Flow variables

Vacuum flow is usually described with flow variables different from those used for normal pressures, which often leads to confusion. Pumping speed S is the actual volumetric flow rate of gas through a flow cross section. Throughput Q is the product of pumping speed and absolute pressure. In the SI system, Q has units of Pa m vs. 

Turbulent flow occurs when the Reynolds number exceeds a critical value above which laminar flow is unstable the critical Reynolds number depends on the flow geometry. There is generally a transition regime between the critical Reynolds number and the Reynolds number at which the flow may be considered fully turbulent. The transition regime is very wide for some geometries. In turbulent flow, variables such as velocity and pressure fluctuate chaotically statistical methods are used to quantify turbulence. 

Time Averaging In turbulent flows it is useful to define time-averaged and fluctuation values of flow variables such as velocity com-... 

Subdivision or discretization of the flow domain into cells or elements. There are methods, called boundary element methods, in which the surface of the flow domain, rather than the volume, is discretized, but the vast majority of CFD work uses volume discretization. Discretization produces a set of grid lines or cuives which define a mesh and a set of nodes at which the flow variables are to be calculated. The equations of motion are solved approximately on a domain defined by the grid. Curvilinear or body-fitted coordinate system grids may be used to ensure that the discretized domain accurately represents the true problem domain. 

Approximation of the unknown flow variables by means of simple functions. 

THonomf No. 2.1.3.2.1.2 Equipment Description TRANSMtl l ERS PNEUMATIC-FLOW-VARIABLE AREA ... 

Instrument operational settings. This includes settings such as zone pressures, temperatures, voltages, and flow variables. If alfernalive instrumenfs may be used, fheir operational variables should be listed. 

Reciprocating-piston pumps deliver a constant flow at si fixed backpressure. At high pressures some minor flow variability ziay arise due to the compressibility of the mobile phase. Soms instruments incorporate a flow controller which provides a fixadi backpressure for the pump to work against, independent of the column backpressure. The influence of pressure fluctuations, solvent compressibility, and solvent viscosity on the volumetrie output of the pump are thereby eliminated. Reciprocating-piston pumps can provide continuous solvent delivery, fast solvent change--... 

Because of the rapid changes in the flow variables adjacent to the exit plane, Eq. (3-131), which includes high-Mach-number data, should be used in preference to Eq. (3-132) when M > 0.7. With this provision, the above equations can be applied to flows in differing pipe lengths, provided the flow conditions (i.e., the pressure ranges) are similar to those obtaining in the experiments. 

We will use the Bernoulli equation in the form of Eq. (6-67) for analyzing pipe flows, and we will use the total volumetric flow rate (Q) as the flow variable instead of the velocity, because this is the usual measure of capacity in a pipeline. For Newtonian fluids, the problem thus reduces to a relation between the three dimensionless variables ... 

The focus of RANS simulations is on the time-averaged flow behavior of turbulent flows. Yet, all turbulent eddies do contribute to redistributing momentum within the flow domain and by doing so make up the inherently transient character of a turbulent-flow field. In RANS, these effects of the full range of eddies are made visible via the so-called Reynolds decomposition of the NS equations (see, e.g., Tennekes and Lumley, 1972, or Rodi, 1984) of the flow variables into mean and fluctuating components. To this end, a clear distinction is required between the temporal and spatial scales of the mean flow on the one hand and those associated with the turbulent fluctuations on the other hand. 

Solution. Twelve mass flow variables can be defined for this process. Let xv x, x3 be the mass input flows of A to each process. Similarly let jc4, jc5, jc6, and jc7 be the individual reactant flows of B and C, and define jc8, jc9, and jc10 as the three mass product flows (E, Ff G). Let Jtn and xl2 be the total amounts of A and B used as reactants (C is the same as jc7). Thus, we have a total of 12 variables. 

Rerun the base case with 72 fixed at 1 and 73 at 0, thus forcing process 2 to be used rather than 3 while optimizing over the continuous flow variables. 

Figure 7.2. Sketch of flow variables for the /th grid cell and its four neighbors.

Process Flow, Variables, and Responses Syrups, Suspension, and Drops Products... 

The effects of many flow variables on the phenomena at the gas-liquid interface, and on... 

The major product flow variables and cost parameters associated with the material flows throughout the production network are also shown in Figure 20. Based on the assumption that a supplier with lowest landed costs is selected outside the model per raw material and site, raw material flows are not modeled explicitly. Supplier selection could however also be included in the model analogous to the extension to include make-or-buy decisions for intermediate products (cf. Chap. 3.4.3). 

A two-dimensional, Two-Fluid model has been developed for modeling the steady-state flow of particulate materials through vertical pneumatic dryer. Two-dimensional flow field interpretations provide information about properties of the continuous and dispersed phases at every point of the flow field. Axial and radial profiles were obtained for the flow variables. 

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