Exit effects

AM(from equation 46) + AM(bypass flow) + AM(entrance/exit effects) + AM (baffle plates)... 

Entrance and Exit Effects In the entrance region of a pipe, some distance is required for the flow to adjust from upstream conditions to the fuUy developed flow pattern. This distance depends on the Reynolds number and on the flow conditions upstream. For a uniform velocity profile at the pipe entrance, the computed length in laminar flow required for the centerline velocity to reach 99 percent of its fully developed value is (Dombrowski, Foumeny, Ookawara and Riza, Can. J. Chem. Engr, 71, 472 76 [1993])... 

If the pressure drop over the tubes is not to exceed 2 kN/m2, calculate the minimum number of tubes that are required. Assume that the tube walls are smooth and that entrance and exit effects can be neglected,... 

Determine the excess head loss terms for the pipe (using Equation 4-30), for the fittings (using Equation 4-38), and for any entrance and exit effects (using Equation 4-39). Sum the head loss terms, and compute the net frictional loss term using Equation 4-29. Use the velocity at point 2. 

The K factors for the entrance and exit effects are determined using Equation 4-39. The K factor for the gate valve is found in Table 4-2, and the K factor for the pipe length is given by Equation 4-30. For the pipe entrance,... 

For this solution only the pipe friction will be considered and the exit effects will be ignored. The first consideration is whether the flow is sonic. The sonic pressure ratio is given in Figure 4-13 (or the equations in Table 4-4). For y = 1.4 and Kf = 8.56... 

In an attempt to test the surface renewal theory of gas absorption, Danckwerts and Kennedy measured the transient rate of absorption of carbon dioxide into various solutions by means of a rotating drum which carried a film of liquid through the gas. Results so obtained were compared with those for absorption in a packed column and it was shown that exposure times of at least one second were required to give a strict comparison this was longer than could be obtained with the rotating drum. Roberts and Danckwerts therefore used a wetted-wall column to extend the times of contact up to 1.3 s. The column was carefully designed to eliminate entry and exit effects and the formation of ripples. The experimental results and conclusions are reported by Danckwerts, Kennedy, and Roberts110 who showed that they could be used, on the basis of the penetration theory model, to predict the performance of a packed column to within about 10 per cent. 

Fellinger 25) used a 450 mm diameter column with downcomers and risers in an attempt to avoid the problem of determining any entrance or exit effects. Some of the results for H0G are shown in Table 12.2, taken from Perry s Chemical Engineers Handbook 261. Further discussion on the use of transfer units is included in Section 12.8.8 and in Chapter 11. 

Figure 7.70 Schematic representation of the capillary pressure along its axis curve a, without exit effects curve b with exit effects. From Z. Tadmor and C. G. Gogos, Principles of Polymer Processing. Copyright 1979 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Similarly, one must worry about exit pressure effects, or end corrections. Experimentally, it has been observed that there is a nonzero gange pressnre at the capillary exit, Pex (cnrve b of Fignre 7.70). It has been found that the ratio of exit to entrance effects, Pex tAPent, is between 0.15 and 0.20 and that althongh APgnt does not depend on L/Do, Pex decreases up to L/Dq = 10 and then remains constant. With these observations in mind, we can rewrite Eq. (7.68) to inclnde both entrance and exit effects ... 

The final table of this section shows the corresponding exit effectiveness factors, the apparent rates of reactions of the components at the exit, and the intrinsic rates. 

M 72] [M 73] [P 65] The analysis of cross-sectional velocity profiles (water as fluid Re =12) shows that the intersecting structures have intricate gradient fields near the bars of the internals, while the helical device displays entrance and exit effects over more than one-quarter of the flow field (see [155] e.g. for fluid flow through macroscopic helical static elements) [2],... 

The concentration polarization occurring in electrodialysis, that is, the concentration profiles at the membrane surface can be calculated by a mass balance taking into account all fluxes in the boundary layer and the hydrodynamic conditions in the flow channel between the membranes. To a first approximation the salt concentration at the membrane surface can be calculated and related to the current density by applying the so-called Nernst film model, which assumes that the bulk solution between the laminar boundary layers has a uniform concentration, whereas the concentration in the boundary layers changes over the thickness of the boundary layer. However, the concentration at the membrane surface and the boundary layer thickness are constant along the flow channel from the cell entrance to the exit. In a practical electrodialysis stack there will be entrance and exit effects and concentration... 

These, together with the small Reynolds number in the film, justifies the use of the lubrication approximation. Moreover, the same considerations lead us to neglect exit effects (at x = W), and precise entrance conditions (at x = 0) need not be specified. 

In viscometry, it is usually necessary to correct for end effects (e.g., entrance and exit effects in axial flow instruments) and for slip between sample and viscometer surfaces. 

If this is not the case, neglecting entrance and exit effects can lead to erroneous interpretations [27]. 

Entrance region Fully developed flow region Exit effect region... 

In glass capillary viscometers, both entrance and exit effects depend on the kinetic energy of the fluid stream in the capillary. Based on extensive experimental data, the kinematic viscosity, v = r]/p, data with a correction term for kinetic energy is expressed ... 

In most experimental devices, the main problem is to eliminate the different sources of error. For pressure drop measurements, the pressure sensors must not be intrusive and interfere with the physical phenomenon. In most pubhshed works, the pressure sensors are added to the circuit and the fitting itself can create a singular pressure loss. Two experiments are presented. The first one has a rectangular channel whose hydraulic diameter varies from 100 pm to 1 mm with pressure sensors on either side of the test channel and includes entrance effects. The second one whose hydrauhc diameter is 7.1 pm has the pressure taps far from the inlet and outlet to eliminate entrance and exit effects. 

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