Flow measurement compressible fluid

Simmer the audible or visible escape of fluid between the seat/disk of a pressure-relieving valve at an inlet static pressure below the popping pressure, but at no measurable capacity of flow. For compressible fluid service. 

The mass flow rate under adiabatic conditions is always somewhat greater than that under isothermal conditions, but the difference is normally <20%. In fact, for long piping systems (L/D > 1000), the difference is usually less than 5% (see, e.g., Holland, 1973). The flow of compressible (as well as incompressible) fluids through nozzles and orifices will be considered in the following chapter on flow-measuring devices. 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

The Navier-Stokes equations have been derived and written in a form that exposes V-V explicitly. In large measure this is done in anticipation of the simplifications that accrue for incompressible flow where V-V = 0. It is also important to recognize situations in which compressible fluids (i.e., gases) behave as though they were incompressible, thus permitting the incompressible-flow simplifications. 

From the subsection Flow Measurement of Compressible Fluids [following Eq. (10.86)]... 

Because the thermal diffusivity of SC water is comparable to that of many high quality insulation materials, gross radial temperature gradients can easily exist in a flow reactor. As shown in Figure 2, radial temperature gradients within the annular flow reactor are negligible. A computer program, which accurately accounts for the effects of the various fluid (solvent, solvent and solute, air) compressibilities on flow measurements, calculates mass and elemental balances for each experiment. A typical experiment evidences mass and elemental balances of 1.00+0.05. 

In the integration of equation 12 to give equation 13 it was assumed that Q was not a function of pressure. However, when a compressible fluid such as a gas is flowing this assumption is not valid. As the gas flows through the porous medium from a high pressure to a low pressure it expands as the pressure decreases. Consequently for a compressible fluid Q must be measured at the mean pressure of the system, that is, at a pressure equal to (Pi -f- P2) /2. If Boyle s Law applies to the gas it is evident that... 

Keeping in mind that two-phase flows include both liquid-liquid systems and gas-liquid systems, the different behavior of a gas and liquid must be emphasized before discussing two-phase flows. The average distance between molecules in a gas phase is one order of magnitude higher than the diameter of its molecules, while it approaches the molecular diameter in a liquid phase. Therefore, in some microdevices the gas is compressed when the pressure strongly changes. The Mach number (Ma) is a dynamic measure of fluid compressibihty and is defined as the ratio of flow velocity (v) to sound speed (a) ... 

With GCs made before the 1990s, carrier flow rate was controlled indirectly by controlling the carrier inlet pressure, or "column head pressure." The actual flow rate was measured at the outlet of the column or the detector with an electronic flow meter, or a bubble flow meter, and could be an involved, time consuming, and frustrating process. The pressure setting was not able to be varied during the run, and thus the flow was essentially constant during the analysis. The relation between flow rate and inlet pressure is calculated with Poiseuille s equation for compressible fluids. 

Varying the flow of a compressible fluid controls the pressure in a large volume. This process is dominated by a single large capacitance with no dead time. The measurement is normally noise free and, owing to its capacitive nature, is characterized by a slow response and a small process gain. As shown for liquid level control, a proportional controller is more than adequate for gas pressure control. 

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. 

As mentioned by Mathias et al. [9], reliable methods to measure the thermal conductivity of diffusion layers as a function of compression pressures are very scarce in the open literature. Khandelwal and Mench [112] designed an ex situ method to measure accurately the thermal conductivities of different components used in a fuel cell. In their apparatus, the sample materials were placed between two cylindrical rods made out of aluminum bronze (see Figure 4.28). Three thermocouples were located equidistantly in each of the upper and lower cylinders to monitor the temperatures along these components. Two plates located at each end compressed both cylinders together. The temperatures of each plate were maintained by flowing coolant fluids at a high flow rate through channels located inside each of the plates. A load cell was located between two plates at one end so that the compression pressure could be measured. 

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