Hydrostatic Approach Research Articles

Approximate modelling of 2D curvilinear open channel flows

The common treatment of open channel flow involves the hydrostatic pressure approach. However, many flows are curvilinear and a higher-order approach is needed to deal with the non-hydrostatic pressure distribution. The current models are based on linear relationships for the variation of streamline curvature and inclination along the equipotential curves of the flow net, yet this approach is not verified with 2D results. In the present study typical 2D free surface flow nets are analysed to investigate the variations of streamline curvature and inclination. From the detailed 2D information, approximate relationships describing the curvature and inclination are proposed. It was found that streamline curvature and inclination do not vary linearly in general. The higher-order energy and momentum curvilinear equations are improved with this approach, thereby approximating the real flow net geometry. The implications of these findings on curvilinear flow modelling are discussed using several test cases.

Steady open channel flows with curved streamlines: the Fawer approach revised

Rapidly varied open channel flows are characterized by curvilinear streamlines, thereby resulting in a pressure field different from the hydrostatic approach proposed in the standard gradually varied flow theory. This problem is related to environmental hydraulic problems such as the undular hydraulic jump and flow over round-crested weirs, for which streamline curvature effects are significant. The inclusion of the curvilinear streamline effect in an extended energy equation was firstly by Fawer. Most of the extended energy equations currently employed are therefore modified forms of the original Fawer approach. The aim of the present study is to highlight and remind engineers of the outstanding theory presented by Fawer. Herein, his approach for steady open channel flow with curved streamlines is revised and compared with experimental observations. Computational methods are presented in detail and based on present results, it can be observed that more recent and complex models for these problems are similar to the original proposal of Fawer, and hardly more accurate in some instances. Based on the proposed study an useful framework for theoretical models for steady open channel flows with curved streamlines is proposed.

新潟地域の大規模地すべりと異常高圧熱水系

High salinity Na-Cl-type geothermal waters have often been found in the anticlinal hilly terrains and landslide-prone areas of Niigata Prefecture by boring to depths of more than 1,000 meters. These fluid pressure gradients are much higher than the hydrostatic pressure gradient and approach the lithostatic pressure gradient with increasing depth. The geothermal waters in the Matsunoyama area, Tokamachi City, have the highest orifice temperature in Niigata Prefecture. Eight geothermal water wells in this area were drilled along the anticlinal axis of a nearby hilltop or higher breast of the Matsunoyama dome and ranged in depth from 170 to 1,170 meters and in temperature from 35 to 95°C. For example, the Takanoyu-1 geothermal water well is only 170 meters in depth but has an orifice temperature of 90°C. These waters show geyser action associated with methane gas, and typically have very high salinity with considerable amounts of chloride. Hydrogen and oxygen isotope values and chloride concentration of approximately 9,000mg/L suggest that the origin of the waters is altered fossil seawater trapped in organic-matter-bearing sedimentary rocks. The temperature and depth of the primary reservoir are estimated to be 139°C and 3,000 to 4,000 meters, respectively, using a Li-Mg geothermometer and the mean geothermal gradient of 30-40°C/km in the Niigata sedimentary basin. Na-Cl-type groundwaters emerged from several landslides located in the Higashi-kubiki and Naka-kubiki areas including the Matsunoyama area. Well loggings were carried out to profile the electric conductivity and hydrochemistry of groundwater in the Utsunomata landslide in the neighborhood of the Matsunoyama area. Profiles in the active landslide mass showed sharp increases of the electric conductivity and the NaCl components at around the depth of the sliding surface. In contrast, no significant variations of the profiles were recognized in the inactive landslide mass. Na-Cl-type groundwaters are formed by mixing deep Na-Cl-type geothermal waters with meteoric groundwaters. These phenomena suggest that the geothermal water injection into shallow aquifers in landslide mass generates a partially high pore water pressure around the sliding surface and causes landslides.

