Nearly free molecular flow through an orifice

The problem of the flow through an orifice is a very interesting one in fluid mechanics, as it promises to be one of the few configurations which can be investigated over virtually the whole range of possible motions. For this reason, Liepmann(1) has recently made measurements of the mass flow through an orifice at what are practically infinite pressure rations, through a range of Knudsen numbers covering the transition from continuum to free molecule flow. The mass flow rate per unit area in the Knudsen limit (i.e., at high K = λ1/R where λ1 is the mean free path at upstream infinity and R is the radius of the hole) is well known from kinetic theory to be m = 1/4p1c1 where p1 is the density and c1 the mean molecular speed at upstream infinity. The purpose of this note is to estimate the effect on m of a Knudsen number K that is not so large

The challenge of fluid flow 1. The diversity of flow phenomena

You look up at the sky, and see a lovely cloud; you look down, and may see lovely ripples on a rivulet (or river). On a hot summer afternoon you see dancing dust devils; on a cold winter evening you can see smoke rising lazily from achulah, and hang up there as if it has given up. You peer at a telescope, and see intense supersonic jets, or vast whirling galaxies; you measure in a wind tunnel, and sense powerful tornadoes behind an aircraft wing. The universe is full of fluid that flows in crazy, beautiful or fearsome ways. In our machines and in the lab, as in terrestrial nature, one sees this amazing diversity in the flow of such a simple liquid like water or a simple gas like air. What is it that makes fluid flows so rich, so complex-some times so highly ordered that their patterns can adorn a saree border, sometimes so chaotic as to defy analysis? Do thesame laws governall that extraordinary variety? We begin with a picture gallery of a number of visible or visualized flows, and consider which ones we understand and which ones we do not, which ones we can compute and which ones we cannot; and it will be argued that behind those all-too-common but lovely flows lie deep problems in physics and mathematics that still remain mysteries

Wavelet diagnostics for detection of coherent structures in instantaneous turbulent flow imagery: a review

A review of work over the last decade shows that 2D wavelet techniques applied on flow imagery can provide powerful insights into the nature and lifecycle of coherent structures (the latter through wavelet movies) in turbulent shear flows. The advantage of wavelet techniques in often being able to infer the nature of coherent motion from a single image is emphasized. The techniques are first calibrated by using them on well-known results in the turbulent mixing layer. They are then applied to jets and plumes, and it is shown how off-source heating in such flows can disrupt the coherent structures in the unheated flow. A suitably reduced version of the present method, using discrete wavelet transforms on signals from a finite array of sensors, could be a useful diagnostic tool in near-real-time detection of coherent structures or patterns for the purpose of selecting appropriate control signals to the actuators in a flow-control system

Kosambi and proper orthogonal decomposition

In 1943 Kosambi published a paper titled 'Statistics in function space' in the Journal of the Indian Mathematical Society. This paper was the first to propose the technique of statistical analysis often called proper orthogonal decomposition today. This article describes the contents of that paper and Kosambi's approach to the subject. It was only in 1967 that it began to be appreciated that the method that had gained wide currency in several fields under different names was first set out in Kosambi's 1943 paper

Science, technology and the economy: an Indian perspective

During the first three decades after 1947, the Indian economy grew only 3% per year but there was vast expansion in the science and technology (S&T) infrastructure. Decades later, especially during the last few years, the economy has grown much faster, but the S&T systems have not experienced the transformation that business and industry have. The net result is that the public sector S&T system is facing a major crisis even as the private sector contributes little to the national R&D effort. Wealth generation in India by private S&T services, especially in information technology, has led to greater prosperity for the educated middle class, but has also led to greater inequalities in income. The national scene is one of generally uneven achievement and extraordinary potential. This paper argues that unless another major shift in S&T policy occurs, there is real danger that India will not move beyond its status as a blue-collar S&T power