Flow over

The sum of the annual discounted cash flows over n years SAdcf is known as the net present value (NPV) of the project ... 

In the second part of hla memoir Reynolds gave a theoretical account of thermal transpiration, based on the kinetic theory of gases, and was able CO account for Che above "laws", Chough he was not able to calculate Che actual value of the pressure difference required Co prevent flow over Che whole range of densities. ... 

If a gas flows over the surface of a liquid, certain effects ensue. Only the relative velocity of the liquid surface and gas is important in giving rise to nebulization. Thus, some pneumatic nebulizers... 

When a gas or liquid flows over a surface, the pressure at the surface is reduced according to the formula shown in equation (1), in which d is the density and v is the linear flow velocity of the moving stream. 

The drop in pressure when a stream of gas or liquid flows over a surface can be estimated from the given approximate formula if viscosity effects are ignored. The example calculation reveals that, with the sorts of gas flows common in a concentric-tube nebulizer, the liquid (the sample solution) at the end of the innermost tube is subjected to a partial vacuum of about 0.3 atm. This vacuum causes the liquid to lift out of the capillary, where it meets the flowing gas stream and is broken into an aerosol. For cross-flow nebulizers, the vacuum created depends critically on the alignment of the gas and liquid flows but, as a maximum, it can be estimated from the given formula. 

In a concentric-tube nebulizer, the sample solution is drawn through the inner capillary by the vacuum created when the argon gas stream flows over the end (nozzle) at high linear velocity. As the solution is drawn out, the edges of the liquid forming a film over the end of the inner capillary are blown away as a spray of droplets and solvent vapor. This aerosol may pass through spray and desolvation chambers before reaching the plasma flame. 

In general, the longer a chromatographic column, the better will be the separation of mixture components. In modem gas chromatography, columns are usually made from quartz and tend to be very long (coiled), often 10-50 m, and narrow (0.1-1.0 mm, internal diameter) — hence their common name of capillary columns. The stationary phase is coated very thinly on the whole length of the inside wall of the capillary column. Typically, the mobile gas phase flows over the stationary phase in the column at a rate of about 1-2 ml/min. 

Fig. 10. Stream flow over (a) a broad-crested, rectangular weir (b) a cross-current view of the rectangular and CipoUetti weirs (c) a trape2oidal-notch or CipoUetti weir (d) a sharp-crested, triangular, or V-notch weir (e) a cross-current view of the V-notch and hyperboHc-notch weirs and ( a...

One simple rheological model that is often used to describe the behavior of foams is that of a Bingham plastic. This appHes for flows over length scales sufficiently large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a soHd with the viscous flow of a Hquid. In simple Newtonian fluids, the shear stress T is proportional to the strain rate y, with the constant of proportionaHty being the fluid viscosity. In Bingham plastics, by contrast, the relation between stress and strain rate is r = where is... 

Entrance andExit SpanXireas. The thermal design methods presented assume that the temperature of the sheUside fluid at the entrance end of aU tubes is uniform and the same as the inlet temperature, except for cross-flow heat exchangers. This phenomenon results from the one-dimensional analysis method used in the development of the design equations. In reaUty, the temperature of the sheUside fluid away from the bundle entrance is different from the inlet temperature because heat transfer takes place between the sheUside and tubeside fluids, as the sheUside fluid flows over the tubes to reach the region away from the bundle entrance in the entrance span of the tube bundle. A similar effect takes place in the exit span of the tube bundle (12). 

The oxygen release rate is directly proportional to the cross-sectional area of the candle for a specific composition and also depends on the linear bum rate. Lower fuel contents decrease the bum rate slightly, eg, ca 2 wt % iron is the lower limit for rehable room temperature operation. Low temperature starts require at least 3.5 wt % iron. Another factor is direction of flow of the evolved gas. If the hot oxygen flows over the unbumed portion of the candle, as much as 15% rate iacreases can be produced. The bum time is halved for each 3.4 MPa (500 psi) pressure rise. The highest pressure that can be produced is ca 138 MPa (20,000 psi). 

Heterogeneous hydrogenation catalysts can be used in either a supported or an unsupported form. The most common supports are based on alurnina, carbon, and siUca. Supports are usually used with the more expensive metals and serve several purposes. Most importandy, they increase the efficiency of the catalyst based on the weight of metal used and they aid in the recovery of the catalyst, both of which help to keep costs low. When supported catalysts are employed, they can be used as a fixed bed or as a slurry (Uquid phase) or a fluidized bed (vapor phase). In a fixed-bed process, the amine or amine solution flows over the immobile catalyst. This eliminates the need for an elaborate catalyst recovery system and minimizes catalyst loss. When a slurry or fluidized bed is used, the catalyst must be separated from the amine by gravity (settling), filtration, or other means. 

