Plates laminar flow

Enough space must be available to properly service the flow meter and to install any straight lengths of upstream and downstream pipe recommended by the manufacturer for use with the meter. Close-coupled fittings such as elbows or reducers tend to distort the velocity profile and can cause errors in a manner similar to those introduced by laminar flow. The amount of straight pipe required depends on the flow meter type. For the typical case of an orifice plate, piping requirements are normally Hsted in terms of the P or orifice/pipe bore ratio as shown in Table 1 (1) (see Piping systems). 

A. Laminar, local, flat plate, forced flow... 

O. Laminar flow, vertical parallel plates, forced and natural convection... 

Mori, S., M. Kataya, and A. Tanimoto, Performance of Counter-flows, Parallel Plate Heat Exchangers Under Laminar Flow Conditions, Heat Trans. Eng, V. 2, July-Sept. (1980) p. 29. 

The plate heat exchanger, for example, can be used in laminar flow duties, for the evaporation of fluids with relatively high viscosities, for cooling various gases, and for condensing applications where pressure-drop parameters are not excessively restrictive. 

A note of caution on the use of photo-etched channels has been offered by RAMSHAWfl3 ) who points out that the system is attractive in principle provided that severe practical problems such as fouling are not encountered. With laminar flow in matrices with a mean plate spacing of 0.3-1 mm, volumetric heat transfer coefficients of 7 MW/m3 K have been obtained with modest pressure drops. Such values compare with 0.2 MW/m3 K for shell and tube exchangers and 1.2 MW/m3 K for plate heat exchangers. 

The problem of axial conduction in the wall was considered by Petukhov (1967). The parameter used to characterize the effect of axial conduction is P = (l - dyd k2/k ). The numerical calculations performed for q = const, and neglecting the wall thermal resistance in radial direction, showed that axial thermal conduction in the wall does not affect the Nusselt number Nuco. Davis and Gill (1970) considered the problem of axial conduction in the wall with reference to laminar flow between parallel plates with finite conductivity. It was found that the Peclet number, the ratio of thickness of the plates to their length are important dimensionless groups that determine the process of heat transfer. 

Which is better for isothermal chemical reactions, pressure driven flow or drag flow between flat plates Assume laminar flow with first-order chemical reaction and compare systems with the same values for the slit width (2Y=H), length, mean velocity, and reaction rate constant. 

Models based on Eqs. (47)-(50) have been used in the past to describe the disruption of unicellular micro-organisms and mammalian (hybridoma) cells [62]. The extent of cell disruption was measured in terms of loss of cell viability and was found to be dependent on both the level of stress (deformation) and the time of exposure (Fig. 25). All of the experiments were carried out in a cone and plate viscometer under laminar flow conditions by adding dextran to the solution. A critical condition for the rupture of the walls was defined in terms of shear deformation given by Eq. (44). Using micromanipulation techniques data were provided for the critical forces necessary to burst the cells (see Fig. 4)... 

Flow chambers are based on the theory of parallel plates. They should provide a defined two-dimensional laminar flow of medium over a monolayer of cells. Based on this theory Levesque et al.[9] described an equation for the calculation of the shear stress. Shear stress i is then given as... 

Deviation from laminar shear flow [88,89],by calculating the material functions r =f( y),x12=f( Y),x11-x22=f( y),is assumed to be of a laminar type and this assumption is applied to Newtonian as well as viscoelastic fluids. Deviations from laminar flow conditions are often described as turbulent, as flow irregularities or flow instabilities. However, deviation from laminar flow conditions in cone-and-plate geometries have been observed and analysed for Newtonian and viscoelastic liquids in numerous investigations [90-95]. Theories have been derived for predicting the onset of the deviation of laminar flow between a cone and plate for Newtonian liquids [91-93] and in experiments reasonable agreements were found [95]. 

