Free Surface of the Liquid-Gas Phase Separation as a Measuring Membrane of a Device for Measuring Small Hydrostatic Pressure Difference Values / Powierzchnia Swobodna Rozdziału Faz Ciecz-Gaz Jako Membrana Pomiarowa Urządzenia Do Pomiaru Małych Wartości Różnicy Ciśnienia Hydrostatycznego

Abstract

Abstract To obtain a correct reading of fluid flow through a porous medium, it is necessary to know the pressure distribution. While in the case of large Reynolds numbers (turbulent flows) finding pressure measurement devices on the market is not a major problem, there are currently no available devices with sufficient accuracy for measurement of laminar flows (i.e. for Re numbers (Bear, 1988; Duckworth, 1983; Troskolański, 1957) in the range from 0.01 to 3). The reasons of this situation has been discussed in a previous articles (Broda & Filipek, 2012, 2013). Therefore, most of the work on this issue relates to testing velocity distribution of the filter medium (Bear, 1988) or pressure distribution at high hydraulic gradient levels (Trzaska & Broda, 1991, 2000; Trzaska et al., 2005). The so-called measurements of the lower limit of the applicability of Darcy’s law for liquid, as well as determining a threshold hydraulic gradient J0 (Bear, 1988) tend to cause especially great difficulty. Such measurements would be particularly important application in determining the infiltration of water into the mine workings, filtering through the foundations of buildings, etc. For several years, the authors (Broda & Filipek, 2012, 2013) have been engaged in the development of methods and measuring instruments (patent applications: P.407 380 and P.407 381), which would allow for measurement of hydrostatic pressure (differences) below 1 Pa. In the course of research, a new concept of methodology for measuring low values of hydrostatic pressure differences was developed, which is the subject of this article. This article seeks to introduce a new concept of using the free surface of liquid-gas separation as the measuring membrane of a device used in measurement of small values of hydrostatic pressure. The focus is mainly on the possibility of building such a device - describing the technical difficulties that occurred during the execution of the idea. Consequently, less attention was paid to the broader considerations related to uncertainty of the proposed method’s measurements, due to the authors’ awareness that this is the first prototype of such a device and, on the basis of this experience, another one will be built and tested. The observations and numerical analysis of the image formed on the screen by the passage of a laser beam through the free surface of the liquid-gas separation show that at low values of pressure difference, the bubble acts as a membrane shifting in the direction of lower pressure, in such way that the displacement is proportional to the pressure difference at both ends of the bubble. The proprietary method of numerical data processing presented in this article, based on analysis of the intensity of color change in a frame moving along a selected line outside of visual changes in the image of the laser beam after passing through the test structure, provided a tool to create first mathematical models to describe the observed changes (2),(3). Presented in this article method of measuring the difference between the free surface levels in two containers, and hence the measurement of hydrostatic pressure difference provides a new tool for laboratory measurements in the fields of science, which were previously unattainable.