Triangular velocity profile

Most Mossbauer spectrometers use triangular velocity profiles. Saw-tooth motion induces excessive ringing of the drive, caused by extreme acceleration during fast fly-back of the drive rod. Sinusoidal operation at the eigen frequency of the vibrating system is also found occasionally and... 

Fig. 3.3 Velocity control and synchronization of data recording by the multi-channel analyzer (MCA) operated in MCS mode with 512 channels. For the common triangular velocity profile shown here the spectrum is recorded twice, because each velocity increment is reached upon sweeping up and down. The sense of the velocity scales may also be opposite to that shown here, which means the MCA sweep may also start at...

Fig. 3.10 Variation of the spectrometer aperture as a function of the source motion for Mossbauer spectrometers operated in constant acceleration mode with triangular velocity profile, and the resulting nonlinear baseline distortion of the unfolded raw spectra. For simplicity a point-source is adopted, in contrast to most real cases (Rib mm active spot for Co in Rh)...

One can see that the index n of a power-law fluid substantially affects the velocity profile. With increasing pseudoplasticity the distribution of the velocity becomes more and more homogeneous, approaching a quasisolid distribution with profile V = (V) = const in the limit as n —> 0. On the contrary, dilatancy makes the flow field more and more nonuniform, and as n - oo the velocity profile approaches the triangular shape given by... 

By substituting (6.4.8) into (6.4.4)-(6.4.7), one can find the basic characteristics of motion of a power-law fluid in a circular tube. The results of the corresponding calculations [452, 508] are presented in Table 6.5 and are shown in Figure 6.2. One can see that the velocity profiles become more and more filled as the rheological parameter n decreases. The limit case n -> 0 is characterized by a quasisolid motion of the fluid with the same velocity in the entire cross-section of the tube (it is only near the wall that the velocity rapidly decreases to zero). The parabolic Poiseuille profile corresponds to the Newtonian fluid (n = 1). The limit dilatant flow (n — oo) has a triangular profile, which is characterized by a linear law of velocity variation along the radius of the tube. 

Equilateral Triangular Ducts. For equilateral triangle ducts as shown in Fig. 5.27a, the fully developed laminar flow velocity profile and friction factor have been obtained by Marco and Han [155] ... 

H. Rosenberg, Numerical Solution of the Velocity Profile in Axial Laminar Flow through a Bank of Touching Rods in a Triangular Array, Trans. Am. Nucl. Soc., (1) 55-57,1958. 

The fuUy developed laminar velocity profile for isosceles triangular ducts (see Fig. 5a) can be in general determined by solving numerically Eq. 11 with Eq. 12. Shah and London [4] reported the following approximate closed-form solution for the velocity profile for isosceles triangular channels ... 

The velocity and pressure distribution experiment with Montz-pak (Fig. 69) has been repeated with 10 mm spacing between the packing and the wall. This open space creates wall cannels with a cross-section twice that of the triangular gas flow channels. Compartments 1 and 17, situated below tiie wall channels, are closed to avoid the direct feeding of the wall channels. The velocity profile measured at the top and the pressure profile measured at the bottom are shown in Fig. 70. From the velocity profile it is clear that only part of the gas that reaches the wall flows back into the packing. The low velocity measured for channel 6 indicates that this is more pronounced for the bottom... 

The theoretical answer is quite simple if J can indeed be considered constant throughout the film. The velocity field is no longer strictly vertical, but has a horizontal component precisely equal to J. This results in a triangular profile (Figure 9.22) and a height h = eVj J. 

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