Pressure drop defined

For a reactive process, the reactants must be brought into contact by mixing before a reaction can occur. In a motionless mixer in turbulent flow, the pressure drop defines the turbulent energy dissipation rate, which then determines the macro-, meso-, and micromixing rates. 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

A continuous pressure filter may be defined as a filter that operates at pressure drops greater than 100 kPa and does not require intermption of its operation to discharge the cake the cake discharge itself, however, does not have to be continuous. There is Htfle or no downtime involved, and the dry soHds rates can sometimes be as high as 1750 kg/m h with continuous pressure filters. 

Friction Coefficient. In the design of a heat exchanger, the pumping requirement is an important consideration. For a fully developed laminar flow, the pressure drop inside a tube is inversely proportional to the fourth power of the inside tube diameter. For a turbulent flow, the pressure drop is inversely proportional to D where n Hes between 4.8 and 5. In general, the internal tube diameter, plays the most important role in the deterrnination of the pumping requirement. It can be calculated using the Darcy friction coefficient,, defined as... 

The relationship between the bore fluid pressure drop, AP and its flow rate is defined by Poiseuike s law ... 

Pressure drop in static mixers depends very strongly on geometric arrangement of the inserts. It is simply defined in relation to the pressure drop AP in an empty tube given by Darcy s equation ... 

Although it has been common practice to specify the pressure loss in ordinary valves in terms of either equivalent length of straight pipe of the same size or velocity head loss, it is becoming more common to specify flow rate and pressure drop characteristics in the same terms as has been the practice for valves designed specifically for control service, namely, in terms of the valve coefficient, C. The flow coefficient of a valve is defined as the volume of Hquid at a specified density that flows through the fully opened valve with a unit pressure drop, eg, = 1 when 3.79 L/min (1 gal /min) pass through the valve... 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

The hydrauhc diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function only of the ratio of cross-sectional area to wetted perimeter. For some shapes, the Navier-Stokes equations have been integrated to yield relations between flow rate and pressure drop. These relations may be expressed in terms of equivalent diameters Dg defined to make the relations reduce to the second form of the Hagen-Poiseulle equation, Eq. (6-36) that is, Dg (l2SQ[LL/ KAPy. Equivalent diameters are not the same as hydraulie diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(tiDe/4). Equivalent diameter Dg is not to be used in the friction factor and Reynolds number ... 

Rapid approximate predictions of pressure drop for fully developed, incompressible horizontal gas/fiquid flow may be made using the method of Lockhart and MartineUi (Chem. Eng. Prog., 45, 39 8 [1949]). First, the pressure drops that would be expected for each of the two phases as if flowing alone in single-phase flow are calculated. The LocKhart-Martinelli parameter X is defined in terms of the ratio of these pressure drops ... 

Pressure Drop Methods for estimating fluid-dynamic behavior of crossflow plates are analogous, whether the plates be bubble-cap, sieve, or valve. The total pressure drop across a plate is defined by the general equation (see Fig. 14-29)... 

Katz (R-16) also siwdied wave-plate impingement separators (Fig. 14-Il0b) made up of 90° formed arcs with an 11.1-mm (0.44-iu) radius auda 3.8-mm (0.15-iu) clearance between sheets. The pressure drop is a function of system geometiy. The pressure drop for Katz s system and collection efficiency for seven waves are shown in Fig. 14-111. Katz used the Souders-Brown expression to define a design velocity for the gas between the waves ... 

The incremental pressure drop for wet mesh is not available for all operating conditions or for mesh of different styles. The data of York and Poppele for wet-mesh incremental pressure drop, APi in cm of water, are shown in Fig. 14-122 or parameters of liquid velocity L/A, defined as liquid volumetric flowrate, cmVmin per unit of mesh cross-sectional area in cm" liqiiid density Pl is in g/cm. ... 

Total pressure deerease in the nozzle and outlet diffuser are only from frietional losses. In an ideal nozzle or diffuser the total pressure drop is zero. Isentropie effieieney is defined as the ratio of the aetual work to the isen-tropie enthalpy deerease, whieh is the expansion from the inlet total pressure to the outlet total pressure... 

