Pressure, critical value

Each pure hydrocarbon has a pressure-temperature diagram similar to the one shown in Figure 18. To be sure, the actual vapor pressures, sublimation pressures, critical values, etc., are different for each substance, but the general characteristics are similar. If such a diagram is available for a given substance, it is obvious that it could be used to predict the behavior of the substance as the temperature and pressure are varied. For example, in the diagram shown... 

The critical pressure, critical molar volume, and critical temperature are the values of the pressure, molar volume, and thermodynamic temperature at which the densities of coexisting liquid and gaseous phases just become identical. At this critical point, the critical compressibility factor, Z, is ... 

Be is the critical pressure, MPa. Values of Ap from Table 2-383 are summed for each part of the molecule to yield X Ap. Calculation of the Platt number is discussed under Critical Temperature. Errors in average 0.07 MPa and are less reliable for compounds with 12 or more carbon atoms. 

Turbulent flow occurs when the Reynolds number exceeds a critical value above which laminar flow is unstable the critical Reynolds number depends on the flow geometry. There is generally a transition regime between the critical Reynolds number and the Reynolds number at which the flow may be considered fully turbulent. The transition regime is very wide for some geometries. In turbulent flow, variables such as velocity and pressure fluctuate chaotically statistical methods are used to quantify turbulence. 

Ciepluch (C3) was the first to demonstrate that solid propellants could be extinguished by the rapid venting of gases from the combustion chamber. This was accomplished by suddenly opening a secondary nozzle to achieve the needed venting rate. If the depressurization rate was above a critical value, extinguishment could be achieved if below it, the pressure would seek a new steady state determined by the new chamber ballistics. 

It will be seen when the pressure ratio Pi/Pi is less than the critical value (wr — 0.607) the flow rate becomes independent of the downstream pressure P2. The fluid at the orifice is then flowing at the velocity of a small pressure wave and the velocity of the pressure wave relative to the orifice is zero. That is the upstream fluid cannot be influenced by the pressure in the downstream reservoir. Thus, the pressure falls to the critical value at the orifice, and further expansion to the downstream pressure takes place in the reservoir with the generation of a shock wave, as discussed in Section 4.6. 

Case II. Back-pressure reduced (curves 11). The pressure falls to the critical value at the throat where the velocity is sonic. The pressure then rises to Pei — Pb at the exit. The velocity rises to the sonic value at the throat and then falls to 2 at the outlet. 

As an example, the flow of air at 293 K in a pipe of 25 mm diameter and length 14 m is considered, using the value of 0.0015 for R/pu2 employed in the calculation of the figures in Table 4.1 R/pu2 will, of course, show some variation with Reynolds number, but this effect will be neglected in the following calculation. The variation in flowrate G is examined, for a given upstream pressure of 10 MN/m2, as a function of downstream pressure P2. As the critical value of P /P2 for this case is 3.16 (see Table 4.1), the maximum flowrate will occur at all values of P2 less than 10/3.16 = 3.16 MN/m2. For values of P2 greater than 3.16 MN/m2, equation 4.57 applies ... 

Similar results have been obtained by Bonilla and Perry 79>, Insinger and Bliss 801, and others for a number of organic liquids such as benzene, alcohols, acetone, and carbon tetrachloride. The data in Table 9.9 for liquids boiling at atmospheric pressure show that tile maximum heat flux is much smaller with organic liquids than with water and the temperature difference at this condition is rather higher. In practice the critical value of AT may be exceeded. Sauer et al.m] found that the overall transfer coefficient U for boiling ethyl acetate with steam at 377 kN/m2 was only 14 per cent of that when the steam pressure was reduced to 115 kN/m2. 

An example of a /zctcro-Diels-Alder reaction in SC-CO2 is the cycloaddition of anthracene with 4-phenyl-1,2,4-triazoline-3,5-dione, carried out at 40 °C and at a pressures between 75 and 216 bar [86]. The rate constant increases with decreasing pressure and the highest reactivity was observed at the critical pressure. The value of the rate constant at the critical pressure was higher than that observed in liquid CHCI3 and MeCN at the same temperature. At higher pressures, the rate is slower than that in the polar solvents, which reflects the apolar nature of SC-CO2 as a solvent. 

Supercritical fluids (SCFs) are compounds that exist at a temperature and pressure that are above their corresponding critical values [70,71]. They exhibit the properties of both gases and Hquids. With gases, they share the properties of low surface tension, low viscosity, and high diffusivity. Their main Hquid-like feature is the density, which results in enhanced solubility of solutes compared with the solubility of gases. Furthermore, the solubility of solutes can be manipulated by changes in pressure and temperature near the critical point [72]. 

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