Acceleration-velocity correlation

Figure 13-6 The Eckert flood velocity correlation. (Fp = packing factor, ft"1 see Table 13-7. g = acceleration of gravity, ft/s2. Gvsf = mass velocity of the vapor, superficial, flood, lb/s-ft2. wL = liquid mass flow rate, lb/s. wv = vapor mass velocity, lb/s. pv = density of vapor, lb/ft3. pL = density of liquid, lb/ft3. p, = viscosity of vapor, lb/ft-s. pw — viscosity of water, lb/ft-s.) [J. S. Eckert, Chem. Eng. Prog.. 63(3) 39 (1949), by courtesy American Institute of Chemical Engineers.]...

Figure 10.7. (a) Positions of ions following delayed extraction showing normal mass dependence of space-velocity-correlated focusing, (b) Positions of ions after correction using mass-correlated acceleration. 

The AeroSizer, manufactured by Amherst Process Instmments Inc. (Hadley, Massachusetts), is equipped with a special device called the AeroDisperser for ensuring efficient dispersal of the powders to be inspected. The disperser and the measurement instmment are shown schematically in Figure 13. The aerosol particles to be characterized are sucked into the inspection zone which operates at a partial vacuum. As the air leaves the nozzle at near sonic velocities, the particles in the stream are accelerated across an inspection zone where they cross two laser beams. The time of flight between the two laser beams is used to deduce the size of the particles. The instmment is caUbrated with latex particles of known size. A stream of clean air confines the aerosol stream to the measurement zone. This technique is known as hydrodynamic focusing. A computer correlation estabUshes which peak in the second laser inspection matches the initiation of action from the first laser beam. The equipment can measure particles at a rate of 10,000/s. The output from the AeroSizer can either be displayed as a number count or a volume percentage count. 

S. Han, S. Stapf, B. Bliimich 2000, (Two-dimensional PFG-NMR for encoding correlations of position, velocity and acceleration in fluid transport), J. Magn. Reson. 146, 169. 

The terms represent, respectively, the effect of pressure gradient, acceleration, line friction, and potential energy (static head). The effect of fittings, bends, entrance effects, etc., is included in the term Ke correlated as a number of effective velocity heads. The inclination angle 0 is the angle to the horizontal from the elevation of the pipe connection to the vessel to the discharge point. The term bi is the two-phase multiplier that corrects the liquid-phase friction pressure loss to a two-phase pressure loss. Equation (23-39) is written in units of pressure/density. 

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

We shall see that a conditional acceleration model in the form of (6.48) is equivalent to a stochastic Lagrangian model for the velocity fluctuations whose characteristic correlation time is proportional to e/k. As discussed below, this implies that the scalar flux (u,

joint velocity, composition PDF level, and thus that a consistent scalar-flux transport equation can be derived from the PDF transport equation. 

In a later publication (14) Isbin et al. show the effect of using different void-fraction correlations for the calculation of acceleration effects in horizontal steam-water flow when critical velocities are approached. In this work, additional void-fraction correlations are given The Fauske model (for annular flow when velocities are very high) results in... 

Also, one classical question is whether dust formation initiates mass-loss or whether dust is formed as a result of mass-loss. It is to be noted that the latter process may be rather easy, once mass-loss occurs by another mechanism. This problem can be examined on the basis of recent observations of CO radio emission lines, by which stellar mass-loss rate has been determined with better accuracy than by any other method for a large sample of red giant stars, and terminal flow velocities have also been determined with high accuracy( e.g.,Knapp,Morris,1985). The result revealed that the momentum in the stellar wind and that in the stellar radiation do not necessarily show good correlation(e.g.,Zuckerman,Dyck,1986). Also, a necessary condition for the winds to be accelerated by radiation pressure on dust( Mv [Pg.160]

The important point to note here is that the 2nd moment of Ky(t) depends on the 2nd and 4th moments of y(t). The 2nd moments of each of the three previously mentioned autocorrelation functions may be calculated from ensemble averages of appropriate functions of the positions, velocities, and accelerations created in the dynamics calculations. Likewise, the 4th moment of the dipolar autocorrelation function may also be calculated in this manner. However the 4th moments of the velocity and angular momentum correlation functions depend on the derivative with respect to time of the force and torque acting on a molecule and, hence, cannot be evaluated directly from the primary dynamics information. Therefore, these moments must be calculated in another manner before Eq. (B.3) may be used. 

It has been defined vaguely as shattering power , and attempts were made to correlate it with empirical tests, such as the Sand Test, and with properties such as detonation velocity or pressure, or energy output. More recently, it has been defined as the ability to accelerate metal, as measured by a modified Cylinder Wall Test. Data in Table 5 show that TNT has low brisance compared to other expls regardless of the test used Power... 

Early RPB researchers discovered that this flooding correlation for packed towers applied equally well to RPBs when the gravity term (g) was replaced by centrifugal acceleration (ra>2). As acceleration increases, the gas flooding velocity (Uq) increases in order to maintain the same value of the first term. Since the ratio of liquid (L) to gas (G) flow remains constant, liquid flow increases commensur-ately with gas flow. Most researchers observed higher gas velocities before the onset of flooding than predicted by the Sherwood correlation (17,26,27). 

Velocity and acceleration, however, may be correlated - they certainly are in a Brownian motion - and the velocity sdf-correlation has therefore in many situations a non-zero initial slope. This is so even for a particle moving quite freely betwemi r tecting walls. 

This implies that flow rate is proportional to disk area while rotational speed should remain constant. Centrifugal acceleration would be increased in proportion to F for this system, as would radial velocity. Mass transfer performance based on the previous correlation would indicate increased performance from this scaling. 

---