Compressible flow of gas

The general mechanical energy-balance equation (2.7-27) can be used as a starting point. Assuming turbulent flow, so that a = 1.0 no shaft work, so that Wg = 0 and writing the equation for a differential length dL, Eq. (2.7-27) becomes 

For a horizontal duct, dz = 0. Using only the wall shear frictional term for dF and writing Eq. (2.10-6) in differential form, 

This is the basic differential equation that is to be integrated. To do this the relation between V and p must be known so that the integral of dp/V can be evaluated. This integral depends upon the nature of the flow and two important conditions used are isothermal and adiabatic flow in pipes. 

To integrate Eq. (2.11-5) for isothermal flow, an ideal gas will be assumed where 

The first term on the right of Eqs. (2.11-9) and (2.11-10) represents the frictional loss as given by Eqs. (2.10-9) and (2.10-10). The last term in both equations is generally negligible in ducts of appreciable lengths unless the pressure drop is very large. 

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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 ... 

As in the case of the venturi, for the measurement of compressible flow of gases in an orifice, a correction factor Y given in Fig. 3.2-3 for air is used as follows. 

Flow of gases and vapors (compressible fluids) through nozzles and orifices. (For flow field importance see References [31]). From [3] ... 

Fig. 3.52 Temperature and velocity profile in a compressible flow of ideal gases, according to (3.354)...

Fig. 3.53 Temperature profiles in compressible flow of ideal gases. Adiabatic wall...

Just as for a liquid, you can also feel the flow of gases that make up the atmosphere if you stand in a breeze. The flow of a gas feels different because the particles that make up a gas are farther apart than those of a liquid. If you blow up a balloon or a tire, you can observe some important properties of gases, as shown in Figure 10.3. From these observations, you see that a gas is flowing, compressible matter that has no definite volume or shape. The particles that make up a gas are much farther apart than they are in solids and liquids, and so, they can be easily pushed together. 

Experimental data [5] indicate that the same relation holds for flow of gases at high veloeities and that the values of / determined from the friction factor plot (Fig. 6,10) for various Reynolds numbers and pipe roughnesses apply equally well to compressible and incompressible fluids. Equation 8.26 may be substituted in Eq. 8.25 and, together with the energy, continuity, and perfect-gas equations, solved to show the change in pressure, temperature, etc., with distance down the pipe. The results are Eq. 8.16, which shows the relation of temperature to Mach number and is the same with or without friction, and... 

The compressor is a device that increases the pressure of air and pumps the compressed air into a tank. The compressed air tank is called a reservoir. The compressed air is then routed to the desired location through transmission lines. Transmission lines are tubing through which the compressed air flows. Control valves regulate the flow of gases. The pneumatic system uses a cylinder with a movable piston to convert its fluid power into mechanical power in the form of linear motion. 

The term fluid covers a wide range of materials—from gases and simple liquids to polymeric materials and semi-solid slurries. Fluids may be classified as either compressible or incompressible. The density of a compressible fluid depends on the pressure. Although this is true for all real fluids, the compressibility of liquids is very small under most conditions and they may be considered incompressible. The flow of gases must usually be treated as compressible unless pressure changes are small. 

Flows of gases in isotropic media. Although we have considered liquids (with m = 0) exclusively, complex variables ideas readily extend to steady-state compressible gases. Consider the flow of a gas in homogeneous, isotropic media, following Discussion 4-2. Equations 4-17 and 4-18 suggest that... 

Compressible Vlow. The flow of easily compressible fluids, ie, gases, exhibits features not evident in the flow of substantially incompressible fluid, ie, Hquids. These differences arise because of the ease with which gas velocities can be brought to or beyond the speed of sound and the substantial reversible exchange possible between kinetic energy and internal energy. The Mach number, the ratio of the gas velocity to the local speed of sound, plays a central role in describing such flows. 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

The flow of compressible and non-compressible liquids, gases, vapors, suspensions, slurries and many other fluid systems has received sufficient study to allow definite evaluation of conditions for a variety of process situations for Newtonian fluids. For the non-Newtonian fluids, considerable data is available. However, its correlation is not as broad in application, due to the significant influence of physical and rheological properties. This presentation is limited to Newtonian systems, except where noted. 

Primary emphasis is given to flow through circular pipes or tubes since this is the usual means of movement of gases and liquids in process plants. Flow through duct systems is treated with the fan section of Compression in Volume 3. 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

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