Compressible flows 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 2-38A. Net expansion factor, Y, for compressible flow through pipe to a larger flow area. By permission, Crane Co., Technical Paper U410, Engineering Div., 1957. Also see 1976 edition.

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... 

It is possible to force the incompressible flow equation to match compressible flow equation (9.3) by introducing an expansion factor, Y = Y(y, Pi/p ), into equation (9.1), modified to replace the downstream... 

For the measurement. of compressible flow of gases, the adiabatic expansion fromp, to P2 pressure must be allowed for in Eq. (3.2-7). A similar equation and the same coefficient C are used along with the dimensionless expansion correction factor Y (shown in Fig. 3.2-3 for air) as follows ... 

The pneumatic or electrical signals depict only the analog measured variable. The direct measured variable is not always the desired result, however. Thus, for example, one obtains from flow measurements with diaphragms a differential pressure, not the mass flow, q , which for compressible flow in an orifice is given by Eq. (32), where Ap = pi — pi is the pressure drop between the taps upstream and downstream respectively, pj is the upstream density, Q is an empirical discharge coefficient, Ai is the area of the orifice, Y is a dimensionless expansion factor, and p = 2/ 1 is the ratio of the orifice to the upstream pipe diameter (see Section 12.2.5) [10]. 

In Equation 2.17,7 is an expansion factor (ratio of flow coefficient for a gas to that for a liquid) that plays a similar role to Ci, G is specific gravity and Z is a compressibility factor. Although the form of this equation seems much different than the Fisher one, the results are equivalent. Again, the valve characteristic type and rangeability should he checked. 

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. 

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

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