In addition to flow regime, hold-up and pressure drop are two other important parameters in two-phase gas-liquid flows. Hold-up is defined as the relative portion of space occupied by a phase in the pipe. It can be expressed on a time or space average basis, with the actual method chosen depending on the intended use of the hold-up value, and the measurement method employed. There are numerous correlations in the literature for hold-up, but most are based upon a pressure drop-hold-up correlation. The following expression is a widely recognized empirical relationship between hold-up and pressure drop ... 

This expression can be represented graphically in dimensionless form to simplify its use. It is generally expressed as the so-called filtration number , defined as follows E, = /iR, / 2APT3 jr x . The filtration number, E, is dimensionless and varies from zero at Rf = 0 to a large value when there is an increase in the viscosity of the sludge and Rf or a decrease in pressure drop, auxiliary time, specific cake resistance and the ratio of cake volume to filtrate volume. It may be assumed in practice that F(, = 0 to 10. If washing and drying times are constant and independent of filtration time, they may be added directly to the auxiliary time. In... 

When the cake structure is composed of particles that are readily deformed or become rearranged under pressure, the resulting cake is characterized as being compressible. Those that are not readily deformed are referred to as sem-compressible, and those that deform only slightly are considered incompressible. Porosity (defined as the ratio of pore volume to the volume of cake) does not decrease with increasing pressure drop. The porosity of a compressible cake decreases under pressure, and its hydraulic resistance to the flow of the liquid phase increases with an increase in the pressure differential across the filter media. 

A more sophisticated theory was given by Barth, in which the pressure drop of a cyclone is defined as a function of the swirling velocity head of the fluid in the outlet pipe as follows ... 

Constant pressure drop is maintained during operation. Taking as the basis one revolution of the drum, the time per revolution and submergence fraction, respectively, can be defined as... 

When the relieving scenarios are defined, assume line sizes, and calculate pressure drop from the vent tip back to each relief valve to assure that the back-pressure is less than or equal to allowable for each scenario. The velocities in the relief piping should be limited to 500 ft/sec, on the high pressure system and 200 ft/sec on the low pressure system. Avoid sonic flow in the relief header because small calculation errors can lead to large pressure drop errors. Velocity at the vent or flare outlet should be between 500 ft/sec and MACH 1 to ensure good dispersion. Sonic velocity is acceptable at the vent tip and may be chosen to impose back-pressure on (he vent scrubber. 

Flow coefficients (not resistance) for valves are generally available from the manufacturer. The coefficient of a valve is defined as tlie flow of water at 60°F, in gallons per minute, at a pressure drop of one pound per square inch across the valve [3], regardless of whether the valve ultimately will be flowing liquid or gases/vapors in the plant process. It is expressed ... 

Figure 8-155. Pressure drop for 50% cut baffles at 2.0-ft spacing. The abscissa parameter Zp is defined as Zp = Vv /0.0692 (pg/[>L)° -Used by permission Fair, J. R., Hydrocarbon Processing, V. 72. No. 5 (1993) p. 75, Gulf Pub. Co., all rights reserved.

Total number of actual trays in tower Number of caps per tray Number of slots per bubble cap Valve density, number of valves per ft or Number of valve units on a valve tray Depth of notches in weir, in or Exponent defined by Equations 8-288 and 327 Dry tray pressure drop for 50% cut baffles, in. liquid per baffle or... 

The vertical thermosiphon reboiler is a popular unit for heating distillation column bottoms. However, it is indeed surprising how so many units have been installed with so little data available. This indicates that a lot of guessing, usually on the very conservative side, has created many uneconomical units. No well-defined understanding of the performance of these units exists. Kern s recommended procedure has been found to be quite conservative on plant scale units yet it has undoubtedly been the basis for more designs than any other single approach. For some systems at and below atmospheric pressure operation, Kern s procedure gives inconsistent results. The problem is in the evaluation of the two-phase gas-liquid pressure drop under these conditions. 

Proper operation of a baghouse, regardless of design, depends on frequent cleaning of the filter media. The system is designed to operate within a specific range of pressure drops that defines clean and fully-loaded filter media. The cleaning frequency must assure that the maximum recommended pressure drop is not exceeded. 

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