Non-uniform Pressure Distribution Research Articles

Modified borehole jack method for elastic property determination in rocks : de la Cruz, R V Rock Mech, V10, N4, April 1978, p221–239

A method is described for the determination of the elastic parameters of rock from in situ tests using friction strain gauge and an extended borehole jack. Tangentially orientated friction strain gauges are positioned on opposite quadrants of the borehole, both other quadrants being fitted with a borehole jack, in order to measure load and deformation simultaneously. Equations are developed from which the modulus of elasticity of the rock mass is obtained. It is shown that a non-uniform pressure distribution and the plate-wall contact area have an insignificant effect on the accuracy of the results. Secondly effects are reduced by carrying out measurements only in the centre of the specimen. This new method has the same advantages as the established Goodman-Jack method. Of great importance is that the theoretical basis is exact. Although the method is only applicable for an ideal elastic material it can also be used for other in situ measurements in addition to the determination of the elastic modulus, for example linearity, anisotropy, inhomogenity, tensile strength and the primary stress condition. (TRRL)

Measurement of electron loss cross sections for 0.25- to 5-keV hydrogen atoms in atmospheric gases

Absolute electron loss cross sections have been measured for fast hydrogen atoms incident on He, H2, N2, O2, CO, CO2, and CH4 in the 0.25- to 5-keV energy range important in studies of proton aurorae. The fast hydrogen atoms produced by charge transfer passed through a cell containing the target gas. The current of fast protons arising from electron loss collisions of these H atoms with the target gas was measured. Particular attention was paid to complete collection of product ions and to elimination of effects resulting from nonuniform pressure distributions near the gas cell orifices. Techniques for absolute determination of fast hydrogen atom flux are also described.

Compressor-Diffuser Interaction with Circumferential Flow Distortion

An analytical and experimental study of axial compressor-diffuser interaction in circumferentially non-uniform flow is reported. An analysis of non-axisymmetric flow in an annular diffuser is presented, based on an inviscid rotational core flow plus the use of a diffuser effective area ratio to account for boundary layer blockage. The analysis is applied to the prediction of the diffuser flow field associated with the presence of a circumferential total pressure distortion. It is found that large static pressure non-uniformities can exist at the inlet of diffusers that are short compared with their mean circumferences, as is usually the case in turbomachinery applications. The analysis is coupled to an asymmetric compressor flow field prediction to provide a method for calculating the effect of an exit diffuser on compressor performance with distortion. It is shown that the velocity defect seen by the compressor can be substantially increased by the presence of the diffuser.The experiments were directed at assessing the method used to predict the flow in the diffuser. Measurements were carried out of the inlet static pressure distortion associated with a circumferentially non-uniform total pressure distribution. The results are found to be in good agreement with the theoretical predictions.

Porous−wall BeO capillary waveguide laser

Small−bore capillary tubes exhibit very high optical gains and saturation intensities in flowing gas CO2 systems. However, these parameters may vary greatly in the axial direction due to the nonuniform axial pressure distribution. Use of porous−wall BeO capillary tubes makes it possible to attain a more uniform pressure distribution and to usefully scale capillary waveguide amplifiers to longer lengths.

Some design and performance considerations of diaphragm type pressure cells using strain gauges

The two basic types of earth pressure cells that are commonly used are the piston type, which has a very rigid active face (where a change in pressure is reflected by the movement of the whole of this face), and the diaphragm type, which consists of a fairly flexible diaphragm clamped to a rigid edge. One of the intrinsic disadvantages of the diaphragm type of earth pressure cell is that it is most vulnerable to non-uniform stress distribution across its diaphragm. To overcome this problem special attention is paid to providing a uniform stress distribution during calibration and also trying to attain a fairly uniform distribution in the field by placing the cells with extreme care. However, it must be realized that a non-uniform distribution of earth pressure is the norm rather than the exception in nature. Even the most carefully placed earth pressure cell cannot avoid some degree of minor non-uniformity in pressure distribution. It is the purpose of this note to investigate this effect of non-uniform stress distribution on a diaphragm type earth pressure cell which uses strain gauges on the active diaphragm. From these studies, it is intended to find some means of minimizing the effect of this non-uniform pressure distribution in the initial design stage and of detecting the degree of this non-uniformity in pressure distribution so as to be able to assess the acceptability of the earth pressure cell readings during the final operation stage. /TRRL/

Limit analysis of rectangular R.C. slabs on ground

A method is presented for obtaining lower bound on the carrying capacity of reinforced concrete foundation slab-structures subject to non-uniform contact pressure distributions. Functional approach suggested by Vallance for simply supported square slabs subject to uniform pressure distribution has been extended to simply supported rectangular slabs subject to symmetrical non-uniform pressure distributions. Radial solutions, ideally suited for rotationally symmetric problems, are shown to be adoptable for regular polygonal slabs subject to contact pressure paraboloids with constant edge pressures. The functional approach has been shown to be well suited even when the pressure is varying along the edges.

