Deflection angle

When actual mass flow through the expanders is lowered, efficiency varies according to power loss, deflective angle of gas in the leading edge of the rotating blades, and pressure drop across the inlet butterfly valve. The pressure drop increases as the valve closes. 

As long as the volume flow is kept near design point, both the deflection angle and pressure drop can be corrected. Temperature differential increase is limited by metallurgy, so it is neglected in analytical calculations. This evaluation is based on inlet pressure changes. The new volume at a different pressure is calculated by the ideal gas equation ... 

Figure 7.84 shows the approximate relation between the wake size and the angle of cone deflection for the typical hood. Wake size increases ( effective suction area decreases) with an increase in the angle of the hood deflection. Thus, it can be recommended that the value for hood deflection angle not exceed tf/4. 

Determine the deflection tool-face orientation, tool deflection angle and tool facing change from original course line angle if the data are as follows ... 

Describe a circle about p.B with a radius of CB = 4°6 (read off from the diagram). This is the desired tool deflection angle. 

The original hole direction and inclination were measured to be S60°W and 6°, respectively. To obtain a new hole direction of S75°W with an inclination angle of 7°, a whipstock with the deflection angle of 2° was used and oriented correctly. 

After drilling 90 ft, a checkup measurement was performed that revealed that the hole direction is S72°W and the inclination is 6°30 . Determine the magnitude of roll-off for this system and the real deflection angle of the whipstock. How should the whipstock be oriented to drill a hole with a direction of S37°W and inclination of 5.5° ... 

Describe a circle about p.A with a radius of OB = 1°36 which is the whipstock true deflection angle. 

What is the tool orientation and deflecting angle (dogleg) necessary to achieve this turn and build ... 

From semiclassical scattering theory [68,69], it is known that a negative dependence of (0, E) on 0 indicates scattering into positive deflection angles, and vice versa. The terms nearside and farside are sometimes used to describe these two types of scattering (see Fig. 12). Hence, the reason that GP effects cancel in the state-to-state ICS is that the 1-TS and 2-TS paths scatter in opposite senses (with respect to the center-of-mass). There is thus a mapping between the sense in which the reaction paths loop around the Cl (clockwise for 1 -TS, counterclockwise for 2-TS), and the sense in which the products scatter into space. 

To complete the explanation of why GP effects cancel in the ICS, we need to explain why the 2-TS paths scatter into negative deflection angles. (It is well known that the 1-TS paths scatter into positive deflection angles via a direct recoil mechanism [55, 56].) We can explain this by following classical trajectories, which gives us the opportunity to illustrate a further useful consequence of the theory of Section II. 

Figure 12. Diagram illustrating the difference between nearside scattering into positive deflection angles 0, and farside scattering into negative . The arrow (chains) represents the initial approach direction of the reagents in center-of-mass frame the gray rectangle represents the spread of impact parameters in the initial plane wave. Most of the 1-TS paths scatter into positive , and most of the 2-TS paths into negative 0.

Figure 14 shows a representative 2-TS trajectory, which demonstrates that the 2-TS paths follow a direct S-bend insertion mechanism. The trajectory passes through the middle of the molecule, and avoids the Cl this forces the products to scatter into negative deflection angles. The 2-TS QCT total reaction... 

Figure 13. Density plot of the correlation between the deflection angle, 0, and the total angular momentum, J, for 1-TS (open diamonds) and 2-TS (circles) trajectories at 2.3-eV total energy. Note, only 5000 trajectories are plotted for each type for clarity.

Figure 14. Classical trajectories for the H + H2(v = l,j = 0) reaction representing a 1-TS (a-d) and a 2-TS reaction path (e-h). Both trajectories lead to H2(v = 2,/ = 5,k = 0) products and the same scattering angle, 0 = 50°. (a-c) 1-TS trajectory in Cartesian coordinates. The positions of the atoms (Ha, solid circles Hb, open circles He, dotted circles) are plotted at constant time intervals of 4.1 fs on top of snapshots of the potential energy surface in a space-fixed frame centered at the reactant HbHc molecule. The location of the conical intersection is indicated by crosses (x). (d) 1-TS trajectory in hyperspherical coordinates (cf. Fig. 1) showing the different H - - H2 arrangements (open diamonds) at the same time intervals as panels (a-c) the potential energy contours are for a fixed hyperradius of p = 4.0 a.u. (e-h) As above for the 2-TS trajectory. Note that the 1-TS trajectory is deflected to the nearside (deflection angle 0 = +50°), whereas the 2-TS trajectory proceeds via an insertion mechanism and is deflected to the farside (0 = —50°).

Fig. 2. The geometry of the two-angle fiber can be characterized by the deflection angle 6 and the dihedral angle 0. Also indicated is B, characterizing the linker length, and the nucleosome diameter 2Rq. For simplicity, the nucleosomes are represented by spheres connected via links, the linker DNA. The arrows indicate the nucleosomal superhelix axis.

In the expansion wave, the flow velocity is increased and the pressure, density, and temperature are decreased along the stream line through the expansion fan. Since Oj > 02, it follows that Mi flow through an expansion wave is continuous and is accompanied by an isentropic change known as a Prandtl-Meyer expansion wave. The relationship between the deflection angle and the Mach number is represented by the Prandtl-Meyer expansion equation.l - l... 

In the following, we discuss the detection limit of the optical beam deflection method. First, the relation between the variation of tip height Az and the deflection angle 0 at the end of the cantilever with length I is, according to Eq. (F.24),... 

We define a scattering (or deflection) angle, x, as in Fig. 2.2, an azimuth, solid angle, Q, so that d2Q = sin dx dq>. The differential scattering cross section is defined as the number AN of particles scattered every second into the solid angle A 2 around x,

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Before we use Eq. (30) to determine the deflection angles of the light near the proton in the range Xce-Xcp, it is necessary to find out how this equation can be applied for distances r > Xce, where gravitational constant G is valid. 

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