Bends transition losses

Transition losses—Head losses in expansions, contractions, bends, and the like. Turbomachine—Fluid machine that turns or tends to turn about an axis. 

Eastwood and Sarginson described the experimental investigation of the effect of transition curves on the head loss in flow through 90° bends in pipelines [41]. They observed that for purely circular bend the loss at the bend could be expressed in terms of the equivalent length (L ) of the straight pipe to cause the same loss. 

In addition to the radiation loss associated with bending of a fiber, there is a transition loss due to abrupt changes in curvature, as occur at the cross-sectional plane AA of the fibers in Fig. 23-4. As we show below, there is a mismatch between the fields on AA, and, consequently, the incident field on one side excites both the local modes and the radiation field on the other side. The power in the radiation field accounts for the transition loss [4-6]. 

The transition losses discussed in Section 23-10 do not account for power reflected into backward-propagating modes from junctions or changes in bending radius. In Section 20-2, we showed that negligible power is reflected from the endface of a weakly guiding fiber, and consequently, we are justified in ignoring reflection losses. 

Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Viscous Transport. Low velocity viscous laminar dow ia gas pipes is commonplace. Practical gas dow can be based on pressure drops of <50% for low velocity laminar dow ia pipes whose length-to-diameter ratio may be as high as several thousand. Under laminar dow, bends and fittings add to the frictional loss, as do abmpt transitions. 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

Based on these experiments, a kind of flow-pattern map was proposed describing a region of laminar flow where viscous losses dominate, an intermediate region with secondary flow where inertial losses dominate (albeit still not turbulent) and a region of fully developed turbulent flow (see Figure 1.142) [151]. The transitional Reynolds number from the pure laminar to the secondary-flow regime increases with the ratio of bend length to hydraulic diameter. 

The photoinduced CO loss from Cr(CO)6 occurs following a symmetry and spin-allowed transition to produce the a 7 u MLCT excited state. A Jahn-Teller active (f2g bending) mode promotes motion to a conical intersection close to the Frank-Condon state. This provides an efficient barrierless transition to the E component derived from the a 7 g state. This process takes approximately 12.5 fs. The E component is unbound with respect to the M-CO interaction. As the M-CO bond lengthens a further conical intersection with the E component derived from the a 7, u state,... 

It is now convenient to make the approximation that most of the frequencies in the molecule remain constant and that it is only the transitional frequencies which change with R. Thus, in the case of H loss from CH4, it is only the two C—H bends that are transitional. These are the ones that are converted into orbital angular momentum and are thus lost in the course of the reaction. The C—H stretch is the reaction coordinate, while the others remain intact. Hase (1972) and Quack and Troe (1974) introduced the idea of modeling the frequencies in a smooth manner from molecule to products by the use of switching functions. In the spirit of the bond energy bond order (BEBO) model (Johnston, 1966), the transitional frequencies are assumed to vary exponentially according to... 

Calculated from one stretching and one bending frequency, assuming complete loss of the isotopic zero-point energy difference of the reactant in attaining the transition state. 

An insight into the nature of the transition state was provided by deuterium kinetic isotope effect studies in which 1 /1 for conversion of 5-methyl-CPD to 1-methyl-CPD using the perdeuterio compound was used to determine A . Here, log /l = -1.0 - 2450/2.3RT, which indicates hydrogen, and not deuterium, tunneling although the large temperature dependence was also attributed to a non-linear transition state with nearly complete loss of one C-H bending mode (Scheme 6.2). ... 

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