Radius designation

Here the chromophores can be farther apart (10-100 A long-range interactions) since this mechanism does not require any overlapping of orbitals. The Forster radius designates the distance between donor and acceptor at which the efficiency of energy transfer amounts to exactly 50%. Half of the excited donor molecules are then deactivated by fluorescence resonance energy transfer, and the other 50% by fluorescence or phosphorescence. 

It is a well accepted concept that the movement of the molecule is restricted in the pore of diameters which are comparable to those of solute molecules. Many groups have attempted so far to describe the restricted molecular motion in small pores quantitatively. Even though the degree of restriction depends on the distance of the solute molecule from the pore wall (11), it has been common in the literature to express the frictional force as a function of the ratio of the molecular radius to the pore radius, designated as A. 

A in this work). The pore radius used in the Polseuille equation should be, therefore, the smaller radius designated by R]. On the other hand, the interaction force expressed by a potential function such as eq 13 or the frictional function such as eq 39 are exerted throughout the larger pore radius R2. 

The additional electron movement occurs along a circle smaller than r (the electron radius designated in Figure 5.24 as r ). A circular electric current corresponds to this movement... 

It is essential for the rotating-disc that the flow remain laminar and, hence, the upper rotational speed of the disc will depend on the Reynolds number and experimental design, which typically is 1000 s or 10,000 rpm. On the lower lunit, 10 s or 100 rpm must be applied in order for the thickness of tlie boundary layer to be comparable to that of the radius of the disc. 

This expression is the sum of a transient tenu and a steady-state tenu, where r is the radius of the sphere. At short times after the application of the potential step, the transient tenu dominates over the steady-state tenu, and the electrode is analogous to a plane, as the depletion layer is thin compared with the disc radius, and the current varies widi time according to the Cottrell equation. At long times, the transient cunent will decrease to a negligible value, the depletion layer is comparable to the electrode radius, spherical difhision controls the transport of reactant, and the cunent density reaches a steady-state value. At times intenuediate to the limiting conditions of Cottrell behaviour or diffusion control, both transient and steady-state tenus need to be considered and thus the fiill expression must be used. Flowever, many experiments involving microelectrodes are designed such that one of the simpler cunent expressions is valid. 

Figure 12, Results for the C2H molecule as calculated along a circle surrounding Che 2 A -3 A conical intersection, The conical intersection is located on the C2v line at a distance of 1,813 A from the CC axis, where ri (=CC distance) 1.2515 A. The center of the circle is located at the point of the conical intersection and defined in terms of a radius < . Shown are the non-adiabatic coupling matrix elements tcp((p ) and the adiabatic-to-diabatic transformation angles y((p i ) as calculated for (ii) and (b) where q = 0.2 A (c) and (d) where q = 0.3 A (e) and (/) where q = 0.4 A. Also shown are the positions of the two close-by (3,4) conical intersections (designated as X34).

Figure 9.5a shows a portion of a cylindrical capillary of radius R and length 1. We measure the general distance from the center axis of the liquid in the capillary in terms of the variable r and consider specifically the cylindrical shell of thickness dr designated by the broken line in Fig. 9.5a. In general, gravitational, pressure, and viscous forces act on such a volume element, with the viscous forces depending on the velocity gradient in the liquid. Our first task, then, is to examine how the velocity of flow in a cylindrical shell such as this varies with the radius of the shell.

Beckman Elutriation Method. The Beckman elutriation method uses a chamber designed so that the centrifugal effect of the radial inward fluid flow is constant (Fig. 3). The separation chambers are made of transparent epoxy resin which faciUtates observation of the movements of the cell boundary in strobe light illumination. This enables detection of the radius at which the cells are separating. When a mixture of cells, eg, mononuclear white cells, enters the chamber, separation can be achieved by fine tuning centrifuge speed and inward fluid flow to the specific cell group. This is a laboratory method suitable for relatively small numbers of cells. Chambers are available in sizes to handle 2-3 x 10 , 1 2 x 10 , and 1 x 10 ° cells. The Beckman chambers can be appHed to collect mononuclear cells from bone marrow aspirates. 

Elastic Behavior. In the following discussion of the equations relevant to the design of thick-walled hoUow cylinders, it should be assumed that the material of which the cylinder is made is isotropic and that the cylinder is long and initially free from stress. It may be shown (1,2) that if a cylinder of inner radius, and outer radius, is subjected to a uniform internal pressure, the principal stresses in the radial and tangential directions, and <7, at any radius r, such that > r > are given by... 

Provided the design is such that it can be represented by coordinates which fall within the unshaded area, then the residual stress will not exceed the yield strength of the material. When the cylinder is built up of n components of the same material, it can be shown (35,36) that the interference per unit radius required for all cylinder mating operations is given by... 

Katz (R-16) also siwdied wave-plate impingement separators (Fig. 14-Il0b) made up of 90° formed arcs with an 11.1-mm (0.44-iu) radius auda 3.8-mm (0.15-iu) clearance between sheets. The pressure drop is a function of system geometiy. The pressure drop for Katz s system and collection efficiency for seven waves are shown in Fig. 14-111. Katz used the Souders-Brown expression to define a design velocity for the gas between the waves ... 

The design states that the roll must not deflect by more than 0.01 mm at its centre. To achieve this bending stiffness, each roll is to be backed up by one secondary roll as shown in Fig. 14.9(b). Calculate the secondary roll radius needed to meet the specification. The central deflection of the secondary roll is given by... 

Consider the design of a glass window for a vacuum chamber (Fig. 18.6). It is a circular glass disc of radius R and thickness f, freely supported in a rubber seal around its periphery and subjected to a uniform pressure difference Ap = 0.1 MPa (1 atmosphere). The pressure bends the disc. We shall simply quote the result of the stress analysis of such a disc it is that the peak tensile stress is on the low-pressure face of... 

You have been asked to prepare an outline design for the pressure hull of a deep-sea submersible vehicle capable of descending to the bottom of the Mariana Trench in the Pacific Ocean. The external pressure at this depth is approximately 100 MPa, and the design pressure is to be taken as 200 MPa. The pressure hull is to have the form of a thin-walled sphere with a specified radius r of 1 m and a uniform thickness t. The sphere can fail in one of two ways ... 

Component reliability will vary as a function of the power of a dimensional variable in a stress function. Powers of dimensional variables greater than unity magnify the effect. For example, the equation for the polar moment of area for a circular shaft varies as the fourth power of the diameter. Other similar cases liable to dimensional variation effects include the radius of gyration, cross-sectional area and moment of inertia properties. Such variations affect stability, deflection, strains and angular twists as well as stresses levels (Haugen, 1980). It can be seen that variations in tolerance may be of importance for critical components which need to be designed to a high reliability (Bury, 1974). 

At flows different from design eonditions, there exists a eireumferential pressure gradient at the impeller tip and in the volute at a given radius. 

Hatch. J.E., Giamati, C.C., and Jackson, R.J., Application of Radial Equilibrium Condition to Axial-Flow Turbomachine Design Including Consideration of Change of Enthropy with Radius Downstream of Blade Row, NACA RM E54A20 (1954). 

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