Annulus, average velocity

The average velocity in the annulus flow rate ratio ir and... 

Laminar Flow in a Cylindrical Annulus. Derive all the equations given in Example 3.8-4 showing all the steps. Also, derive the equation for the average velocity Wj Finally, integrate to obtain the pressure drop from z = 0 for p = po to z = L for p = pi. 

In multiwafer LPCVD systems, the convection contribution to the transport of reactants to surface sites in the interwafer region is usually neglected [22]. Consider laminar flow with a velocity profile in the annulus, between the wafers and the reactor walls. This velocity profile is assumed to be constant and contains the ratio of wafer radius to that of the reactor denoted by k. Then in this case, an average velocity, Vavg can be described by [14]... 

As the fluid density and average velocity increases, the particle velocity increases in the annulus. Therefore, particles are easier to be carried out of the borehole by the drilling fluid. 

Results obtained with loop experiments with 0.04 m UO2SO4 solution (F.,-2-10 and L-2-17) are illustrated by the curves in Fig. 5-17 [59]. A portion of line B from Fig. 5-16 is included in Fig. 5-17 for comparison. Corrosion rates for channel specimens in this solution are greater at the same power density than those for specimens in 0.17 m UO2SO4 solutions. The. shape of the curve through the channel data is also different. As will be discussed later, these channel data may l>e interpreted in terms of a beneficial effect of solution velocity on corrosion. The approximate locations of. specimens in the channel with respect to the power density to which the specimen was cxpo.sed and the average velocity of solution at the specimen are indicated in Fig. 5-17. The annulus specimens, which were exposed at low. solution velocities, corroded at higher rates than the channel specimens. 

Heat is to be transferred from one process stream to another by means of a double pipe heat exchanger. The hot fluid flows in a 1 in. sch 40 tube, which is inside (concentric with) a 2 in. sch 40 tube, with the cold fluid flowing in the annulus between the tubes. If both fluids are to flow at a velocity of 8 ft/s and the total equivalent length of the tubes is 1300 ft, what pump power is required to circulate the colder fluid Properties at average temperature p = 55 lbm/ft3, p = 8 cP. 

In an earlier phase of this work [9] the intensities of axial and circumferential components of velocity fluctuation were measured in the TC annulus, using Laser Doppler Velocimetry (LDV), for a wide range of cylinder rotation speeds. On average, the intensities of axial velocity fluctuations were found to be within 25% of the intensities of circumferential velocity fluctuations [9]. As in Ronney et al. [5], turbulence intensities were found to be nearly homogeneous along the axial direction and over most of the annulus width, and to be linearly proportional... 

In order to obtain the kinetic energy term for use in the energy balance equation, it is necessary to obtain the average kinetic energy per unit mass in terms of the mean velocity. The kinetic energy of the fluid flowing per unit time in the annulus between a and... 

FIGURE 55.7 Two-dimensional transmitral velocity profiles recorded at the level of the mitral annulus in a pig [Kim et al., 1994]. (a) systole (b) peak E-wave (c) deceleration phase of early diastole (d) mid-diastolic period (diastasis) (e) peak A-wave (f) time averaged diastolic cross-sectional mitral velocity profile. (Reprinted with permission from the American College of Cardiology, /. Am. Coll Cardiol 24 532-545.)... 

It has to be mentioned that, from the previous definitions, the values of the ratio (W/E) in the region of varying density and the average downward velocity of the particle in the annulus can be calculated according to the following relations ... 

Even though the model is in an development stage, it appears to be very attractive RTD curves can be computed along with the axial variations of the solid recirculation rate and of the average downward velocity of the solid in the annulus. Various parameters have been defined in the model, but no sensitive study has been performed extensively at this time. Only qualitative comparisons have been made between experimental and simulated RTD curves. 

Inside the Wurster tube, the particles show a high rotation (average rotational velocity equals 253.2 rad/s for the study case 1), which is very desirable for the homogenous distribution of the spray droplets on the particle surface to produce a homogenous and closed film. However in a moment only 3.48% of aU particles are situated inside the tube. This results in a smaller number of collisions in comparison with the dense bed in the annulus... 

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