Over a plate

The extent of entrainment of the liquid by the vapour rising over a plate has been studied by many workers. The entrainment has been found to vary with the vapour velocity in the slot or perforation, and the spacing used. Strang 60-1, using an air-water system, found that entrainment was small until a critical vapour velocity was reached, above which it increased rapidly. Similar results from Peavy and Baker 6 11 and Colburn 62 have shown the effect on tray efficiency, which is not seriously affected until the entrainment exceeds 0.1 kmol of liquid per kmol of vapour. The entrainment on sieve trays is discussed in Section 11.10.4. 

Spread 10 pL over a plate and 100 pL over another plate. 

It may be noted that the case flow over a flat plate while the case of equal to 7r, i.e., m equal to one, corresponds to flow over a plate set normal to the direction of the undisturbed freestream as shown in Fig. 3.11. The latter flow closely represents flow near the stagnation point on a bluff body. 

The program, as available, will calculate flow over a plate with a varying freestream velocity and varying surface temperature. These variations are both assumed to be described by a third-order polynomial, i.e., by ... 

The above analysis dealt with the effects of dissipation on the flow over an adiabatic flat plate. Attention is now turned to flow over a plate that is kept at a uniform temperature of Tw. 

The temperature distribution in flow over a plate kept at a uniform temperature when there are no dissipation effects and the temperature distribution in flow over an adiabatic plate accounting for dissipation effects have thus now been obtained. These two solutions were denoted by and 0a, respectively. Because the energy equation is linear, it is to be expected that the solution for flow over a plate kept at a uniform temperature when dissipation is accounted for will be some form of linear combination of these two solutions [9]. To investigate this possibility, the following dimensionless temperature will be introduced ... 

Hence, it seems reasonable to assume that in the case of flow with viscous dissipation over a plate kept at a uniform temperature the solution will have the form ... 

Consider turbulent boundary layer flow over a plate which has a local temperature of Tw. The flow situation is shown in Fig. 6.2. 

Modify the integral equation analysis of flow over a plate with an unheated leading edge section that was given ir this chapter to apply to the case where the plate has a heated leading edge section followed by an adiabatic section. 

In forced convective turbulent boundary layer flow over a plate the velocity and temperature distributions are approximately given by ... 

The above set of equations are, of course, very similar to the boundary layer equations governing free convective flow over a plate. 

The major advantage of the spiral configuration over a plate-and-frame configuration is that there is minimal leakage associated with the spiral configuration. The spiral wound module does not require periodic tightening of nuts and bolts to prevent leaks, unlike plate-and-frame modules. Limitations of the spiral configuration include inferior current and flow distribution relative to plate-and-frame modules, as well as difficulty in assembly and field membrane replacement.17... 

The mass balance equation of a component i over a plate k when steady state is reached is... 

In the case of fixed-bed operations (elution chromatography, SMB, etc.), if the column is simulated to a series of mixed cells, the mass balance equation of a component i over a plate k is... 

By setting (i.S prod/Reynolds number, and hence the minimum entropy production at known values q and./,. For a laminar flow over a plate, we have... 

For a turbulent flow over a plate, the optimum Reynolds number becomes... 

The accuracy of liquid-handling operations in HTS is analyzed by three key parameters derived from test experiments in which equal volume aliquots are pipetted or dispensed over the plate. The trueness over the plate is a measure of the deviation of the average of the actual volume dispensed over a plate from the intended volume. It is measured gravimetrically and is defined as... 

As in the case of the fluid flow over a plate, a boundary layer is also formed. With the liquid phase considered as analogous to the plate, a gas phase boundary layer is formed with the gas phase considered as analogous to the plate, the liquid phase boundary layer is formed (see figures). These boundary layers are also called films. 

THE BOUNDARY LAYER IN TURBULENT FLOW OVER A PLATE... 

Tlie hypothetical line of u 0.99V divides the flow over a plate into two regions the boundary layer region, in which the viscous effects and the velocity changes are significant, and tlie irrotational flow region, in which the frictional effects are negligible and the velocity remains essentially constant. 

C What is the physical significance of the Reynolds number How is it defined for external flow over a plate of length L ... 

The geometric and flow conditions are not the only parameters which have a considerable influence on the relationship between the Nusselt number and the other dimensionless numbers. The thermal boundary conditions also affect heat transfer. An example of this is, with the same values of Re and Pr in parallel flow over a plate, we have different Nusselt numbers for a plate kept at constant wall temperature dw, and for a plate with a constant heat flux qw at the wall, where the surface temperature adjusts itself accordingly. 

Equations (1.198) and (1.199) are also known as Lewis equations. The mass transfer coefficients f3m calculated using this equation are only valid, according to the definition, for insignificant convective currents, fn the event of convection being important they must be corrected. The correction factors C, = /3 n/l3m for transverse flow over a plate, under the boundary layer theory assumptions are shown in Fig. 1.50. They are larger than those in film theory for a convective flow out of the phase, but smaller for a convective flow into the phase. 

Vertical Flat Plates. Following the earlier work by Bromley [190] on cylinders (see below), Hsu and Westwater [191] derived an expression for laminar film boiling on a vertical plate that is analogous to that for laminar film condensation. The average value of hc over a plate of height L is given by... 

In the manufacture of percussion caps and detonators the copper blanks are cut from copper strips and stamped to the required shape. The blanks are then plaeed in a gun-metal plate, with the concave side uppermost—a tool composed of a plate of gim-metal, in which are inserted a number of copper points, each of the same length, and so spaced apart as to exactly fit each point into a cap when inverted over a plate containing the blanks. The points are dipped into a vessel containing the cap composition, which has been previously moistened with methylated spirit. It is then removed and placed over the blanks, and a slight blow serves to deposit a small portion of the eap mixture into each cap. A similar tool is then dipped into shellac... 

Laminar boundary layer flow of power-law liquids over a plate... 

A study of the effect of gap thickness on band formation in HPC + water solutions was conducted [87]. The apparatus used had a parallelism of about 20 pm over a plate length of about 10 cm. Note that this was a linear and not a rotary parallel plate apparatus. The gap was varied between 150 and 1000 pm. A rest time of 5-6 h was allowed between sample loading and initiation of shear. Since the time scale of changes in the band structure was slow, of the order of minutes, there was plenty of time for detailed examination. 

N = number of transfer units supplied by a plate Lj = length of travel of liquid over a plate Lu = length of a transfer unit... 

Equation (X.27) was derived for flow over a plate with zero angle of attack. For an angle of attack varying from 0° to a (with a < 90°), the thickness of the laminar sublayer is given by... 

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