Pressure drop in compressible flow

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

The symbol i is used to denote the enthalpy instead of the customary h to avoid confusion with the heat-transfer coefficient.) The subscripts 1 and 2 refer to entrance and exit conditions to the control volume. To calculate pressure drop in compressible flow, it is necessary to specify the equation of state of the fluid, viz., for an ideal gas,... 

Pressure Drop in Compressible Flow. Methane gas is being pumped through a... 

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. 

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). 

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. 

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,... 

Methods have been given for the calculation of the pressure drop for the flow of an incompressible fluid and for a compressible fluid which behaves as an ideal gas. If the fluid is compressible and deviations from the ideal gas law are appreciable, one of the approximate equations of state, such as van der Waals equation, may be used in place of the law PV = nRT to give the relation between temperature, pressure, and volume. Alternatively, if the enthalpy of the gas is known over a range of temperature and pressure, the energy balance, equation 2.56, which involves a term representing the change in the enthalpy, may be employed ... 

Note that while the fluid density may be a function of the pressure in the bed in a compressible flow, the superficial mass velocity is constant. The Ergun equation in the form given in eq. (3.450) is more convenient when analyzing the effects of pressure drop in the fluid density. 

Eqs. (3.448) and (3.449) assume constant fluid density, in other words, diey hold for incompressible flow. However, in compressible flow, die density of the fluid is a function of the pressure drop (see Section 5.3.4). Then, we have to use the differential forms of... 

The initial flow rate decrease is caused by the NiCd battery discharge characteristic. Direct error can also result from the effect of inlet pressure changes on flow as shown in Figure 2(3). Since the pump is working on a compressable fluid, air, any increase in the pressure drop reduces the flow rate. 

We have developed a technique specifically designed to measure the resistance to flow and the amount of compression as a function of flow rate. The technique is used to design biofllters. As a rule, a biofilter should not allow a pressure drop in... 

If the pressure drop in a pipeline is less than 40% of Pla then the Darcy-Weisbach incompressible flow calculation may be more accurate than the Weymouth or Panhandles A and B for a short pipe or low flow. In main pipelines, compressible flow calculations are generally used. 

Figure 28 shows that the pressure drop of a conical bed reaches a maximum value at the initial fluidization point (GR)i, and it drops at higher fluid rates. Inherent in this drooping pressure-drop characteristic lies the instability of conical bed operation, especially with gas as the fluidizing medium, for as soon as fluid rate reaches (GR) , the decrease in pressure drop induces higher flow from a compressible medium. As the pressure expends itself, fluid flow drops to even lower values, only to permit reaccumulation of pressure because of reversion to the higher pressure-drop region of the system. 

The scale-up of a chromatographic process to industrial scale can be difficult to achieve while maintaining an acceptable throughput and yield of product. Problems may occur which are not met at the laboratory scale, for example, the flow distribution pattern through a large-diameter column, excessive pressure drop in a longer column due to compression of some matrices, and the need to maintain equipment cleanliness over an extended number of purification cycles. 

In a pressure regime high enough, the permeate flux becomes independent of the applied pressure, which is the critical flow of the process. The presence of a layer of particles trapped and compressed on the surface of the membrane leads to the maintenance of a constant pressure drop in the gel layer polarization, and this pressure is the critical pressure of the system. Considering that the thickness of the layer retained on the membrane surface is very small, relative to the diameter of the pore channel, we can neglect its effect in relation to the hydraulic conditions of flow, and thus, the flow on the surface can be given as zero, thus characterizing the critical flow. 

For the ammonia process in Example 5.3, consider operation of the reactor at 932°F and 400 atm. Use a simulator to show how the product, recycle, and purge flow rates, and the mole fractions of argon and methane, vary with the purge-to-recyclc ratio. How do the power requirements for compression vary, assuming 3 atm pressure drop in the reactor and I atm pressure drop in the heat exchanger. 

Heat is usually applied in various amounts and in different locations, whether in a metal plasticating barrel (extrusion, injection molding, etc.) or in a metal mold/die (compression, injection, thermoforming, extrusion, etc.). With barrels a thermocouple is usually embedded in the metal to send a signal to a temperature controller. In turn, it controls the electric power output device regulating the power to the heater bands in different zones of the barrel. The placement of the thermocouple temperature sensor is extremely important. The heat flow in any medium sets up a temperature gradient in that medium, just as the flow of water in a pipe sets up a pressure drop, and the flow of electricity in a wire causes a voltage drop. 

---