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This paper considers the problem of determining the inviscid, subsonic compressible (or incompressible) blade-to-blade flow field through a turbomachine blade row, and presents two computer solutions, known as the ‘matrix’ and ‘streamline curvature’ methods, for solving this elliptic problem. In the former method the equations of motion are formulated in terms of a stream function and the numerical solution is based on finite difference approximations; in the latter, the equations of motion are solved in conjunction with the equation of continuity by an iterative process starting from a guess for the streamline pattern. Solutions for several blade profiles, giving flow patterns and blade surface velocity distributions, are included.

After an introduction to the aerodynamic problems facing the designer of large steam turbines, two analytical methods that have been used to analyse the flow in such turbines are reviewed, and their limitations discussed. Results are given for an analysis of a single-stage machine similar to that found in an intermediate pressure steam turbine using the matrix through-flow programme to investigate the effects of varying blade twist, tilt, blade thickness, and camberline shape. In addition, details are given of a comparison made between results obtained from a streamline curvature and a matrix through-flow programme used to analyse a single-stage turbine. Finally, the problems of using these programmes are discussed, and details of the effect of grid shape and damping factor are given.

The distribution of pressure and velocity within the rotor of a radial flow gas turbine is computed using a two-dimensional streamline curvature method. Solutions are obtained on the meridional plane and also on three blade-to-blade surfaces at the hub, mid-blade position, and at the shroud. The torque, as calculated from the blade-to-blade flows, agrees with the measured torque over a speed range of approximately 2:1 with sufficient accuracy to support the usefulness of the flow structure as indicated by two-dimensional calculation methods applied to radial turbomachines.

The classical description of the critical point leads to infinities in such properties as the compressibility and the heat capacity at constant pressure, Cp, as the critical point is approached along a path in the homogeneous fluid. However, this description does not require a singularity in the heat capacity at constant volume, Cv, and supposes that the Helmholtz free-energy, A, is everywhere an analytic function of volume, V, and temperature, T. It is now clear that this description is inadequate, that Cv is infinite at the critical point and that A is a non-analytic function of V and T. The classical description must, therefore, be abandoned and it is shown that we have, in its place, a set of inequalities between the degrees of the singularities in such thermodynamic functions as Cv, compressibility, coefficient of thermal expansion along the orthobaric curve, and the curvature of the vapour pressure line. These inequalities provide powerful tests of even the best modern measurements and enable us to give a fairly complete thermodynamic description of the singularities of the critical region. The transport properties are not so well understood. It is probable that the shear viscosity is non-singular whilst the thermal conductivity is known to be highly singular. This last singularity is probably related to the infinity in Cv. The dimensionless functions—Rayleigh number, Prandtl number, and Grashof number—all become infinite at the critical point.

The streamline curvature technique for the numerical solution of the equations of motion for two-dimensional flow has been analysed. By considering a simple flow case an optimum damping factor for the quasi-orthogonal method was derived as a function of grid aspect ratio, Mach number, and differentiation formula, and the number of iterations required for a given accuracy was found. The stability and accuracy properties of numerical methods for finding the second derivative of a curve were also investigated, and it was found that, in this context, finite difference methods using polynomials were the best and spline methods the worst.

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In his paper, Tuman found that, surprisingly, in all cases studied the minimum travel time of acoustic waves was along a curved path in a formation surrounding a borehole. The curvature resulted from velocity variations around the borehole in formations which show a nonlinear stress‐strain relationship. However, the results of these calculations may be in error due to the use of incorrect stresses selected for the determination of the local acoustic wave velocity. In particular, the use of the radial stress distribution for this purpose is doubtful for the calculation of a curved travel path which in general does not deviate much from the vertical direction.

An instrument to determine the stiffness of paper is described. The specimen is bent through a given angle, and the bending moment is measured as the torque in two lengths of piano wire, between which the clamp that holds the specimen is suspended. Stiffness of paper is defined as the bending moment per unit of width of specimen producing unit curvature. This quantity was evaluated for eight types of paper, for various lengths and widths of specimen, and for bending angles from 5° to 30°. The stiffness value for a given specimen remained substantially constant when the width and bending angle were varied, but increased somewhat as the length of the specimen was increased.

