Flow-through systems, definition

The characteristics of the pump relate the applied pressure on the cake to the flowrate at the exit face of the filter medium. The cake resistance determines the pressure drop. During filtration, liquid flows through the porous filter cake in the direction of decreasing hydraulic pressure gradient. The porosity (e) is at a minimum at the point of contact between the cake and filter plate (i.e., where x = 0) and at a maximum at the cake surface (x = L) where sludge enters. A schematic definition of this system is illustrated in Figure 2. 

The value of the Reynolds number which approximately separates laminar from turbulent flow depends, as previously mentioned, on the particular configuration of the system. Thus the critical value is around 50 for a film of liquid or gas flowing down a flat plate, around 500 for flow around a sphere, and around 2500 for flow through a pipe. The characteristic length in the definition of the Reynolds number is, for example, the diameter of the sphere or of the pipe in two of these examples. 

If, in an infinite plane flame, the flame is regarded as stationary and a particular flow tube of gas is considered, the area of the flame enclosed by the tube does not depend on how the term flame surface or wave surface in which the area is measured is defined. The areas of all parallel surfaces are the same, whatever property (particularly temperature) is chosen to define the surface and these areas are all equal to each other and to that of the inner surface of the luminous part of the flame. The definition is more difficult in any other geometric system. Consider, for example, an experiment in which gas is supplied at the center of a sphere and flows radially outward in a laminar manner to a stationary spherical flame. The inward movement of the flame is balanced by the outward flow of gas. The experiment takes place in an infinite volume at constant pressure. The area of the surface of the wave will depend on where the surface is located. The area of the sphere for which T = 500°C will be less than that of one for which T = 1500°C. So if the burning velocity is defined as the volume of unbumed gas consumed per second divided by the surface area of the flame, the result obtained will depend on the particular surface selected. The only quantity that does remain constant in this system is the product u,fj,An where ur is the velocity of flow at the radius r, where the surface area is An and the gas density is (>,. This product equals mr, the mass flowing through the layer at r per unit time, and must be constant for all values of r. Thus, u, varies with r the distance from the center in the manner shown in Fig. 4.14. 

However, equation (A8.13) must be solved by trial and error and it is therefore more convenient to use the plot of the solutions to the above equations, given in Figure A8.2, of Gc and r c versus . r c can be used to check whether the flow through a frictionless nozzle would be choked. Leung13,4] has also published some equations which are numerical solutions for Gc and r c f°r vapour pressure systems, but these make use of a slightly different definition of Omega (see A8.4.1). 

Another example would be a 6-pack of soft drink cans. The container is the can and the bundle of six cans may be the unit load. Many people would find it difficult or awkward to carry six (loose) cans at one time. When the cans are held together with the white plastic holder, however, it becomes much easier to handle them. This underlines the significance of the unit load concept and the inclusion of support structures in its definition. Of course, a 12-pack carton is another example of a unit load. Multiple 12-pack cartons stacked on a pallet (as one might see in a grocery store) would be yet another example of a unit load. Clearly, multiple types of unit loads may flow through one or more systems as cans are bundled into 6-pack or 12-pack loads, which are then stacked on pallets. 

A flux F is defined as the amount that flows through a unit area per unit of time F = Ag/qAr (q area). Flux in this definition is a vector. However, in general flux in earth system research relates to the movement of a substance between compartments. This looser usage (Chapter 2) is equivalent to a rate (change of mass per time) sometimes, the term specific rate is used in the more exact sense of time-and area-related flux. Generally, the terms rate and flux as well as velocity and speed are often not separated in the literature in such an exact physical sense, but used synonymously. 

There is also a continuity equation for the host gas, usually considered as inert relative to the processes of (2.6,7). In addition, complete macroscopic specification would require the conservation equations of energy and momentum, which would be coupled to (2.6,7). The effects of turbulence can be introduced through stochastic definitions for the macroscopic variables of the system. This approach has been used in describing "dusty gas" flows [2.8] and in analysis of gas dynamics of expansion flows with condensation [2.4]. 

The ACP as a whole can be modeled by a central block with several connections to subsystems and components, as well as flow ports, in this case two, indicating the passenger flow through the ACP. The important point to notice is that the block definition diagram does not show an actual instance of a system but the elements and their relations in a potential instance of the system. 

The rate of energy dissipation, per unit area of bed cross-section, in a gas flowing through a system that gives rise to a total unrecoverable pressure loss AP is, by definition, /qAP. For a fluidized bed, AP remains constant (equal to APb) regardless of the fluid flux 7q. For a slugging bed, however,... 

Exact performance can be given only by the manufacturer for a specified turbine selected to operate at a particular set of conditions. However, estimates can be made which are usually quite satisfactory for general evaluations and comparisons. The most useful criteria are the steam rate and the system cost. Steam rate is the flow of steam in pounds per brake horsepower output per hour through the turbine. It is established for a definite shaft horsepower output, given steam pressure and temperature, exhaust system pressure, and shaft rpm ... 

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