Exit pressure method

The exit pressure method assumes that flow is fully developed at the exit plane or that the extent of flow disturbances at the exit plane is negligibly small for all intents and purposes. The subject of flow disturbances near the exit plane of a die has been... 

It can therefore be concluded that, for all intents and purposes, the extent of flow disturbances near the die exit may be considered to be negligible for strongly viscoelastic polymer melts at high a (say, a > 25 kPa), justifying the extrapolation procedure used to obtain and thus making the exit pressure method valid (see Table 5.1). However, this conclusion cannot be extended to dilute polymer solutions and very weakly elastic polymer melts. 

Figure 6.1 Plots of log rj versus log y and log N- versus log y for an LDPE (PE 510) at various temperatures (°C) (O, ) 180, (A, A) 200, and ( , ) 220. Open symbols denote data taken with a cone-and-plate rheometer, and filled symbols denote data taken with a capillary rheometer and analyzed with the exit pressure method as described in Chapter 5.

Figure 12.4 gives log versus log y plots for CaC03-filled PP composites with varying amounts of CaC03 at 200 °C, where denotes steady-state first normal stress difference that was determined from the exit pressure method described in Chapter 5. Note that the experimental data used to calculate values of given in Figure 12.4... 

A) 10, ( ) 20, and (V) 40. The exit pressure method described in Chapter 5 was used to determine values of Nj from a slit die with the dimensions given in Figure 12.1. (Reprinted from Flan, Journal of Applied Polymer Science 18 821. Copyright 1974, with permission from John Wiley Sons.)... 

A new method of solution is required when the valve becomes choked. If the valve exit pressure has fallen below the value needed to produce choking, any variation below that pressure will have no effect on the flow, nor on upstream conditions. A considerable measure of decoupling occurs between upstream parameters and downstream parameters, although the two sections of pipe will carry the same flow, of course. In the calculation, the upstream conditions are determined first, and then the downstream conditions, subject to the constraint that the two pipe sections are linked by a common flow and a common stagnation enthalpy. 

The isentropic method is also applied to an expander. Eq. (15.7) is used for calculating the isentropic exit temperature, but taking into account possible condensation of the gas. Like the exit pressure, the exit temperature will be less than the inlet value. Then, the exit isentropic enthalpy is computed, from which Eq. (15.8) is used to calculate the power recovered, which will be a negative value. The effect of the expander efficiency is just the opposite of the compressor efficiency, as indicated by a revision of Eq. (15.9) for applicability to expanders ... 

Hydraulic Calculations. Fluid friction and turbulence within a heat exchanger cause the exit pressure of each fluid to be lower than its entrance pressure. It is desirable to minimize this pressure drop. If a fluid is made to flow by a pump, increased pressure drop will require more pumping power. As with convection resistance, pressure drop depends on many factors and is difficult to predict accurately. Empirical methods are again used. Generally, design changes that reduce the convection resistance will increase the pressure drop, so engineers must reach a compromise between these issues. 

None of the above methods, with the possible exception of the exit pressure drop method (where calibration may be impossible), is likely to be feasible for large-scale commercial CFB systems. Hence industrial CFB systems usually operate without Gg being known. 

Extrapolation of the pressure profile in a sUt right up to the exit sometimes results in a positive nonzero value. If fully developed flow were to exist right up to the exit, it could then be shown that the first normal stress difference could be extracted from this exit pressure, and the method has been used. It is easy to show. 

Here the exit pressure affects a diaphragm and holds a valve in an equilibrium position against the force of a spring. If the pressure rises, this closes the cross-section of the plug against the seat, and if the pressure lowers it opens again. This is also the method of operation of the pressure controllers in pneumatic transmission lines. Supply pressure-reducing valves are controllers without auxiliary power. 

In Eqs. 196 and 197, Pq is the exit pressure which can be well approximated by the pressure drop through an orifice of the same radius as the die and n is the PL exponent which is obtained from capillary data (with die radius and length given by R and L, respectively). Cogswell s method, as well as other alternative methods for obtaining the uniaxial viscosity, have been compared against direct measurements in an extensional rheometer by Laun and Schuch [23]. 

