Compressing flow

The governing equations used in this case are identical to Equations (4.1) and (4.4) describing the creeping flow of an incompressible generalized Newtonian fluid. In the air-filled sections if the pressure exceeds a given threshold the equations should be switched to the following set describing a compressible flow... 

Fig. 9. Compressible flow in a converging—diverging no22le where A represents no flow, C subsonic flow, and F through H supersonic flow. See text.

Example 8 Compressible Flow with Friction Losses. 6-25... 

Equation (6-95) is valid for incompressible flow. For compressible flows, see Benedict, Wyler, Dudek, and Gleed (J. E/ig. Power, 98, 327-334 [1976]). For an infinite expansion, A1/A2 = 0, Eq. (6-95) shows that the exit loss from a pipe is 1 velocity head. This result is easily deduced from the mechanic energy balance Eq. (6-90), noting that Pi =pg. This exit loss is due to the dissipation of the discharged jet there is no pressure drop at the exit. 

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]). 

In chemical process applications, one-dimensional gas flows through nozzles or orifices and in pipelines are the most important apphcations of compressible flow. Multidimensional external flows are of interest mainly in aerodynamic applications. 

Isothermal Gas Flow in Pipes and Channels Isothermal compressible flow is often encountered in long transport lines, where there is sufficient heat transfer to maintain constant temperature. Velocities and Mach numbers are usually small, yet compressibihty effects are important when the total pressure drop is a large fraction of the absolute pressure. For an ideal gas with p = pM. JKT, integration of the differential form of the momentum or mechanical energy balance equations, assuming a constant fric tion factor/over a length L of a channel of constant cross section and hydraulic diameter D, yields,... 

Adiabatic Frictionless Nozzle Flow In process plant pipelines, compressible flows are usually more nearly adiabatic than isothermal. Solutions for adiabatic flows through frictionless nozzles and in channels with constant cross section and constant friction factor are readily available. 

FIG, 6"22 Adiabatic compressible flow in a pipe with a well-rounded entrance. 

Example 8 Compressible Flow with Friction Losses Calculate the discharge rate of air to the atmosphere from a reservoir at 10 Pa gauge and 20 G through 10 m of straight 2-in Schedule 40 steel pipe (inside diameter = 0.0525 m), and 3 standard radius, flanged 90 elhows. Assume 0.5 velocity heads lost for the elhows. 

With flashes carried out along the appropriate thermodynamic paths, the formalism of Eqs. (6-139) through (6-143) applies to all homogeneous equihbrium compressible flows, including, for example, flashing flow, ideal gas flow, and nonideal gas flow. Equation (6-118), for example, is a special case of Eq. (6-141) where the quahty x = and the vapor phase is a perfect gas. 

For isothermal compressible flow of a gas with constant compressibility factor Z through a packed bed of granular solids, an equation similar to Eq. (6-114) for pipe flow may be derived ... 

Atomization = Eotvos numher, Eo Two-phase flows, free surface flows Compressible flow, hydraulic transients Cavitation... 

Flow of Bingham plastics Pulsating gas flow Compressible flow... 

For the compressible flow cases. Regimes 1 and 3, and Regime 2 with q, > q, making use of Eq. (26-90), integration of Eq. (26-93) gives Compressible Fluid Orifice Discharge by HEM... 

The general-case solution for compressible, inclined pipe flow is next stated, then the solution is developed for the special case of horizontal compressible flow... 

The general compressible flow solution simplifies for horizontal pipe flow to ... 

Stanitz, J.D., Two-Dimensional Compressible Flow in Conical Mixed-Flow Compressors, NACA TN-1744, 1948. 

Stewart, W.L., Investigation of Compressible Flow Mixing Losses Obtained Downstream of a Blade Row, NACA RM E54120 (1954). 

The Lapple charts for compressible fluid flow are a good example for this operation. Assumptions of the gas obeying the ideal gas law, a horizontal pipe, and constant friction factor over the pipe length were used. Compressible flow analysis is normally used where pressure drop produces a change in density of more than 10%. 

Loeb used Lapple s compressible flow work, techniques, and reasoning to develop graphs useful for direct calculations between tw o points in a pipe. Lapple s graphs were designed for pressure drop estimations for flow from a large vessel into a length of pipe (having static velocity in the reservoir). 

About the time it appears that there is some order to all the chaos of compressible flow, there comes another complication to worry about. It has been implied that k is constant over the compression path. The sad fact is that it is not really true. The k value has been defined in Equation... 

Compressible flow capability Available (including supersonic) Available Available (including supersonic) Weakly compressible. Mach. No. up to 0.2 Not available... 

Shapiro, A. H., 1953, Dynamics and Thermodynamics of Compressible Flow, 1, Wiley, New York,... 

For larger pressure drops in long lines of a mile or greater in length than noted above, use methods presented with the Weymouth, Panhandle Gas formulas, or the simplified compressible flow equation. 

The general procedures oudined previously for handling fluids involving the friction factor, f, and the R, chart are used with the above relations. This is applicable to compressible flow systems under the following conditions [3]. 

Figure 2-30. Pressure drop in compressible flow lines. By permission. Crane Co., Technical Paper 410, Engineering Div. 1957. Also see 1976 edition.

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