Velocity profile down channel

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...

Velocity Profile Effects Many variables can influence the accuracy of specific flow measurement methods. For example, the velocity profile in a closed conduit affects many types of flow-measuring devices. The velocity of a fluid varies from zero at the wall and at other stationary solid objects in the flow channel to a maximum at a distance from the wall. In the entry region of a conduit, the velocity field may approach plug flow and a constant velocity across the conduit, dropping to zero only at the wall. As a newtonian fluid progresses down a... 

To obtain the velocity profile of the polymer in down channel direction, v, we start with the appropriately simplified equation of motion in rectangular coordinates... 

In macroscopic reactors, knowledge of the velocity profile in the channel cross-section is a necessary and sufficient prerequisite to describe the material transport. In microscopic dimensions down to a few micrometers, diffusion also has to be considered. In fact, without the influence of diffusion, extremely broad residence time distributions would be found because of the laminar flow conditions. Superposition of convection and diffusion is called dispersion. Taylor [91] was among the first to notice this strong dominating effect in laminar flow. It is possible to transfer his deduction to rectangular channels. A complete fluid dynamic description has been given of the flow, including effects such as the influence of the wall, the aspect ratio and a chemical wall reaction on the concentration field in the cross-section [37]. 

Figure 6.3 Down-channel velocity profiles for different pumping situations with a single screw extruder.

If we combine the flow generated by the down channel and cross channel flows, a net flow is generated in axial or machine direction (w ) of the extruder, schematically depicted in Fig. 6.5. As can be seen, at open discharge, the maximum axial flow is generated, whereas at closed discharge, the axial flow is zero. From the velocity profiles presented in Fig. 6.5 we can easily deduce, which path a particle flowing with the polymer melt will take. 

Figure 6.5 Down channel, cross channel and axial velocity profiles for various situations that arise in a single screw extruder.

Fig. 6.14 Cross-channel, down-channel, and axial velocity profiles for various Qp/Qj values, in shallow square-pitched screws [Reproduced by permission from J. M. McKelvey, Polymer Processing, Wiley, New York, 1962.]...

Let us next consider the simple isothermal drag flow (dP/dz = 0) of a shear-thinning fluid in the screw channel. The cross-channel flow, induced by the cross-channel component of the barrel surface velocity, affects the down-channel velocity profile and vice versa. In other words, the two velocity profiles become coupled. This is evident by looking at the components of the equation of motion. Making the common simplifying assumptions, the equation of motion in this case reduces to... 

The cross- and down-channel velocity profiles are (see Section 6.3) ... 

Thus, the operating conditions affect the down-channel velocity profile, but not the crosschannel velocity profile. At closed discharge conditions (Qp/Qd = — 1), both the down-channel and cross-channel velocities vanish at / 2/3, implying that the whole plane at... 

Fig. 10.15 (a) Velocity profile in the down-channel direction on a helically wound plane in the... 

The SSE is an important and practical LCFR. We discussed the flow fields in SSEs in Section 6.3 and showed that the helical shape of the screw channel induces a cross-channel velocity profile that leads to a rather narrow residence time distribution (RTD) with crosschannel mixing such that a small axial increment that moves down-channel can be viewed as a reasonably mixed differential batch reactor. In addition, this configuration provides self-wiping between barrel and screw flight surfaces, which reduces material holdback to an acceptable minimum, thus rendering it an almost ideal TFR. 

Problem 3-2. Film Flow. A liquid film is flowing down an inclined wall as illustrated in the figure. The channel is configured so that the air in the channel is open to the atmosphere. Assume that the interface is flat and parallel to the walls. Determine the steady-state velocity profile in the liquid film and the volumetric flow rate (per unit width) down the wall when I12 -> oo. How large must I12 be in order to neglect the presence of the upper wall on the volumetric flow rate of the liquid Discuss the limiting cases of the angle 0 —> 0 and 6 - n/2. In all cases determine the force exerted by the fluid on the lower wall. 

Laminar Flow. The Graetz or Leveque solutions25 26 for convective heat transfer in laminar flow channels, suitably modified for mass transfer, may be used to evaluate the mass transfer coefficient where the laminar parabolic velocity profile is assumed to be established at the channel entrance but where the concentration profile is under development down the full length of the channel. For all thin-channel lengths of practical interest, this solution is valid. Leveque s solution26 gives ... 

From the velocity profile in the down-channel direction the throughput of the pump zone of a single-screw extruder can be obtained by integration ... 

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