A brief summary is given of the paper by Stiles. The line-element suggested by Stiles is shown to be the sum of the squares of total differentials of three magnitudes. Therefore, the corresponding color threefold is Euclidean. For the same reason, the line-element originally proposed by Helmholtz also defined a Euclidean color space. The customary parameters of colorimetry correspond to curvilinear coordinates in the color space of both Helmholtz and Stiles. In both of those spaces, constant luminosity is represented by curved surfaces. The forms of the line-elements of both Helmholtz and Stiles imply that geodesics, representing series of colors which exhibit the least number of just-perceptible differences between any two colors, are straight lines in the Euclidean spaces defined by those line-elements. They also imply that ordinary length measured along these lines is proportional to the number of just-perceptible differences between the colors represented by the terminal points. No direct tests of these implications are known. MacAdam’s data on the discrimination of equiluminous colors determine a surface of constant luminosity in the color discrimination space for at least one observer (PGN). This surface exhibits such severe (and irreducible) curvature that the straight lines drawn between most pairs of considerably different equiluminous colors are, at their midpoints, far from the surface of constant luminosity. The line-elements of both Stiles and Helmholtz, therefore, imply that the series of colors exhibiting the least number of just-perceptible differences between two equiluminous colors includes many colors of very different luminosity. Although no observational tests are known, it seems unreasonable to expect that considerable departures from the common luminosity of the terminal colors will reduce the number of differences perceptible in any series between them. Attention is called to the criterion of probability of errors in color matching as an alternative to just-perceptible differences for investigations of visual sensitivities to color differences. This concept leads to a definition of the line-element independently of any assumption of the applicability to color discrimination of Fechner’s law or its modifications.

Response of roots to a gravitational stimulus consisting of a sudden artificial change of orientation in the gravitational field can be resolved into a phase of very rapid curvature and reduced growth-rate which dies out rapidly and is followed by a phase of very slow response and normal growth-rate. A somewhat similar two-phased response to sudden reorientation is found in certain plagioand diageotropic organs. The mechanism is discussed. Starch column chromatography has been used in an attempt to isolate growth factors which according to one postulate might be involved, and the significance of the findings is discussed. This technique is shown to be convenient for effecting volatile active substances which are lost in paper chromatography.

This is the simplest problem of mechanism synthesis as there are infinite degrees if freedom and the problem can be reduced to the computation of the envelope generated by a simple form, the follower in its motion relative to the cam plane. For the most usual follower geometries standard programs have been prepared that give directly the design of the cam, the pressure angle and curvature diagrams, and even a paper tape to drive a N/C machine (Fig. 18-20). This can also be done when the follower is not a simple lever but any kind of mechanism which can be described by MEDES. This is done by inverting the movement of the mechanism (that is driven elements become motors) analyzing the movement by a postprocessor of MEDES to find the locus of the center of the follower seen on a plane which rotates at constant speed around the can shaft (Fig. 21-22).

OWING to the great variability in growth-rate and tropic curvature of the coleoptile shown by oat (Avena) seedlings similarly treated, it is for many experimental purposes desirable to be able to take successive measurements of growth or curvature on the same individuals rather than on a fresh sample each time. Thus in experiments involving curvatures, in view of the difficulty in obtaining really straight seedlings to start with, doubtless partly due to nutation1, it is most desirable to have initial records before treatment; it may also be useful to record the degree and kind of curvature at successive intervals after stimulation or application of growth substance. This is, however, unsafe with the usual technique, in which the shadowgraphs are taken with white light, since the exposure itself induces curvature. Schneider and Went1 therefore constructed their ingenious “photokymograph” ; but this is only suitable for decapitated coleoptiles and for curvature but not growth measurements: it is, moreover, somewhat elaborate for routine or class use. The essence of the present technique is simply to use more-or-less panchromatic photographic paper for the successive shadowgraphs, and to make the exposures with light passed through an orange or red filter such that no phototropic or growth response can be detected even when the photographically necessary exposure is multiplied many times. These requirements have been met by the use of Kodak RP 15 “Reflex” paper and light from a tungsten filament lamp passed through a single layer of ‘Chromex 2202/C10’ orange cellulose acetate filter which has a cut-off at about 0.530 µ wave-length and a high transmission throughout the red. With a total intensity, at the position occupied by the seedlings, of 0.08 foot-candles, adequate shadowgraphs can be obtained with one minute's exposure. One hour's exposure of intact seedlings under these conditions has been found to cause no detectable growth response or subsequent curvature. It should therefore be safe to take a long series of successive records of the same seedlings.