Non-Linear Response of Deforming Drops

WHEN a liquid drop is suddenly exposed to an external flow-field, its initial response is either vibration or continuous deformation algebraically with time. Harper, Grube and Chang1 have approximated the transition between these two states and have concluded that the drop ceases to vibrate at a critical Weber number Wec of about 7.3. (We is the ratio of the forces due to aerodynamic pressure and surface tension, that is, We=(ρgU2 ∞ rσ) where ρg is the gas density, U∞ the flow velocity, r the drop radius and σ the surface tension.) Above the critical value, the non-uniform surface pressure distribution exerted by the external flow causes the drop to deform continuously and ultimately to burst. This communication describes observations of the non-linear response (at Weber numbers near Wec) after the drop distortion has become large compared with the initial radius.

Thermal constriction resistance due to non-uniform surface conditions; contact resistance at non-uniform interface pressure

Thermal constriction resistance due to nonuniform metal surface conditions, considering macroscopic contact resistance for nonuniform interface pressure distribution

Influence of the degree of particle deformation in a pressed compact on grain growth during heating

1. An investigation has been conducted into the influence of the degree of particle deformation in pressed compacts on the grain-growth process during subsequent heating. It is demonstrated that higher compaction pressure promotes a reduction in grain size when the compact is held for a short time at the required temperature. 2. The inhibiting effect of the pores on the grain-growth process has been confirmed once again. 3. A study was made of grain growth in porous compacts during isothermal holding. It is shown that the crystalline grains in compacts with 10% of pores have a greater capacity for growth in the course of time than the grains in compacts with 20% of pores. 4. A comparison has been made of grain growth in a pressed compact and in a compact re-pressed under the same pressure. It is demonstrated that interfacial boundaries between the powder particles provide additional recrystallization centers. 5. The influence of nonuniform pressure distribution in the pressed compacts on grain growth during subsequent heating has been established.

Transient Stresses and Displacement Around a Wellbore Due to Fluid Flow in Transversely Isotropic, Porous Media: I. Infinite Reservoirs

Abstract Equations of elasticity for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure were formulated. Using an analogy between thermal and porous body stresses, it was shown that the solution for a transversely isotropic porous body may be obtained by incorporating body forces and the stresses due to a boundary load into the corresponding solution for the thermal stress problem. Equations of elasticity and the thermal analogy method were used to determine transient horizontal, tangential, and vertical s tresses and radial displacement in a semi-infinite cylindrical region when either a constant pressure or a constant rate of flow is maintained at the wellbore. The vertical and tangential displacements are zero from the conditions of the problem. A numerical analysis was made of the solutions obtained by using a digital computer to determine the relative influence of each system variable. Considering rock as a porous body with internal fluid pressure generally gives results significantly different than considering the rock to be nonporous; the directional character of rocks leads to significant differences as compared to results based upon the common assumption of isotropy. Stress gradients are high near the wellbore but die out away from the well. Radial stresses are compressive or neutral, whereas tangential stresses are tensile, neutral or compressive, depending upon the boundary conditions and physical properties of the system. Vertical stresses are compressive for an unbounded system. For constant wellbore injection rate, the vertical stress is proportional to the rate of fluid injection and decreases with time, whereas the radial and tangential stresses increase with time. At a given location, the radial displacement generally is very dependent upon time. INTRODUCTION A realistic appraisal of the state of stress in subsurface rock formations would be of considerable interest and use to the petroleum industry. For example, knowing the state of stress in proximity to a wellbore would be of fundamental importance in designing a fracturing operation or, more important, of clearly understanding the conditions necessary to produce rock failure of desired dimensions and geometry. Understanding conditions necessary for rock failure at the wellbore would also be of utility in a preventive sense. For example, borehole stability is an important consideration for many rock formations, and knowledge of the stress state at and near the wellbore under conditions of substantial pressure gradient due to fluid flow would be of great value. When fluid flows through a porous body which is initially at some uniform stress level, the following forces generate stresses at any point in the body.Forces due to nonuniform pressure distribution. With increasing pressure the elements of a body are compressed. Such compression cannot proceed freely in a continuum when the pressure is not uniform throughout, and thus, stresses due to flow of fluid are set up.Pore fluid pressure. This gives rise to normal stresses whose value at any point is the product of areal porosity and the fluid pressure. Although the fluid exerts uniform pressure, the stresses it creates in an anisotropic body may not be the same in all directions since the areal porosity in an anisotropic porous body is a direction-dependent quantity. This consideration leads to the concept of directional porosity.

