layer is accounted for (D3e, H8). Similar invariant relationships hold for the laminar diffusion layer at a flat plate in forced convection (D4), in which case the mass-transfer rate is proportional to the square root of velocity, and in free convection at a vertical plate (Dl), where it is proportional to the three-fourths power of plate height. 

A reciprocal proportionality exists between the square root of the characteristic flow rate, t/A, and the thickness of the effective hydrodynamic boundary layer, <5Hl- Moreover, f)HL depends on the diffusion coefficient D, characteristic length L, and kinematic viscosity v of the fluid. Based on Levich s convective diffusion theory the combination model ( Kombi-nations-Modell ) was derived to describe the dissolution of particles and solid formulations exposed to agitated systems [(10), Chapter 5.2]. In contrast to the rotating disc method, the combination model is intended to serve as an approximation describing the dissolution in hydrodynamic systems where the solid solvendum is not necessarily fixed but is likely to move within the dissolution medium. Introducing the term... 

For a free vortex, it is shown in Volume 1, Chapter 2, that the product of the tangential velocity and the radius of rotation is a constant. Because of fluid friction effects, this relation does not hold exactly in a cyclone separator where it is found experimentally that the tangential velocity is more nearly inversely proportional to the square root of radius,... 

It should be noted in passing that Mulliken also examined the isotope effect on the quadratic terms in the equations for the band heads. These ratios should theoretically show an isotope effect proportional to the reduced masses of the diatomic molecules (rather than the square root of the reduced masses). While Mulliken concludes that these ratios also confirm that the molecule is BO rather than BN, the four experimental ratios show a fairly large scatter so that the case for identifying the molecule is not as strong as that from the experimental a and b ratios. He also measured some of the rotational lines in the spectra of BO and considered the measured and theoretical isotope effects. Here one experimental isotope ratio checks the theoretically calculated ratio quite well, but for the other two the result was unsatisfactory. However, Mulliken judged the error to be within the experimental uncertainty. 

It should, however, be mentioned that Mulliken s study of the BO system has been followed over the years by many others, An extensive study by Jenkins and McKellar (1932) should be mentioned explicitly. This study involved the long wavelength band of BO. The same method as that used by both Jevons and Mulliken to produce the BO was used in this work. The new (present day) quantum mechanics was used in the theoretical interpretation. Both the vibrational and the rotational isotope effects were observed and agree with theory. One motivation for this work was to determine how well the isotopic ratio of the square roots of the two relevant isotopic masses (10B and nB) agrees with the ratio obtained from Aston s mass spectrometric measurements and hence how well isotopic mass ratios determined from band spectra compare with those obtained using Aston s mass spectrograph. 

This allocation of experiments has the effect of making the normalized uncertainty and normalized information contours more axially symmetric (the design isn t quite rotatable there are still only four mirror-image planes of reflection symmetry). However, because no experiments are now being carried out at the center point, the amount of uncertainty is greater there (and the amount of information is smaller there). The overall effect is to provide a normalized information surface that looks like a slightly square-shaped volcano. 

Recent microwave data for the potential interstellar molecule Sis is used together with high-level coupled-cluster calculations to extract an accurate equilibrium structure. Observed rotational constants for several isotopomers have been corrected for effects of vibration-rotation interaction subsequent least-squares refinements of structural parameters provide the equilibrium structure. This combined experimental-theoretical approach yields the following parameters for this C2v molecule re(SiSi) = 2.173 0.002A and 0e(SiSiSi) = 78.1 O.2 ... 

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