Downstream dimensional requirement

Orifice flanges need not be accessible from grade or a platform but should be positioned at a location and elevation that can be reached by a portable ladder. Care must be taken at horizontal banks of lines to allow for adequate space for side-oriented taps and, when required, close-coupled transmitters. liqjend-ing on service, orifice flanges can be mounted in the vertical and horizontal seaions of piping, as shown in Exhibit 14-21, or with specific upstream and downstream dimensional requirements, as shown in Exhibit 14-22. For less common flow instruments (e.g., Pitot tubes and Annubars), advice from the instrument engineer is necessary for location and dimensional requirements. 

The tendency of premixed flames to detach from the flame holder to stabilize further downstream has also been reported close to the flammability limit in a two-dimensional sudden expansion flow [27]. The change in flame position in the present annular flow arrangement was a consequence of flow oscillations associated with rough combustion, and the flame can be particularly susceptible to detachment and possible extinction, especially at values of equivalence ratio close to the lean flammability limit. Measurements of extinction in opposed jet flames subject to pressure oscillations [28] show that a number of cycles of local flame extinction and relight were required before the flame finally blew off. The number of cycles over which the extinction process occurred depended on the frequency and amplitude of the oscillated input and the equivalence ratios in the opposed jets. Thus the onset of large amplitudes of oscillations in the lean combustor is not likely to lead to instantaneous blow-off, and the availability of a control mechanism to respond to the naturally occurring oscillations at their onset can slow down the progress towards total extinction and restore a stable flame. 

Low-molecular-weight products, generally secondary metabolites such as alcohols, carboxylic and amino acids, antibiotics, and vitamins, can be recovered using many of the standard operations such as liquid-liquid extraction, adsorption and ion-exchange, described elsewhere in this handbook. Proteins require special attention, however, as they are sufficiendy more complex, their function depending on the integrity of a delicate three-dimensional tertiary structure that can be disrupted if the protein is not handled correcdy. For this reason, this section focuses primarily on protein separations. Cell separations, as a necessary part of die downstream processing sequence, are also covered. 

The flow velocities in flame systems are such that transport processes (diffusion and thermal conduction) make appreciable contributions to the overall flows, and must be considered in the analysis of the measured profiles. Indeed, these processes are responsible for the propagation of the flame into the fresh gas supporting it, and the exponential growth zone of the shock tube experiments is replaced by an initial stage of the reaction where active centres are supplied by diffusion from more reacted mixture sightly further downstream. The measured profiles are related to the kinetic reaction rates by means of the continuity equations governing the one-dimensional flowing system. Let Wi represent the concentration (g. cm" ) of any quantity i at distance y and time t, and let F,- represent the overall flux of the quantity (g. cm". sec ). Then continuity considerations require that the sum of the first distance derivative of the flux term and the first time derivative of the concentration term be equal to the mass chemical rate of formation q,- of the quantity, i.e. 

The graphs in Fig. 6-21 are based on accurate calculations, but are difficult to interpolate precisely. While they are quite useful for rough estimates, precise calculations are best done using the equations for one-dimensional adiabatic flow with friction, which are suitable for computer programming. Let subscripts 1 and 2 denote two points along a pipe of diameter D, point 2 being downstream of point 1. From a given point in the pipe, where the Mach number is M, the additional len h of pipe required to accelerate the flow to sonic velocity (M = 1) is denoted and may be computed from... 

A two-dimensional model is required for the wind running onto a forest edge or onto a finite-length fetch (green belts or shelterbelts). In this case, the significant two-dimensional transformation of the air flow takes place from the entry towards the downstream region, where the flow adjusts to an equilibrium state (1.4). A suitable mathematical model uses partial differential equations [155] ... 

For classification in routine lymphocyte subset analysis, expert analysis is often fully adequate. For polychromic flow cytometry, particularly when both lineage and functional phenotypes are being evaluated, more sophisticated analysis may be required. Indeed, more sophisticated analysis can define subpopulations that cannot be discriminated by any combination of two-dimensional projections of multicolor data (Zamir et al., 2005). One of the first steps in enabling more sophisticated downstream analysis is ensuring acquisition of robust data. Some of the recently described analytical methods for high-dimensional flow cytometry data are listed in Table 4.2-1. 

The business-customer encounter now defined as a key to delivering individually required services to the individual customer may be further modeled by considering the information blocks contributing to actual encounter. Three main service dimensional blocks exist within the virtual service value encounter. These are the business-related upstream strategie dimensions, the performance encounter dimensions, and the downstream customer-demanded value dimensions. Each block comes under the influenee of the fourth block— the external environment. This model is displayed as Figure 3. 

Rockwell (1969) used the method of characteristics to solve the equations for a one-dimensional model of aortic blood flow. By specifying distal and proximal boundary conditions, Rockwell calculated the flow and pressure waveform development from the aortic valve to points as far distal as the abdominal aorta. Features such as the steepening of the aortic pressure waveform as one proceeds downstream of the valve were predicted and found to confirm in vivo results (McDonald, 1974). Womersley s (1957) original linear model failed to predict this, and Rockwell s results thus have established the importance of non-linear effects in modeling arterial flow. Van der Werff (1974) also used the method of characteristics to study aortic blood flow, but with a statement of only proximal boundary conditions (here both the pressure and flow waveforms are required as inputs) and employing the fact that the solution is periodic. 

An analysis of extrusion from a die requires three-dimensional flow modeling of the fluid between a plane, d ii, positioned in the die and a second plane, in the jet. The first plane must be placed far enough upstream so that the effect of extrusion is not yet sensed. The downstream plane is placed at a position where the final shape of the extrudate has been achieved. Here, not only must three components of velocity and pressure be determined in the die and extrudate but the shape of the extrudate must be determined as well. 

Zero-dimensional, compressible-fluid theory can also be used to analyze the pressure change that occurs across the Mach disk. Momentum, energy, and continuity equations are written for both the upstream (3x) and downstream (3y) sides of the Mach disk, with the ideal gas law being used as the equation of state. In addition, the second-law requirement that the entropy must either increase or remain constant across the disk is used. Simultaneous solution of these equations (the classical solution technique is graphical) followed by considerable algebraic manipulation yields the downstream Mach number Msy as a function of y and the upstream Mach number M3X (21) ... 

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