Plastic indentation in metals with cones : A. G. Atkins and D. Tabor, J. Mech. Phys. Solids, 13 (1965) 149–164; 13 figs., 3 tables, 22 refs.

The present sensor is, as reported previously, a brass sheet having a ridged surface which is inserted into the tool-workpiece interfaces to measure the width of flattened plateau of the ridges as the index of the pressure exerted during forging. In order to examine the reliability of the response of the sensor to non-uniform pressure distribution, pressure distributions over some tool surfaces were determined in several plane-strain extrusion processes of fully work-hardened aluminium specimens and the results were compared with the theoretical results obtained from the slip-line field analysis. The discrepancies were found to be within 5 to 10 per cent.The sensers were then applied to determine pressure distributions in some plane-strain and axisymmetric cold forging processes of work-hardened and annealed specimens. Generally the pressure distribution of hardened aluminium over a tool surface showed a more marked non-uniformity than did that of the annealed. A simple law that correlates the container pressure with the extrusion pressure was obtained. Thus, for a given extrusion geometry, the non-deforming portion of annealed specimen exerted a higher pressure over the container surface than did that of the hardened, while the latter required a higher extrusion pressure.

Influence of Oblique Channel Ends on Screw-Pump Performance

Congruent velocity distributions in parallel channel cross sections are assumed in conventional flow theories for screw pumps. That assumption leads to nonuniform pressure distributions along the oblique channel ends. These pressures should be uniform when screw-pump inlet and discharge connections do not restrict flow. A new theory for isothermal flow through channels with large aspect ratios is derived based on uniform pressures along oblique ends. End-effect correction factors for drag flow and pressure back-flow rates are given as functions of L/D and helix angle. Calculated pressure distributions, streamlines, and the end factor for pressure backflow are compared with experimental values.

Acoustic Radiation Damping of Vibrating Structures

Existing theories for predicting the acoustic radiation damping of structures are reviewed. A uniform pressure approximate theory for predicting the acoustic radiation damping of a single flexible panel, forming part of an otherwise rigid plane baffle, formulated by D. J. Mead [“The Effect of a Damping Compound on Jet Efflux Excited Vibrations,” Aircraft. Eng. 32, 374 (1960)], is developed into an exact theory, taking into account the nonuniform pressure distribution over a vibrating surface; a general expression is also developed to include any form of panel boundary support. The equations developed have been evaluated numerically by computer, for ease in predicting the acoustic damping factor for a wide range of panel sizes. The acoustic damping of a single panel forming part of a flat baffle and also of a cylindrical baffle has been measured experimentally by three methods.

Olivine-spinel equilibria at high pressure in the system Ni2GeO4-Mg2SiO4

Olivine-spinel solid solution equilibria in the system Ni2GeO4–Mg2SiO4 have been studied over the pressure range 0 to 90 kilobars at 600°C. The solid solubility of Mg2SiO4 in Ni2GeO4 (spinel) increases from 27 to 70 mole per cent over this pressure range. The corresponding solid solubility of Ni2GeO4 in Mg2SiO4 (olivine) decreases from 12 to less than 5 mole per cent over the same pressure interval. Extrapolation of the phase boundaries in conjunction with a consideration of possible errors leads to the conclusion that an olivine-spinel transition will occur in Mg2SiO4 at 130±20 kilobars at 600°C. Experiments were carried out in a uniaxial pressure apparatus using 15 different starting compositions. The errors which are likely to arise as a result of nonuniform pressure distribution between the pistons are discussed. Mean uniaxial pressure, internal consistency, and reproducibility are believed to be accurate within ±5 per cent, and absolute pressure is probably correct to 10 per cent. A detailed study is made of the effects of pressure and composition on the lattice parameters of spinel solid solutions. The variation is found to be complex, with large positive deviations from Vegard's rule. The extent of these deviations decreases at very high pressures. It appears that the irregularities are due to an order-disorder equilibrium involving the distribution of Mg and Ge ions between normal and inverse sites in the spinel lattice. The minimum density change accompanying the olivine-spinel transition in Mg2SiO4 is determined by extrapolation to be 9 per cent.

