Volume 5, Issue 3, 01 March 1934
Index of content:
5(1934); http://dx.doi.org/10.1063/1.1745231View Description Hide Description
The problem of a transformer of n windings, each connected to a circuit containing a source of electromotive force, is treated. The assumptions are pure reactance windings, perfect couplings and linear loads. The equations for the current in any circuit, the open‐circuit voltage across any winding, the short‐circuit current in any winding, the impedance looking in at any winding, the voltage transformation ratios, the current transformation ratios and the impedance transformation ratios are given. The ideal n‐winding transformer, which is a more restricted case, is also treated.
5(1934); http://dx.doi.org/10.1063/1.1745232View Description Hide Description
The mathematical treatment relating to mixture of fluids in a container maintained at constant pressure and volume is developed, assuming perfect and instantaneous diffusion, free efflux and no reaction between the components of the mixture. For comparison, the equations for mixture within a container from which no efflux takes place are given and also a treatment applicable to intermediate conditions. Specific applications are developed pertaining to conditions involving inert gas, such as carbon dioxide, flue gas or engine exhaust gas, released into an inclosure by automatic or manual means to extinguish fire, and to the subsequent ventilation of spaces thus deluged to reduce the toxic gas content and raise the oxygen content to limits making such spaces safe for entry.
5(1934); http://dx.doi.org/10.1063/1.1745233View Description Hide Description
In Part I the general partial differential equations are derived for the flow of compressible liquids and of gases through porous media, on the basis of the generalized Darcy law that: for all homogeneous fluids the fluid velocity is directly proportional to the pressure gradient. The equation for compressible liquids turns out to be the Fourier heat conductionequation with the density as the dependent variable, while for gases a nonlinear parabolic equation is obtained. The steady state solutions for these equations for linear and plane radial flow are derived and discussed in Part II. The heat conductionequation, in polar coordinates with radial symmetry, for compressible liquids, is then solved in Part III for systems in which (a) the density is specified over both concentric circular boundaries of an annular region, (b) the density is given over one boundary and the normal derivative over the other, and (c) the normal derivative is given over both boundaries. For the last case a new elementary solution is introduced, not given in the standard English texts. The cases where the internal boundary reduces to an infinitesimal sink are also given explicit solutions. Applications are made to (1) production history from a well whose pressure is reduced discontinuously to its final value; (2) production history from a well whose pressure is lowered so that the fluid density at the well drops linearly with the time; (3) the pressure rise in a well after shutting in; (4) pressure decline in the ``East Texas'' oil field; (5) production decline from a single well at constant pressure in a closed reservoir; and (6) pressure decline in a closed reservoir drained at a constant rate by a central well. The Green's function, corresponding to a well displaced from the center of a closed reservoir, is derived and is applied to the problem of the interference between two wells draining the same circular reservoir. The solutions for all these problems correspond to similar heat conduction problems which have not been previously solved explicitly in the literature. In Part IV an approximation theory is given for the non‐isothermal gas flow from a closed circular reservoir into a central well, and is illustrated by a numerical example showing the pressure and production decline for such a reservoir on a sudden lowering of the well pressure from an initially uniform value.
5(1934); http://dx.doi.org/10.1063/1.1745234View Description Hide Description
X‐ray diffraction patterns of aqueous solutions of the oxazine dye, Nile blue sulfate, yield direct evidence of a varying molecular association as a function of concentration, which was previously indicated by Cohen's potentiometric and spectrophotometric data. Solutions of the order of millionth molar approach obedience to the laws of dilute solutions; in moderate concentrations of the order of 5×10−4 molar the dye molecules associate to micellar structures; and in concentrated solutions the association proceeds to the stage of precipitation. The largest change in the value of the identity spacing d corresponding to the inner edge of the principal diffraction halo is found to begin with about 10−4 molar solutions. The attempt is then made to measure pore sizes in cotton fibers from the relative absorbability of the dye from its solutions over such a range of molecular and aggregate dimensions. Nile blue sulfate and methylene blue solutions before and after addition of absorbent cotton were subjected to spectrophotometric analysis. Again it is indicated in the case of the former that there is a large increase in dye absorption by the cotton corresponding to the change with increasing dilution from micellar to molecular dimensions which are compatible with predominating cotton pore sizes.