Compressible pipe-flow

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.,... 

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 ... 

HEM for Two-Phase Pipe Discharge With a pipe present, the backpressure experienced by the orifice is no longer qg, but rather an intermediate pressure ratio qi. Thus qi replaces T o iri ihe orifice solution for mass flux G. ri Eq. (26-95). Correspondingly, the momentum balance is integrated between qi and T o lo give the pipe flow solution for G,p. The solutions for orifice and pipe now must be solved simultaneously to make G. ri = G,p and to find qi and T o- This can be done explicitly for the simple case of incompressible single-phase (hquid) inclined or horizontal pipe flow The solution is implicit for compressible regimes. 

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 ... 

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%. 

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. 

Figure 9-2 provides a convenient way of solving compressible adiabatic flow problems for piping systems. Some iteration is normally required, because the value of K( depends on the Reynolds number, which cannot be determined until G is found. An example of the procedure for solving a typical problem follows. 

For steady flow in a pipe or tube the kinetic energy term can be written as m2/(2 a) where u is the volumetric average velocity in the pipe or tube and a is a dimensionless correction factor which accounts for the velocity distribution across the pipe or tube. Fluids that are treated as compressible are almost always in turbulent flow and a is approximately 1 for turbulent flow. Thus for a compressible fluid flowing in a pipe or tube, equation 6.4 can be written as... 

A large number of models exist for performing compressible gas flow calculations in pipes. For pressure relief sizing purposes, it is essential to chose a model which is suitable for high velocity calculations and which correctly models choking. Many available models do not do this. A suitable code, COMFLOW , is to be provided with reference 3. 

Care is needed when modeling compressible gas flows, flows of vapor-liquid mixtures, slurry flows, and flows of non-Newtonian liquids. Some simulators use different pipe models for compressible flow. The prediction of pressure drop in multiphase flow is inexact at best and can be subject to very large errors if the extent of vaporization is unknown. In most of these cases, the simulation model should be replaced by a computational fluid dynamics (CFD) model of the important parts of the plant. 

For compressible fluid flow in plant piping, one can use Mak s Isothermal flow chart (Figure 1). Mak s chart was provided originally for relief valve manifold design and adopted by API. The relief valve manifold design method, and its derivation, is discussed in Section 20, Safety. Mak s methods can be applied to other common plant compressible flow situations. 

According to the equations for supersonic pipe flow, pressure increases and velocity decreases in the direction of flow. However, this flow regime is unstable, and a supersonic stream entering a pipe of constant cross section undergoes a compression shock, the result of which is an abrupt and finite increase in pressure and decrease in velocity to a subsonic value. 

Gas phase viscosity data, iTq, are used in the design of compressible fluid flow and unit operations. For example, the viscosity of a gas is required to determine the maximum permissible flow through a given process pipe size. Alternatively, the pressure loss of a given flowrate can be calculated. Viscosity data are needed for the design of process equipment involving heat, momentum, and mass transfer operations. The gas viscosity of mixtures is obtained from data for the individual components in the mixture. 

The computer program PROG34 determines the overall pressure drop for the 6-inch tail pipe having a relieving rate of 27,000 Ib/hr. Table 3-11 illustrates both the input data and computer output. The Mach number at inlet condition is 0.0169, and at the critical condition is 0.8874. The critical pressure is 7.985 psia and the overall pressure drop is 0.213 psi. The compressible fluid flow pattern through the pipe is SUBSONIC. 

COMPRESSIBLE FLUID FLOW CALCULATIONS IN A PIPE LINE ... 

FLOW PATTERNS OF COMPRESSIBLE FLUID FLOW IN A PIPE (Subsonic, Sonic Supersonic). 

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