Converging hydrostatic and hydromechanic concepts of preferential flow definitions

The boundary between preferential flow and Richards-type flow is a priori set at a volumetric soil water content θ⁎ at which soil water diffusivity D ( θ⁎) = η (= 10 − 6 m 2 s − 1 ), where η is the kinematic viscosity. First we estimated with a hydrostatic approach from soil water retention curves the boundary, θ K, between the structural pore domain, in which preferential flow occurs, and the matrix pore domain, in which Richards-type flow occurs. We then compared θ K with θ⁎ that was derived from the respective soil hydrological property functions of same soil sample. Second, from in situ investigations we determined 96 values of θ G as the terminal soil water contents that established themselves when the corresponding water-content waves of preferential flow have practically ceased. We compared the frequency distribution of θ G with the one of θ⁎ that was calculated from the respective soil hydrological property functions of 32 soil samples that were determined with pressure plate apparatuses in the laboratory. There is support of the notion that θ K ≈ θ G ≈ θ⁎, thus indicating the potential of θ⁎ to explain more generally what constitutes preferential flow. However, the support is assessed as working hypothesis on which to base further research rather than a procedure to a clear-cut identification of preferential flow and associated flow paths.

High hydrostatic pressure approach proves RNA catalytic activity without magnesium

High hydrostatic pressure (HHP) technique was used to evaluate a mechanism of RNA hydrolysis with RNA. We showed that hammerhead ribozyme specifically cleaves RNA substrate at HHP in the absence of Mg 2+. A deoxyribozyme “10–23” was active in the same conditions. These results pointed out that the hydrolytic activity of nucleic acid depends on proper tertiary structure of a complex with a substrate. They prove that magnesium ion is not directly involved in catalysis process. On that basis we show the mechanism of RNA hydrolysis catalyzed with nucleic acids at HHP.

XMM–NEWTON observation of Abell 1835: Temperature, mass and gas mass fraction profiles

We present a study of the medium distant cluster of galaxies Abell 1835 based on X- data. The high quality of X- data enable us to perform spectro-imaging of the cluster up to large radii. We determine the gas and total mass profiles based on the hydrostatic approach using the β-model and the temperature profile. For the determination of the temperature profile of the , which is needed for the mass determination, we apply a double background subtraction, which accounts for the various kinds of background present (particle and astrophysical background). We find a basically flat temperature profile up to 0.75r200 with a temperature decrease towards the center linked to the cooling flow. We obtain a gas mass fraction of (20.7 ± 3.7)%, which is a lower limit on the baryon fraction in this cluster. Using this value as baryon fraction for the entire Universe, we obtain by combining our results with results based on primordial nucleosynthesis, an upper limit for Ωm < 0.5h −1/2 50 , which is in good agreement with other recent studies.

Gas generation and overpressure: Effects on seismic attributes

Drilling of deep gas resources is hampered by high risk associated with unexpected overpressure zones. Knowledge of pore pressure using seismic data, as for instance from seismic‐while‐drilling techniques, will help producers plan the drilling process in real time to control potentially dangerous abnormal pressures. We assume a simple basin‐evolution model with a constant sedimentation rate and a constant geothermal gradient. Oil/gas conversion starts at a given depth in a reservoir volume sealed with faults whose permeability is sufficiently low so that the increase in pressure caused by gas generation greatly exceeds the dissipation of pressure by flow. Assuming a first‐order kinetic reaction, with a reaction rate satisfying the Arrhenius equation, the oil/gas conversion fraction is calculated. Balancing mass and volume fractions in the pore space yields the excess pore pressure and the fluid saturations. This excess pore pressure determines the effective pressure, which in turn determines the skeleton bulk moduli. If the generated gas goes into solution in the oil, this effect does not greatly change the depth and oil/gas conversion fraction for which the hydrostatic pressure approaches the lithostatic pressure. The seismic velocities versus pore pressure and differential pressure are computed by using a model for wave propagation in a porous medium saturated with oil and gas. Moreover, the velocities and attenuation factors versus frequency are obtained by including rock‐frame/fluid viscoelastic effects to match ultrasonic experimental velocities. For the basin‐evolution model used here, pore pressure is seismically visible when the effective pressure is less than about 15 MPa and the oil/gas conversion is about 2.5% percent.

