Fluid flow expansion factor

For flow of compressible fluids use the net expansion factor Y (see later discussion) [3] ... 

For the discharge of compressible fluids from the end of a short aiping length into a larger cross section, such as a larger pipe, vessel, or atmosphere, the flow is considered adiabatic. Corrections are applied to the Darcy equation to compensate for fluid property changes due to the expansion of the fluid, and these are known as Y net expansion factors [3]. The corrected Darcy equation is ... 

Figure 2-38B. Net expansion factor, Y, for compressible flow through nozzles and orifices. By permission, Crane Co., Technical Paper 410, Engineering Div., 1957. Also see 1976 edition and Fluid Meters, Their Theory and Application, Part 1, 5th Ed., 1959 and R. G. Cunningham, Paper 50-A-45, American Society of Mechanical Engineers.

If the fluid is compressible, the specific weight will decrease from uq to w2 as the pressure drops from pi to p2 and the value of w determined by Eq. (10.89) will be larger than the true value W as given by Eq. (10.88). Therefore, we use an expansion factor Y such that W = YW. Therefore, the true flow rate for a compressible fluid is... 

FIGURE 5.23 Expansion factor for square-edged orifice and nozzle or venturi meter (a) k= 1.3, (b) k= 1.4. (From Crane Co., Flow of Fluids through Valves, Fittings, and Pipe, Technical Manual 410, Crane Co., New York (1978).)... 

Consider a short clock-time interval dt. In this time interval a small amount of feed, of volume fb dt, enters the reactor, expands by the factor 6V to volume Svfo dt, and forces an equal volume out of the reactor. In addition, during the same time interval the volume expansion factor pertaining to the contents of the reactor increases by some amount d5w and this causes the whole body of fluid in the reactor to expand from total volume V to V(5v+ d5v)/5v The extra volume Vd6 (5 thus generated is therefore also forced out of the reactor. Combining these two effects, we see that the volume exiting the reactor in time dt is dV = 6vfo dt + Vd(6v/6v). The outlet flow rate, f = dV/dt, is then ... 

The value of the term T—the expansion factor—can be derived for a Venturi meter by assuming that the fluid is an ideal gas and the flow is isentropic ... 

The liquefied helium is subdivided into two states He I and He II with a sharp transition point of 2.18 K at 5.04 kPa, the so-called A,-point. He I behaves like a normal liquid, whereas He II exhibits interesting properties of a superfluid or quantum fluid. During expansion of liquid He I below this pressure, the previously even surface forms a sharp meniscus at the wall of the container since at the 7.-point the viscosity decreases by the factor 10 and the thermal conductivity rises by the same factor. The thermal conductivity of He II is about 200 times higher than that of copper at 20 °C. Close to the absolute zero point, the viscosity turns zero and He II becomes an inviscid superfluid. He II flows over obstacles, which lie higher than the surface of the liquid, to reach the lowest level. If two containers of different temperatures are filled with He 11 and connected to each other by a capillary or another He Il-film, He II flows from the cold container into the warmer one. 

Expansion jactor A factor in compressible fluid flow which accounts for changes in fluid properties due to expansion of the fluid. 

The three most extensively used types of flow-metering devices are the thin-plate square-edged oriflce, the flow nozzle, and the venturi tube. They are differential-head instruments and require secondaiy elements for measimement of the differential pressure produced by the primary element. The Supplement to ASME Power Test Codes Instruments and Apparatus, describes construction of the above primary flow-measuring elements and their installation as well as installation of the secondary elements. The method of flow measimement, the equations for flow computation, and the limitations and accimacy of measurements are discussed. Diagrams and tables showing the necessary flow coefficients as a function of Reynolds number and diameter ratio are included in the standards. Diagrams of the expansion factor for compressible fluids are given. 

When a fluid flows through a meter, there is a pressure drop as it passes through the constriction. When a compressible fluid flows through a meter, the resulting pressure drop causes a change in fluid density at the constriction. As a result, the fluid densities at the meter inlet and within the meter are different. The expansion factor corrects for density differences between pressure taps due to expansion to the lower pressure. 

The discussion so far relates to the motion of a single spherical particle in an effectively infinite expanse of fluid. If other particles are present in the neighbourhood of the sphere, the sedimentation velocity will be decreased, and the effect will become progressively more marked as the concentration is increased. There are three contributory factors. First, as the particles settle, they will displace an equal volume of fluid, and this gives rise to an upward flow of liquid. Secondly, the buoyancy force is influenced because the suspension has a higher density than the fluid. Finally, the flow pattern of the liquid relative to... 

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