However, two other methods for obtaining normal stress data from slit rheometry have had reasonable success the exit pressure and particularly the pressure hole method. These are discussed in Sections 6.3.2 and 6.3.3. 

Slit rheometers are more difficult to build and use but are preferred for research studies, because the flat flow channel makes it possible to mount pressure sensors and to make optical measurements. It has been proposed that measurement of the exit pressure or hole pressure [129] might be used to infer the first normal stress difference using a slit rheometer [9,p. 309], but these approaches have been little used because of the difficulty of measuring the small pressures or pressure differences involved. As in the case of capillary rheometers, there are established methods for calculating the true wall shear stress and shear rate from experimental slit data [9, 81]. 

Method 1. Equip a 1 litre three-necked flask (or bolt-head flask) with a separatory funnel, a mechanical stirrer (Fig. II, 7, 10), a thermometer (with bulb within 2 cm. of the bottom) and an exit tube leading to a gas absorption device (Fig. II, 8, 1, c). Place 700 g. (400 ml.) of chloro-sulphonic acid in the flask and add slowly, with stirring, 156 g. (176 ml.) of pure benzene (1) maintain the temperature between 20° and 25° by immersing the flask in cold water, if necessary. After the addition is complete (about 2 5 hours), stir the mixture for 1 hour, and then pour it on to 1500 g. of crushed ice. Add 200 ml. of carbon tetrachloride, stir, and separate the oil as soon as possible (otherwise appreciable hydrolysis occurs) extract the aqueous layer with 100 ml. of carbon tetrachloride. Wash the combined extracts with dilute sodium carbonate solution, distil off most of the solvent under atmospheric pressure (2), and distil the residue under reduced pressure. Collect the benzenesulphonyl chloride at 118-120°/15 mm. it solidifies to a colourless sohd, m.p. 13-14°, when cooled in ice. The yield is 270 g. A small amount (10-20 g.) of diphen3 lsulphone, b.p. 225°/10 mm., m.p. 128°, remains in the flask. 

Example 6 Solvent Rate for Absorption Let us consider the absorption of acetone from air at atmospheric pressure into a stream of pure water fed to the top of a packed absorber at 25 C. The inlet gas at 35 C contains 2 percent by volume of acetone and is 70 percent saturated with water vapor (4 percent H2O by volume). The mole-fraction acetone in the exit gas is to be reduced to 1/400 of the inlet value, or 50 ppmv. For 100 kmol of feed-gas mixture, how many Idlomoles of fresh water should be fed to provide a positive-driving force throughout the pacldug How many transfer units will be needed according to the classical adiabatic method What is the estimated height of pacldug required if Hqq = 0.70 m ... 

Lapple s method is useful when the upstream pressure of a header is known and the downstream pressure has to be calculated. However, it is often required to develop the pressure profile of the flare headers as a function of the distance from the stack. For this reason, it is more convenient to calculate the pressure drop backward, starting from the flare stack exit where the pressure is atmospheric. Figure 20 provides another plot which enables the pressure loss calculation when the downstream pressure is known. 

Calculation of the specific work and the arbitrary overall efficiency may now be made parallel to the method used for the a/s cycle. The maximum and minimum temperatures are specified, together with compressor and turbine efficiencies. A compressor pressure ratio (r) is selected, and with the pressure loss coefficients specified, the corresponding turbine pressure ratio is obtained. With the compressor exit temperature T2 known and Tt, specified, the temperature change in combustion is also known, and the fuel-air ratio / may then be obtained. Approximate mean values of specific heats are then obtained from Fig. 3.12. Either they may be employed directly, or n and n may be obtained and used. 

Using either of the above approaches we have measured the thermal rate constants for some 40 hydrogen atom and proton transfer reactions. The results are tabulated in Table II where the thermal rate constants are compared with the rate constants obtained at 10.5 volt cm.-1 (3.7 e.v. exit energy) either by the usual method of pressure variation or for concurrent reactions by the ratio-plot technique outlined in previous publications (14, 17, 36). The ion source temperature during these measurements was about 310°K. Table II also includes the thermal rate constants measured by others (12, 13, 33, 39) using similar pulsing techniques. 

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