Grater Wear. Crater wear (Fig. 2a) is caused by a chemical interaction between the rake face of a metal-cutting insert and the hot metal chip flowing over the tool. This interaction may involve diffusion or dissolution of the tool material into the chip. 

The lye boHer is usuaHy steam heated but may be direct-fired. Separation efficiency may be iacreased by adding a tower section with bubble-cap trays. To permit the bicarbonate content of the solution to buHd up, many plants are designed to recirculate the lye over the absorber tower with only 20—25% of the solution flowing over this tower passiag through the boHer. Several absorbers may also be used ia series to iacrease absorptioa efficieacies. 

Experimental techniques to visualize flows have been extensively used to define fluid flow in pipes and air flow over lift and control surface of airplanes. More recently this technology has been appHed to the coating process and it is now possible to visualize the flow patterns (16,17). The dimensions of the flow field are small, and the flow patterns both along the flow and inside the flow are important. Specialized techniques such as utilizing small hydrogen bubbles, dye injection, and optional sectioning, are required to visualize these flows. 

Another method that has great potential for the preparation of advanced prepregs and has been explored extensively requites fine powders. The reinforcing fibers are coated with fine particles of the resin and, when heated, the resin flows over the fiber. This method requites finely divided particles either in aqueous solution, in an inert volatile solvent, or as high dielectric material that can be charged and coated by electrostatic attraction to the fiber. Synthetic methods that make fine particles, similar to that described for PEEK (23), are needed. 

In advancing-front or layer melt crystallizations, mother Hquor flows over a cooled surface on which material is crystallized. The advancing front of crystals grows in the direction from the cooled surface into the mother Hquor. A variety of techniques can be used to take advantage of this type of Operation. 

The alcohol swells the poly (ethyl methacrylate) beads, rapidly promoting diffusion of the plasticizer into the polymer. As a result of the polymer-chain entanglement, a gel is formed. The conditioner is applied to the denture and provides a cushioning effect alcohol and plasticizer are slowly leached out, and the material becomes rigid. To ensure resiliency, the conditioner must be replaced after a few days. Some materials exhibit high flow over a short period compared with others with low initial flow the latter remain active longer. 

In addition, every effort should be made to avoid flow over a cold catalyst bed for any extended period of time, as a process stream containing volatile organics may condense on a cold catalyst bed (5). 

Similarity Variables The physical meaning of the term similarity relates to internal similitude, or self-similitude. Thus, similar solutions in boundaiy-layer flow over a horizontal flat plate are those for which the horizontal component of velocity u has the property that two velocity profiles located at different coordinates x differ only by a scale factor. The mathematical interpretation of the term similarity is a transformation of variables carried out so that a reduction in the number of independent variables is achieved. There are essentially two methods for finding similarity variables, separation of variables (not the classical concept) and the use of continuous transformation groups. The basic theoiy is available in Ames (see the references). 

For water flowing over a horizontal tube, data for several sizes of pipe are roughly correlated by the dimensional equation of McAdams, Drew, and Bays [Trans. Am. Soc. Mech. Eng., 62, 627 (1940)]. 

R Liquid film flowing over solid particles with air present, trickle bed reactors, fixed bed... 

For flow over a sharp-crested weir of width b and height L, from a liquid depth H, the flow rate is given approximately by... 

Flat Plate, Zero Angle of Ineidenee For flow over a wide, thin flat plate at zero angle of incidence with a uniform free-stream velocity, as shown in Fig. 6-47, the eritieal Reynolds number at which the boundaiy layer becomes turbulent is normally taken to be... 

FIG. 6-56 Computational fluid dynamic simulation of flow over a square cylinder, showing one vortex shedding period. (From Choudliuty, et al., Trans. ASME Fluids Div, TN-076[1994].)... 

Laminar Flow With highly viscous fluids the linear velocity along a streamline varies with the radial position. Laminar flow is charac teristic of some polymeric systems. Figure 23-21 shows how the conversion is poorer in laminar flow than with uniform flow over the... 

An (NPV) or (DCFRR) estimation will be no better than the accuracy of the projec ted cash flows over the life of the project. Clearly, one is likely to predict cash flows more accurately for 2 or 3 years ahead than, say, for 9 or 10 years ahead. However, since the cash flows for the later years are discounted to a greater extent than the cash flows for the earher years, the latter have less effec t on the overall estimation. Nevertheless, the difficulty of predicting cash flows in later years and the inherent lack of confidence in these predictions are serious disadvantages of the (DCFRR) method. In this respec t (NPV)s are more usefm since they are calculated for each year of a project. Thus, a project with a favorable (NPV) in the early years is a promising one. 

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