National Physical Laboratory

About: National Physical Laboratory is a facility organization based out in London, United Kingdom. It is known for research contribution in the topics: Dielectric & Thin film. The organization has 7615 authors who have published 13327 publications receiving 319381 citations.

On the flow of air behind an inclined flat plate of infinite span

Abstract: The general form of the flow behind an infinitely long thin flat plate inclined at a large angle to a fluid stream of infinite extent has been known for many years past. The essential features of the motion are illustrated in the smoke photograph given in fig. 1, Plate 6. At the edges, thin bands of vorticity are generated, which separate the freely-moving fluid from the “dead-water” region at the back of the plate; and at some distance behind, these vortex bands on account of their lack of stability roll up and form what is now commonly known as a vortex street (see fig. 2). Various theories for calculating the resistance of the plate have also been advanced from time to time. One of the earliest is the theory of “discontinuous” motion due to Kirchhoff and Rayleigh, who obtained the expression π sin α/4 + π sin α ρV2 b (see symbols) for the normal force per unit length of the plate. More recently Karman has obtained a formula for the resistance of a plate normal to the general flow, in terms of the dimensions of the vortex system at some distance behind the plate. In spite, however, of these and other important investigations, much more remains to be discovered before it can be said that the phenomenon of the flow is completely understood. No attempt has hitherto been made, as far as the writers are aware, to determine experimentally, at incidences below 90°, the frequency and speed with which the vortices pass downstream; the dimensions of the vortex system; the average strength of the individual vortices; or the rate at which vorticity is leaving the edges of the plate. The present investigation has been undertaken to furnish information on these features of the flow.

On the partition of energy between elastic waves in a semi-infinite solid

Abstract: Expressions are derived for the power radiated in the compressional, shear and surface waves set up by a circular disk vibrating normally to the free surface of a semi-infinite isotropic solid. The total radiated power is also calculated independently by integrating the displacement velocity over the area of the source. The theory is extended to a general type of multi-element radiator in the form of an array of elements on the circumference of a circle. The calculation of the total power here involves a ‘mutual admittance’ function, a table of which is given for the case when the Poisson’s ratio of the medium is equal to ¼. The theory is applied to a three-element radiator of a type used in a recent geophysical investigation, and it is shown that the efficiency of radiation in the compressional mode can be varied between wide limits by varying the distance between the elements. Finally, an approach is suggested for problems in which the most suitable idealized boundary condition is one of known displacement under the radiator, the stress being zero elsewhere on the free surface. It is shown that the stress under the radiator satisfies an integral equation whose kernel is derived from the mutual admittance function.

Error Analysis of Direct Methods of Matrix Inversion

Abstract: 1. In order to assess the relative effectiveness of methods of inverting a matrix it is useful to have a priori bounds for the errors in the computed inverses. In this paper we determine such error bounds for a number of the most effective direct methods. To illustrate fully the techniques we have used, some of the analysis has been done for floating-point computat ion and some for fixed-point. In all cases it has been assumed tha t the computat ion has been performed using a precision of t binary places, though it should be appreciated tha t on a computer which has both fixed and floating-point facilities the number of permissible digits in a fixed-point number is greater than the number of digits in the mantissa of a floating-point number. The techniques used for analyzing floating-point computat ion are essentially those of [8], and a familiarity with tha t paper is assumed. 2. The error bounds are most conveniently expressed in terms of vector and matr ix norms, and throughout we have used the Euclidean vector norm and the spectral matrix norm except when explicit reference is made to the contrary. For convenience the main properties of these norms are given in Section 9. In a recent paper [7] we analyzed the effect of the rounding errors made in the solution of the equations

Rounding-off errors in matrix processes

Abstract: A number of methods of solving sets of linear equations and inverting matrices are discussed. The theory of the rounding-off errors involved is investigated for some of the methods. In all cases examined, including the well-known 'Gauss elimination process', it is found that the errors are normally quite moderate: no exponential build-up need occur. Included amongst the methods considered is a generalization of Choleski's method which appears to have advantages over other known methods both as regards accuracy and convenience. This method may also be regarded as a rearrangement of the elimination process.

On vortex shedding from a circular cylinder in the critical Reynolds number régime

Abstract: The flow around a circular cylinder has been examined over the Reynolds number range 105 to 7·5 × 105, Reynolds number being based on cylinder diameter. Narrow-band vortex shedding has been observed up to a Reynolds number of 5·5 × 105, i.e. well into the critical regime. At this Reynolds number the Strouhal number reached the unusually high value of 0·46. Spectra of the velocity fluctuations measured in the wake are presented for several values of Reynolds number.