Volume 7, Issue 9, 01 September 1936
Index of content:
7(1936); http://dx.doi.org/10.1063/1.1745401View Description Hide Description
An important error in Pidduck's special solution is pointed out. Special solutions for a perfect and an imperfect gas are obtained. Modifications to take account of projectile friction and the burning of the powder are given.
7(1936); http://dx.doi.org/10.1063/1.1745402View Description Hide Description
A method is described for studying the flow of gas‐liquid mixtures through unconsolidated sands. Results are given for experiments on four sands of widely different permeabilities using carbon dioxide and water as the fluids. A relation between permeability and liquid‐saturation of the sand is found which permits the correlation of saturation and the steady state flow of the gas and liquid components. Generalization of these results for all unconsolidated sands seems permissible. The phenomena of equilibrium permeability and equilibrium liquid‐saturation are described and their significance discussed. It is believed that the experimental attack and type of analysis is applicable to the general problem of the flow of gas‐liquid mixtures through porous media.
7(1936); http://dx.doi.org/10.1063/1.1745403View Description Hide Description
The empirical results established by R. D. Wyckoff and H. G. Botset on the flow of gas‐liquid mixtures through unconsolidated sands have been formulated into basic differential equations governing the motion of general heterogeneous fluids through porous media under both steady state and transient conditions. This formulation is based upon a representation of the porous medium as having a macroscopically local structure defined by the liquid saturation, or volume composition of the gas‐liquid mixture, this saturation in turn determining the separate permeabilities of the medium to the liquid and gas phases. The steady state solutions of these equations are derived for the cases of linear, radial, and spherical flow, and the distributions of the pressure, permeability, and saturation are given graphically. It is found that the properties of these flow systems change but little from the corresponding ones for homogeneous fluids as long as the pressure exceeds about half the saturation pressure of the gas, except for the fact that the liquid saturation is very approximately equal to the equilibrium value and the liquid permeability has a value very near to its equilibrium value. The drop in liquid permeability and saturation is highly localized about the outflow surfaces and in those regions where the pressure is very much less than the saturation pressure, the increase in the pressure gradients above their normal homogeneous fluid values being also largely confined to these regions. For the study of the early stages of transient types of flow an analytical theory is derived, in the case of the linear system, based upon a representation of the transient as a continuous succession of steady states. For the investigation of the complete history of the linear transient system a numerical method is presented in which is developed a stepwise integration of the simultaneous partial differential equations for the pressure and liquid saturation, after the replacement of the various derivatives by their appropriate differences. The specific problem is treated in which a linear column of sand of unit length filled with liquid saturated with an ideal gas to a pressure of 10 units is suddenly exposed at one terminal to a pressure of 1 unit, which is thereafter permanently maintained at that value while the other end is permanently kept closed. The results of the calculations for this problem are given graphically in the form of sets of curves showing the history of the saturation and pressure distributions within the flow channel, the time variation of the flux from the system, and the time variation of the gas‐liquid ratio associated with the liquid efflux. It is found that the liquid saturation at the time of physical depletion of the system, corresponding to an equalization of the pressures to that maintained at the outflow terminal, is quite uniform, being only 5 percent less at the outflow terminal than at the closed terminal of the linear column. The gas‐liquid ratio is found to increase monotonically with the time. The bearing of these results on such problems as well spacing and gas recycling in the production of oil from underground reservoirs, and the manner of treatment of other typical heterogeneous fluid systems so as to include both the deviations from the ideal behavior of the free gas phase and the effect of gas segregation are discussed in detail.
7(1936); http://dx.doi.org/10.1063/1.1745404View Description Hide Description
It is shown that, making the assumption that oils as used in engine lubrication cannot stand absolute tension, and taking into account the observed tendency of the bearing faces of piston rings to wear into an uneven shape with the ``high'' point near the middle and a very gentle slope to each edge, Reynolds' theory of bearing lubrication can be extended to ringlubrication. A practical application of this extension is outlined and illustrated. Results of calculations, based on this extension, of ring clearance and wear under average working conditions are in substantial agreement with a number of observations.
7(1936); http://dx.doi.org/10.1063/1.1745405View Description Hide Description
In an extension of the work of N. Rashevsky, the problem is treated of the determination of the distribution of concentrations and consequent distribution of osmotic forces in a metabolizing liquid sphere subject to a general infinitesimal deformation. The principle of virtual displacements in the form of an inequality is applied as a criterion of the instability (tendency to divide) of the system. This gives an algebraic equation determining the critical radius at which the system becomes unstable, and the equation is analyzed in detail with reference to the influence of the physical parameters of the system. In particular, it is found that, for a certain range of size of the system, this critical value is practically independent of the surface tension. Finally, the diffusion equations are integrated for a system where the rate of reaction is not constant, but a linear function of the concentration, and a procedure similar to the above is outlined.