Terminal cross-sectional area

Denote the superficial liquid-solids velocity ratio (.L/pfA)/(S/psA) by N, and let (S/psut) =At. which is the minimal cross-sectional area if the solids were to flow at their terminal velocity, up in the absence of fluid flow, and can, therefore, be called terminal cross-sectional area. Then Eq. (2) can be reduced to a dimensionless form in terms of a reduced area, A, defined as follows... 

Flues must be of the correct cross-sectional area in order to remove the products of combustion in a safe and efficient manner. The flue terminal should be fitted with a bird guard. 

Here, Vt is the terminal velocity of the particle in a gravitational field and is the cross-sectional area of the gravity settling tank that would be required to remove the same size particles as the centrifuge. This can be extremely large if the centrifuge operates at a speed corresponding to many g s. 

Ar = d3ppfgAp/ju2, Archimedes number, dimensionless At Cross-sectional area based on particle terminal velocity, cm ... 

Vertical Blowdown Drum/Catch Tank (See Fig. 23-51.) Some of the basic equations used for sizing horizontal separators can be applied to vertical separators however, the superficial vapor velocity for vertical separators is based on the total vessel cross-sectional area, and the vapor velocity must be less than the terminal settling velocity for the droplet size selected as the basis of design. 

The conductance measured between the cell terminals is multiplied by (he cell constant given in reciprocal units of length to calculate the conductivity. To calculate the resistivity, the measured resistance between the cell terminals is divided by die cell constant. Althuugh the cell constant (in reciprocal units nf length) can he calculated from the dimensions of the conductivity cell by dividing the length of Ihe electrical path through the solution by the cross-sectional area of the path, in practice, these measurements are difficult to make and arc only used to approximate the cell constant, which is determined by use of standard solutions of known conductivity or by comparison with other conductivity cells which have been so standardized. 

Polycatenars form a broken-layer type 2D density modulated phases because of the mismatch between the cross-section areas required for the terminal chains and for the mesogenic core. For such compounds layers become locally bent to provide more space for tails and, since the bending of layers is finite, this leads to... 

As the oil flows within its designated cross-section area through the horizontal vessel, free water droplets form and begin to drop at a terminal velocity rate. The Vessize program calculates this terminal velocity VTWO. As discussed previously in the oil dehydration section, the Stokes law settling equation is used for the water droplet fall rate VTWO. 

Figure 4.10 displays a typical vertical vessel program run printout. The program calculation output gives a minimum required diameter. This diameter is based on the terminal velocity of liquid drop fall velocity, gas bubble in oil rise velocity, or the water drop fall velocity. The smaller this terminal velocity, the greater the vessel cross-section area required and thus the greater the vessel diameter required. In this example, the oil-phase gas bubble rise terminal velocity is controlling. If you reduce the oil flow to, say, 10,000 lb/h, then the gas-phase liquid... 

As long as p i remains unchanged, the value of pc, and hence of the throat velocity, remains constant thus, the rate of discharge through the venturi tube is unaffected by any further decrease in the pressure at point 3. The value of the pressure at point 3 merely determines the velocity that may be attained at that point and the necessary area of the terminal cross section. 

Analysis of the diffraction pattern of Ar adsorbed on powdered Co3047 produced values for the surface areas of each of the different faces by which the crystals were terminated. The data were shown to be consistent with a surface area for the 110 face of 11 m2 g-1 and a surface area for the 111 face of 27 m2 g 1. In addition the average area occupied by a single argon atom on each face was shown to be 0.216 and 0.189 nm2 respectively. Both these values are significantly higher than the conventional cross-sectional area of an argon atom, 0.152 nm2, used in gas-adsorption estimates of the surface area of a solid. 

Recently there has been an increasing trend to replace the conventional trays depicted in Fig. 5 by trays having receiving pans that terminate some 15 cm above the tray deck. This provides more column cross-sectional area for vapor flow and allows increased vapor capacity. Even greater vapor capacity can be obtained from trays that utilize localized, upward co-current flow of vapor and liquid. But, as each tray then requires a vapor-liquid separation device, they are more expensive and are used only in specialized applications. 

Examination of Fig. 37 shows that, at generation 8, the surface area per Z group in PAMAM dendrimers approaches the cross-sectional area of the amine-terminated branch segment (ca. 33 A2) of the surface cell. Curve B assumes quantitative reactions and 100% branching ideality at each stage. Since our present analytical methods assure branching ideality detection limits of no more than 95%, curve A may more nearly approximate experimental congestion levels. 

A particle possesses both downward terminal velocity v or Vp, and a horizontal velocity (also cdlltd flow-through velocity). Because of the downward movement, the particles will ultimately be deposited at the bottom sludge zone to form the sludge. For the particle to remain deposited at the sludge zone, v should be such as not to scour it. For light flocculent suspensions, should not be greater than 9.0 m/h and for heavier, discrete-particle suspensions, it should not be more than 36 m/h. If A is the vertical cross-sectional area, Q the flow, the depth, W the width, L the length, and the detention time ... 

These dendrimers cannot be arranged in a molecular cylindrical model as that proposed for the smectic phases, since the cross-sectional area of the terminal chains is larger than the area occupied by the mesogenic units. In... 

Pulmonary deposition of an aerosol preparation is determined primarily by its size. Aerosols with a mass median aerodynamic diameter of 1-5 xm produce the best therapeutic results and are the target particle size for inhalation therapy. These small particles penetrate deep within the respiratory tract to ensure drug deposition in peripheral airways. The cross-sectional area (cm ) of the lung increases dramatically at the level of the respiratory zone therefore, the velocity of gas flow during inspiration rapidly decreases at this level. Moderate-sized particles (5-10 (xm) frequently settle out by sedimentation in larger more central airways because the velocity of gas falls rapidly in the region of the terminal bronchioles. 

The velocity of the continuous phase in the downcomer (or upcomer) Vjow, which sets the downcomer cross-sectional area, should be set at a value lower than the terminal velocity of some arbitrarily small droplet of dispersed phase, say, or in (0.08 or 0.16 cm) in diameter otherwise, recirculation of entrained dispersed phase around a tray will result in flooding. The terminal velocity of these small drops can be calculated by using Stokes law , = (gd Ap)/18 lc-... 

This approach is usually not practical for drops less than 100 pm, since for most situations large cross-sectional areas are needed to reduce the bulk velocity below the terminal settling velocities of such drops. An air stream with a 10 ft/s vertical velocity will entrain water drops less than about 700 pm, while a bulk velocity of 1.0 ft/s will entrain drops of about 100 pm or less. Gravity techniques can be used to remove large quantities of die latger-size dispersed-phase materia prior to some other segregation technique. 

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