Transverse velocity

In simple shear flow where vorticity and extensional rate are equal in magnitude (cf. Eq. (79), Sect. 4), the molecular coil rotates in the transverse velocity gradient and interacts successively for a limited time with the elongational and the compressional flow component during each turn. Because of the finite relaxation time (xz) of the chain, it is believed that the macromolecule can no more follow these alternative deformations and remains in a steady deformed state above some critical shear rate (y ) given by [193] (Fig. 65) ... 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

Sirkar and Hanratty (S13) showed, by means of refined measurements using strip electrodes at different orientations with respect to the mean flow, that transverse velocity fluctuations play a significant part in the turbulent transport very close to the wall, and that the eddy diffusivity may well be dependent on the cube of the distance y+, leading to a Sc1/3 dependence of mass-transfer correlations, which is often found experimentally. 

Figure 10. Double differential cross sections (ddcs = Avj

The number of PSRs with known transverse velocities is continuously growing. New velocity determinations are based on a new model of galactic distribution of free electrons (Cordes, Lazio 2002). Unlike the situation 10 years ago, when updated data on free electrons distribution led to nearly doubling of distances (and, correspondingly, transverse velocities), results of Cordes and Lazio brought serious corrections only for distant PSRs. 

Another method, based on an old idea about radiation pressure, uses the local separation of different isotopes in atomic or molecular beams. If the laser beam which crosses the molecular beam at right angles is tuned to an absorption line of a defined isotope in a molecular beam containing an isotopic mixture, the recoil from the absorption of the laser photons results in a small additional transverse velocity component. This leads to a beam deflection for the absorbing molecules which enables the desired isotope to be collected in a separate collector 154g)... 

The results presented above clearly demonstrate the merits of the counter-current shear layer control as a flame stabilization technique. With the use of the high-resolution PIV, the near flame structure is measured with sufficient detail to obtain the velocity gradients with accuracy. Prom these measurements, it is observed that the transverse velocity gradient dU /dr assumes large values at the nozzle exit as compared to that of laminar premixed Bunsen burner flames. 

In the case where fluid flows in the shell side space of a shell-and-tube-type heat exchanger, with transverse baffles, in directions that are transverse, diagonal, and partly parallel to the tubes, very approximate values of the heat transfer coefficients at the tube outside surfaces can be estimated using Equation 5.12a, if is calculated as the transverse velocity across the plane, including the shell axis [1]. 

The uncertainty principle causes a spread of the transversal velocity of the photoion, Av - h/2M Ax its coordinate is accurately determined to be Ax, where M is the mass of the photoion. This spread, Aux, results in a circle of ion scattering on the screen with a diameter d = 2t Ax, where r is the flight time of the particle from the tip to the screen and R is the distance between the tip and screen. On the other hand, the circle of scattering on the screen, d, is also related to the indeterminacy of the coordinate at the point of detachment Ax(Ax = d/K), where K = R/r is the projector magnification coefficient. 

An ejected photoion can have nonzero transversal velocity, Autr, if a part of the excitation energy is converted to kinetic energy during the photodetachment from the surface. It is assumed that the average kinetic energy of the transverse motion of a photoion equals kin- Then, in a way similar to the above procedure, it is possible to estimate the spatial resolution due to this effect. To achieve the spatial resolution Ax of 3-5 A at Fmax = 0.2 eV/A and r - 103 A, it is necessary to realize a very precise MPI of the chro-mophore on the cooled tip with excess of transversal kinetic energy of only = 10-3 eV. 

Figure 15. Visualization of the Doppler shift d caused by a combination of radial velocity Vr and transverse velocity Vt- From this diagram, we see that large redshifts (d is positive) can be caused even when there is a large velocity toward the observer (Vr is negative) if combined with a sufficiently large transverse velocity.

When the transverse velocity is zero, Fig. 15 shows that the Doppler shift (d) increases (redshift) with increasing radial velocity to the right, away from the observer. The Doppler shift is negative (blueshift) when the radial velocity is negative, to the left, toward the observer. When the radial velocity is zero, even the Doppler shift is zero. 

However, when the transverse velocity differs from zero, everything becomes more complicated. Let us, for instance, study a Doppler shift of 0.5, which could be caused by a radial velocity of 0.38c. This could just as well have been caused by zero radial velocity combined with a transverse velocity of some 0.75c. It could even be caused by a radial velocity of 0.62c combined with the same transverse velocity of 0.75c. In the latter case, a motion toward the observer, which should result in a blueshift, results in a redshift when combined with a sufficiently large transverse velocity. 

From the preceding statements, we understand that the true velocity of an object cannot be deduced from the redshift alone. For a given redshift there exists an upper limit to the radial velocity. It would be a great mistake to take for granted that this upper limit represents the actual velocity of the object. This cannot be determined without knowledge of the transverse velocity, and even then there might exist two possible radial velocities for one redshift, as demonstrated in previous example. 

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