Entrance and Exit Effects

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,... 

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 ... 

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... 

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]. 

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. 

The pressure drop requirements could act in direct opposition to the requirements for quick heat-up, for example in the hght-off converter apphcation where small diameter would be most beneficial. Hence, an understanding of the characteristics that influence pressure drop is important for the overall design. The pressure drop through a cellular catalyst support is composed of two parts (7), the first (referred to as the core pressure drop) is proportional to the flow rate while the second (composed of entrance and exit effects) is proportional to the square of the flow rate. At flow rates of interest for most automotive apphcations the hnear part dominates. The core pressure drop is (8) ... 

Dullien (1992) and Ferrand (1992) have applied numerical particle tracking methods to compute dispersion coefficients for such networks. In the study by Ferrand (1992) the conductivity of each bond was calculated using an expression that included entrance and exit effects as fluid moves between larger sites and narrower bonds, as well as the resistance of the bond itself. The lattice dispersivity was shown to increase linearly as the geometric standard deviation of the bond-size distribution was increased. Although not widely used at present, this modeling approach offers much promise for future research on the interplay between pore shape and size distribution in determining the relationship between K and Pn. 

Typically, WPC based on polypropylene and polyethylene show deviation from the Cox-Merz rule. This is due to the different nature of flow. Capillary flow is a pressure-driven flow, including entrance and exit effects, wall slip, friction in the barrel, and orientation effects. Parallel-plate flow is pure drag shear flow, in which particle-particle and matrix-particle interactions result in higher viscosities for filled polymers. In other words, a straightforward question is a 100-fold increase in shear rate and 100-fold increase in frequency result in the same effects the answer would be yes for neat polymers, and no for wood-filled composites. 

For an elementary, unifying review of entrance-and-exit effects in viscoelastic fluids, see Hagler [87], For a thorough analysis of viscoelastic fluids, see Bird et al. [88]. 

Neglect the entrance and exit effects in the tube as well as the changes in kinetic energy. Assume laminar flow in the tube and (i) power-law behaviour, and (ii) Bingham plastic behaviour. 

A number of research investigations have recently been reported to elucidate several interesting aspects of EDL overlap. For example, Qiakraborty and Padhy [3] reported the consequences of induced pressure gradients due to entrance and exit effects in electroosmotically driven flows through nanopores in the presence of EDL overlap. Effects of EDL overlap in flie context of AC electroosmosis have also been recently analyzed in a comprehensive manner [7, 8]. Other than using the traditional approaches... 

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