Flow irregularities at gap angles of 30° were observed in viscoelastic liquids [94]. It has been indicated in theoretical treatments that the possibility of secondary flows [96,97] in rotational devices is to be expected if the gap angle is much greater than 5°. For viscoelastic fluids deviations from laminar flow have only been reported in cone-and-plate geometries with gap angles above 10°. 

Table IV includes theoretical transition times (C2, R14, SI7c) in laminar flow between parallel plates, following a concentration step at the wall (Leveque mass transfer). Clearly, in laminar flow (Re 100 or lower), transition times are comparable to those in laminar free convection. Here, however, the dependence on concentration (through the diffusivity) is weak. The dimensionless time variable in unsteady-state mass transfer of the Leveque type is...

Experimental data relative to unsteady-state mass transfer as a result of a concentration step at the electrode surface are not available. However, for a linear increase of the current to parallel-plate electrodes under laminar flow, Hickman (H3) found that steady-state limiting-current readings were obtained only if the time to reach the limiting current at the trailing edge of the plate (see Section IV,E), expressed in the dimensionless form of Eq. (18), is... 

An analogous situation can be envisioned if the medium is stationary (or a fluid in laminar flow in the x direction) and the temperature difference (7) — T0) is replaced by the concentration difference (Cj — C0) of some species that is soluble in the fluid (e.g., a top plate of pure salt in contact with water). If the soluble species (e.g., the salt) is A, it will diffuse through the medium (B) from high concentration (Cj) to low concentration (Co). If the flux of A in the y direction is denoted by nAy, then the transport law is given by... 

Example 5-9 Flow Down an Inclined Plane. Consider the steady laminar flow of a thin layer or film of liquid down a flat plate that is inclined at an angle 6 to the vertical, as illustrated in Fig. 5-10. The width of the plate is W (normal to the plane of the figure). Flow is only in the v direction (parallel to... 

Flow between two flat parallel plates that are closely spaced (h W) is shown in Fig. 7-1. The hydraulic diameter for this geometry is Db = 4A/Wp = 2h, and the solution for a Newtonian fluid in laminar flow is... 

Fig. 3. Diagrams of electrochemical cells used in flow systems for thin film deposition by EC-ALE. A) First small thin layer flow cell (modeled after electrochemical liquid chromatography detectors). A gasket defined the area where the deposition was performed, and solutions were pumped in and out though the top plate. Reproduced by permission from ref. [ 110]. B) H-cell design where the samples were suspended in the solutions, and solutions were filled and drained from below. Reproduced by permission from ref. [111]. C) Larger thin layer flow cell. This is very similar to that shown in 3A, except that the deposition area is larger and laminar flow is easier to develop because of the solution inlet and outlet designs. In addition, the opposite wall of the cell is a piece of ITO, used as the auxiliary electrode. It is transparent so the deposit can be monitored visually, and it provides an excellent current distribution. The reference electrode is incorporated right in the cell, as well. Adapted from ref. [113],...

The boundary layer thickness gradually increases until a critical point is reached at which there is a sudden thickening of the boundary layer this reflects the transition from a laminar boundary layer to a turbulent boundary layer. For both types, the flow outside the boundary layer is completely turbulent. In that part of the boundary layer near the leading edge of the plate the flow is laminar and consequently this is known as a... 

We might want to increase a> to generate larger limiting currents in order to increase the precision. Improving the precision by this means is valid at low to medium rotation rates (that is, up to about 100 cycles per second) because the motion of solution over the face of the electrode is smooth and reproducible. We say that the flow is laminar. (The word laminar comes from the Latin root lami, meaning thin layer or plate .) We can then see how laminar flow implies that solution readily flows over itself in a smooth and reproducible way. 

Mass transfer can produce films of nonuniform thickness because the deposition rate can depend on the velocity field u over the sohd. Regions with high whl have the highest deposition rates in a mass-transfer-hmited process. For flow over a flat plate of length L the average Sherwood number for laminar flow is given by the expression... 

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