Geometry factor ratio

Marks and co-workers (12) have studied the alkyl substituted compounds 7-16. Assuming that INDO/2 molecular orbital calculations on alkyl radicals can reasonably predict experimental electron-nuclear hyperfine coupling constants, a, they have calculated the a values for each of the alkyl substituents. Taking the ratio of the contact shifts of the ortho positions in 7 and vinylic position in 16 as equal to the ratio of calculated a values and the ratio of the geometry factors as equal to the ratio of pseudocontact shifts, Marks and co-workers could solve for the contact and pseudocontact shifts in 7 and 16. Factoring the... 

Fischer has proposed useful and important methods for factoring the isotropic shifts of uranocenes into contact and pseudocontact components (15) values were reported for uranocene, 1,-1, 3,3, 5,5, 7,7 -octamethyluranocene, and 1 1 -bis(trimethyl-si lyl) uranocene using a non-zero value of Xj Fischer arrived at values of yjj2 and y 2 at several temperatures from the ratio of the geometry factor and the isotropic shift for methyl protons in bis(trimethylsilyl)-uranocene, and bulk magnetic susceptibility data, assuming no contact contributions to the isotropic shift of the methyl protons. From the published data of Fischer, the value of y( - y2 at 30°C is 8.78 BM2. 

A geometry factor, which takes into account the ratio of substrate area to volume of the solution used (s). 

If we now define a geometry factor I as the ratio of the molar rate of the equivalent uniform capillary (eq. 7.4-23d) to the molar rate of the diverging capillary (eq. 7.4-22), we obtain ... 

Three further factors are introduced to allow for joints of differing dimensions. The geometry factor varies according to the length to diameter ratio and the bonding area. A diametrical clearance factor falls below unity as the clearance increases above about 0.07 mm (Fig. 1). The type of assembly - whether a clearance fit, press tit or shrink fit - is allowed for via an assembly factor (Table 1). Data are available for certain types of adhesives. ... 

Fp is piping geometry factor, defined by Eq. (3) P) is control valve inJet pressure, in psia Y is expansion factor X is control valve pressure drop ratio, which is the ratio of control valve pressure drop to control valve inlet pressure (absolute) M is vapor molecular weight Tl is control valve inlet temperature in °R (Rankine) ... 

Up, Hg = Poisson ratio for pinion and gear Ep, Ec = modulus of elasticity for pinion and gear Wt = transmitted tangential load at pitch diameter Co = overload factor Co = dynamic factor C = size factor d = pinion pitch diameter F = face width Cm = load-distribution factor Cf= siuface-condition fector I = geometry factor... 

The spherical geometry assumed in the Stokes and Einstein derivations gives the highly symmetrical boundary conditions favored by theoreticians. For ellipsoids of revolution having an axial ratio a/b, friction factors have been derived by F. Perrin, and the coefficient of the first-order term in Eq. (9.9) has been derived by Simha. In both cases the calculated quantities increase as the axial ratio increases above unity. For spheres, a/b = 1. 

The Rayleigh ratio combines the intensity factors with those associated with the geometry of the experiment ... 

The amplitude of the elastic scattering, Ao(Q), is called the elastic incoherent structure factor (EISF) and is determined experimentally as the ratio of the elastic intensity to the total integrated intensity. The EISF provides information on the geometry of the motions, and the linewidths are related to the time scales (broader lines correspond to shorter times). The Q and ft) dependences of these spectral parameters are commonly fitted to dynamic models for which analytical expressions for Sf (Q, ft)) have been derived, affording diffusion constants, jump lengths, residence times, and so on that characterize the motion described by the models [62]. 

Slip factor is defined as the ratio of catalyst residence time in the riser to the hydrocarbon vapor residence time. Some of the factors affecting the slip factor are circulation rate, riser diameter/geometry, and riser velocity. 

Film thickness is controlled by a number of factors. The grain size of the powder imposes a lower limit on its value and rheological characteristics of the cement affect flow (Jorgensen Peterson, 1963). An increase in the powder/liquid ratio or a delay in seating a restoration leads to an increase in film thickness. The geometry of the surfaces to be cemented also affects flow and hence film thickness (Windeler, 1979). 

---