Fluid flow compressible flows

The temperature of the fluid in compressible flow through a conduit of constant cross section may be kept constant by a transfer of heat through the conduit wall. Long, small, uninsulated pipes in contact with air transmit suflicient heat to keep the flow nearly isothermal. Also, for small Mach numbers, the pressure pattern for isothermal flow is nearly the same as that for adiabatic flow for the same entrance conditions, and the simpler equations for isothermal flow may be used. The maximum velocity attainable in isothermal flow is... 

B. Compressible Fluid Flow. Fluid flow is considered noncompressible if the pressure and temperature changes are small enough to cause insignificant changes in the... 

White, E. M. 2011. Fluid Mechanics, 7th ed. Boston McGraw-Hill. Covers fluid mechanics fundamentals from physical concepts to engineering applications. Includes pressure distribution in a fluid, integral relations for a control volume and differential relations for fluid flow, viscous flow in ducts, compressible flow, open-channel flow, as and turbomachinery. Includes modem day examples such as a flying car and kite-driven ships and new material on microflow concepts. 

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... 

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]). 

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 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%. 

High-pressure fluid flows into the low-pressure shell (or tube chaimel if the low-pressure fluid is on the tubeside). The low-pressure volume is represented by differential equations that determine the accumulation of high-pressure fluid within the shell or tube channel. The model determines the pressure inside the shell (or tube channel) based on the accumulation of high-pressure fluid and remaining low pressure fluid. The surrounding low-pressure system model simulates the flow/pressure relationship in the same manner used in water hammer analysis. Low-pressure fluid accumulation, fluid compressibility and pipe expansion are represented by pipe segment symbols. If a relief valve is present, the model must include the spring force and the disk mass inertia. 

Shapiro, A.H, (1953). The dynamics and thermodynamics of compressible fluid flow. Ronald Press. New York. 

The flow of a compressible fluid through an orifice is limited by critical flow. Critical flow is also referred to as choked flow, sonic flow, or Mach 1. It can occur at a restriction in a line such as a relief valve orifice or a choke, where piping goes from a small branch into a larger header, where pipe size increases, or at the vent tip. The maximum flow occurs at... 

D. Givoli, J. E. Flaherty, M. S. Shephard. Parallel adaptive finite element analysis of viscous flows based on a combined compressible-incompressible formulation. Int J Numer Meth Heat and Fluid Flow 7 880, 1997. 

Cloutman, L. D., C. W. Hirt, and N. C. Romero. 1976. SOLA-ICE a numerical solution algorithm for transient compressible fluid flows. Los Alamos Scientific Laboratory report LA-6236. 

Compressible fluid flow occurs between the two extremes of isothermal and adiabatic conditions. For adiabatic flow the temperature decreases (normally) for decreases in pressure, and the condition is represented by p V (k) = constant. Adiabatic flow is often assumed in short and well-insulated pipe, supporting the assumption that no heat is transferred to or from the pipe contents, except for the small heat generated by fricdon during flow. Isothermal pVa = constant temperature, and is the mechanism usually (not always) assumed for most process piping design. This is in reality close to actual conditions for many process and utility service applications. 

Friction Pressure Drop For Compressible Fluid Flow... 

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]. 

This maximum velocity of a compressible fluid in a pipe is limited by the velocity of propagation of a pressure wave that travels at the speed of sound in the fluid [3]. This speed of sound is specific for each individual gas or vapor or liquid and is a function of the ratio of specific heats of the fluid. The pressure reduces and the velocity increases as the fluid flows downstream through the pipe, wdth the maximum velocity occurring at the downstream end of the pipe. WTien, or if, the pressure drop is great enough, the discharge or exit or outlet velocity will reach the velocity of sound for that fluid. 

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.

M = molecular weight of flowing fluid Z = compressibility factor for deviation from perfect gas if known, otherwise use Z = 1.0 for pressures below 250 psia, at inlet conditions. 

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,... 

The most effective techniques for hyperbolic partial differential equations are based on the method of characteristics [19] and an extensive treatment of this method may be found in the literature of compressible fluid flow and plasticity fields. 

To analyze compressible flow through chokes it is assumed that the entropy of the fluid remains constant. The equation of isentropic flow is... 

Aerated Mud. In aerated mud drilling operations, the drilling mud is injected with compressed air to lighten the mud. Therefore, at the bottom of the well in the annulus, the bottomhole pressure for an aerated mud will be less than that of the mud without aeration. However, an aerated mud drilling operation will have very significant bottomhole pressure capabilities and can easily be used to control potential production fluid flow into the well annulus. 

For compressible fluids flowing through nozzles and orifices use Figures 2-17 and 2-18, using hL or AP as differential static head or pressure differential across taps located one diameter upstream at 0.5 diameters downstream from the inlet face of orifice plate or nozzle, when values of C are taken from Figures 2-17 and 2-18 [3]. For any fluid ... 

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