Pressure, mean

Thus, if measured values of the left hand side of equation (6.4) are plotted against the mean pressure (pj + p2)/2, the theory predicts a straight line with slope B /pu RT and and intercept D /RT at (p +p )/2 = 0, and experiments of Carman [35] confirm that this is the case. In contrast,... 

Knudseci s very careful experiments on a long uniform capillary show that N L/ Pj -p ) passes through a marked minimum when plotted as a function of (P +P2)/2, at a value of the mean pressure such that the capillary diameter and the mean free path length are comparable. At higher values of the mean pressure, N L/(pj " 2 rises linearly, as in the case of a porous medium. 

To prevent this flow, the pressure on the hotter side must be larger than the pressure on the colder side. The required pressure difference depends on the nature of the gas, its mean pressure and absolute temperature, the relation between its density and the pore size, and the temperature difference. However, it does not depend on the thickness of the plate. 

The compressibilities of solvents vary significantly from one solvent to another. The compressibility of cyclohexane is about 0.67% per thousand p.s.i. change in pressure [11] and, thus, for a column operated at 6,000 p.s.i. (mean pressure 3,000 p.s.i.), there will be an error in retention volume measurement of about 2%. In a similar manner, n-heptane has a compressibility of about 1.0% per 1,000 p.s.i. change in pressure [11] and, under similar circumstances, would give an error of about 3% in retention volume measurement. Fortunately, as already discussed in Part 1 of this book, there are other retention parameters that can be used for solute... 

Each compressor unit and condition has its own specific horsepower point or requirement for operation. However, the general characteristic shape will he about the same, and for a reasonable range of conditions, the general shape and effect of varying a particular condition can be relatively established even for gases of other k values. Of course, the curves can be recalculated and drawn for the particular gas under consideration. The peaks will be in about the same ratio. Note that Figures 12-26 and 12-27 were established using a bhp/MMCFD correction factor at a mean pressure of 200 psia for the lower compression ratios where this correction is required. ... 

Bonney Forge, Allentown, Pa. Mean pressure in a gas line [57]. 

If the pressure does not remain uniform during the expansion, we imagine the process divided into a very large number of very small changes of volume, in each of which the pressure may be regarded as constant. Let pv be the mean pressure during an expansion from a volume (v — J8r) to a volume (v + J / ) then the small... 

Although all fluids are to some degree compressible, compressibility is sufficiently great to affect flow under normal conditions only for a gas. Furthermore, if the pressure of the gas does not change by more than about 20 per cent, it is usually satisfactory to treat the gas as an incompressible fluid with a density equal to that at the mean pressure. 

Since vm. the specific volume at the mean pressure in the pipe, is given by ... 

If the pressure drop in the pipe is a small proportion of the inlet pressure, the first term is negligible and the fluid may be treated as an incompressible fluid at the mean pressure in the pipe. 

In a synthetic ammonia plant the hydrogen is fed through a 50 mm steel pipe to the converters. The pressure drop over the 30 m length of pipe is 500 kN/m2, the pressure at the downstream end being 7.5 MN/m2. What power is required in order to overcome friction losses in the pipe Assume isothermal expansion of the gas at 298 K. What error is introduced by assuming the gas to be an incompressible fluid of density equal to that at the mean pressure in the pipe /r — 0.02 mN s/m2. 

The shear flow factor represents additional flow transport introduced by the roughness in relative sliding. It is defined as the mean flow in an element bearing where the two surfaces are in relative sliding, but the mean pressure gradient would be zero. 

It can be seen that the prediction 6a underestimates any results. This is because axial expansion is unrealistic, as indicated in Figure 4.2.8. On the other hand, prediction 5a covers almost all the results, except when the value of Vg is smaller than lOm/s. This is probably because of the usage of the mean pressure averaged over twice the radius of the vortex core in the model by Asato et al. [16], which is in quantitative agreement with the present vortex ring whose core diameter is about 25% the ring diameter. 

As both phases occupy the full flow field concurrently, two sets of conservation equations correspond to these two phases and must be complemented by the set of interfacial jump conditions (discontinuities). A further topological law, relating the void fraction, a, to the phase variables, was needed to compensate for the loss of information due to model simplification (Boure, 1976). One assumption that is often used is the equality of the mean pressures of the two phases, ... 

The reactor will consist of a number of tubes each of 80 mm diameter packed with catalyst with a bulk density of 1440 kg/m3. The ethylbenzene will be diluted with steam, the feed rates are ethylbenzene 1.6 x 10-3 kmol/m2s and steam 29 x 10-3 kmol/m2s. The reactor will be operated at a mean pressure of 120 kN/m2 (1.2 bar) and the temperature will be maintained at 833 K (560°C) throughout. If the fractional conversion of ethylbenzene is to be 0.45, estimate the length and number of tubes required to produce 0.231 kg/s (20 tonne styrene/day). 

The word isochore implies constant pressure, since iso is Greek for same and the root chore means pressure. 

---