雨滴の落下速度について

It is already known that the observed terminal velocity of falling raindrops with a diameter larger than 1mm is considerably smaller than that which may be expected from the drag coefficient of a sphere. This fact is generally attributed to its deformation due to the non-uniform distribution of pressure upon the surface of the drop.In this paper, the author shows theoretically that, if the flow around the drop is a potential one and the deformation is small, the shape of a falling raindrop is an oblate spheroid whose axis is vertical. He then computes the fall velocity, on the assumption that the increase in cross area due to the deformation only causes the decrease in fall velocity, and that the drag coefficient of an oblate spheroid with small eccentricity is approximately equal to that of a sphere whose radius is equal to the major radius of the former. The computed values of fall velocity agree very well with the recent measurements of R. Gunn and J. D. Kinzer in the range of diameters less than 2mm.A more complete one of this paper in English is published in the Geophysical Magazine, Vol. 21, No.3, Tokyo.

Hot-cathode thyratrons: practical studies of characteristics

The paper surveys the main features which determine the characteristics and life of thyratrons in the light of direct experiment and of field experience. These include electron emission from the cathode, ionization and current build-up, grid control, the current-carrying capacity of the valve, the decay of ionization at the end of conduction, and the provision of suitable operating conditions.Emphasis is laid on factors which, while not immediately affecting electrical performance, may determine valve life; one example is positive-ion bombardment, which may cause damage to the cathode.The control characteristics of different types of grid are discussed; particular reference is made to the pentode design, a recent development enabling heavy currents to be controlled from high-impedance grid circuits.The arc voltage drop varies considerably with filling pressure and with current value, abrupt changes being associated with modifications in the form of the discharge. If the current-carrying capacity of the arc path is exceeded, the arc, if it cannot transfer to an alternative path, may suddenly go out, giving rise to generally undesirable high-voltage surges.A method of studying de-ionization time is described, and results are given showing this time as a function of the gas and its pressure. The characteristics of various gas and vapour fillings are discussed. A non-uniform pressure distribution in mercury-vapour valves assists rapid starting.

Pressure distribution in a fluid due to the axial vibration of a rigid disc

The advent of broadcasting has stimulated scientific interest in the reproduction of sound by the aid of moving diaphragms. There is a distinct change in the quality of reproduced music according as one stands in front or at the side of a loud speaker. This is due to non-uniform pressure distribution from the diaphragm at various frequencies. When the wave-length of sound is comparable with the radius of the diaphragm there is a focussing effect. This occurs at the higher audio-frequencies and upsets the tonal balance unless the listener is situated on the axial line of the diaphragm. The purpose of the present paper is to examine analytically the pressure distribution in the space surrounding a flat rigid disc vibrating in a plane of infinite extent. The plane prevents interference of the sound waves emitted by the two sides of the disc.

Sea Level along the Atlantic Coast of the United States and Its Fluctuations

Sea level, or more precisely mean sea level, is a term of frequent use, especially in geographic and geologic literature. It is the universal datum from which the heights on land and the depths in the sea are reckoned. As generally used, the term is apparently free from any ambiguity; indeed, the implication is that the determination of mean sea level is a simple matter. It is only when it becomes necessary to determine the plane of mean sea level accurately, as, for example, in the study of the subsidence or emergence of a coast, that numerous difficulties appear. Even the very definition of mean sea level involves difficulties. The level of the sea is at all times disturbed by wind and tide. Is mean sea level, therefore, to be defined as the surface which the sea would assume if undisturbed by weather and tide? That, obviously, is a perfectly legitimate definition, and it is the one the geodesist prefers. In his own words mean sea level may be defined as the surface which would coincide with the surface of the oceans and their tide water branches if the tide producing forces should cease to act and there were no movements of the air and the barometric pressure were uniform.'' For his investigations on the figure of the earth and for spreading his precise level nets over the interior of the country, the geodesist finds his definition of mean sea level satisfactory. In a sense, however, geodetic mean sea level is a hypothetical surface; for, while the effects of the rise and fall of the tide on sea level balance out if the observations are continued over a considerable period of time, the effects of air movements and of the non-uniform distribution of barometric pressure do not balance out but leave a net effect or resultant in the one or the other direction. And the elimination of these resultant effects is a problem of considerable magnitude.2