3C 295: A Cluster and Its Cooling Flow atz= 0.46

We present ROSAT HRI data of the distant and X-ray-luminous [LX(bol) = 2.6+0.4-0.2 × 1045ergs s-1] cluster of galaxies 3C 295. We fit both a one-dimensional and a two-dimensional isothermal β-model to the data, the latter taking into account the effects of the point spread function (PSF). For the error analysis of the parameters of the two-dimensional model, we introduce a Monte Carlo technique. Applying a substructure analysis by subtracting a cluster model from the data, we find no evidence for a merger, but we see a decrement in emission southeast of the center of the cluster, which might be due to absorption. We confirm previous results by Henry & Henriksen that 3C 295 hosts a cooling flow. The equations for the simple and idealized cooling flow analysis presented here are based solely on the isothermal β-model, which fits the data very well, including the center of the cluster. We determine a cooling flow radius of 60-120 kpc and mass accretion rate of = 400-900 M☉ yr-1, depending on the applied model and temperature profile. We also investigate the effects of the ROSAT PSF on our estimate of , which tends to lead to a small overestimate of this quantity if not taken into account. This increase of (10%-25%) can be explained by a shallower gravitational potential inferred by the broader overall profile caused by the PSF, which diminishes the efficiency of mass accretion. We also determine the total mass of the cluster using the hydrostatic approach. At a radius of 2.1 Mpc, we estimate the total mass of the cluster (Mtot) to be 9.2 ± 2.7 × 1014 M☉. For the gas-to-total mass ratio, we get Mgas/Mtot = 0.17-0.31, in very good agreement with the results for other clusters of galaxies, giving strong evidence for a low-density universe.

Invariance of free energy against a shift of the dividing surface of arbitrary geometry

This paper demonstrates that within the context of the generalized theory of capillarity, the free energy remains invariant against an arbitrary shift of the dividing surface for a general surface geometry. The Gibbs adsorption equation is used to illustrate the importance of being able to shift the dividing surface. The mathematical proof makes use of an equation describing the change of free energy for a shift of the dividing surface, derived in an independent development of a hydrostatic approach to capillarity.

Origin of the McLaughlin Mine sheeted vein complex; metal zoning, fluid inclusion, and isotopic evidence

The McLaughlin deposit is a large hot spring-type gold deposit located in the northern Coast Ranges of California at the faulted lithologic contact between the Coast Range ophiolite and the Great Valley sequence. The McLaughlin deposit is centered around the sheeted vein complex, a large multistage vein swarm, localized in a dilation zone formed by rheologic contrasts in the footwall polymictic melange. The surface expression of the sheeted vein complex is a subaerial sinter terrace, which merges into the sheeted vein complex. Metal zoning in the sheeted vein complex is highly telescoped. The sinter is enriched in mercury, whereas gold and silver are restricted to the upper 350 m. with the proportion of gold to silver decreasing with depth. Gold is typically present as electrum and is associated with silver and base metal-bearing sulfosalts. Below 350 m mineralization is dominated by small quartz veins with base metal sulfides. Fluid inclusion studies indicate that NaCl is the main dissolved salt, in concentrations averaging 2.4 wt percent NaCl equiv. The bulk of the salinity data can be explained by variable amounts of adiabatic boiling and mixing with steam-heated ground water. Fluid inclusion homogenization data ranges from 121 degrees to 263 degrees C with the deepest portion of the system examined having the highest temperatures and the shallowest samples having the lowest temperatures. Fluid inclusion gas concentrations vary with depth below the sinter; CO 2 , and to a lesser extent CH 4 , shows a systematic increase with depth. Fluid pressures, calculated from fluid inclusion homogenization temperatures and gas analysis, are in excess of the hydrostatic pressure and approach, or exceed, lithostatic pressure. Self-sealing of the system and tectonic dilation most likely resulted in catastrophic phase separation and hydrothermal eruption breccias. Geothermometry results, based on fluid inclusion gas ratios, show a reasonable correspondence with the highest fluid inclusion homogenization temperatures. There is a strong trend for decreasing delta 18 O quartz values with depth due to the effect of temperature. The calculated delta 18 O (sub H 2 values are fairly constant at about 9 to 10 per mil. Oxygen and hydrogen isotope values, as well as geologic relationships, are consistent with those of hydrothermal fluids originating as meteoric water; these evolved to increasingly high ones by interaction with Great Valley sequence sedimentary rocks. Lead isotope compositions, of sulfides and potential source rocks, indicate that lead, and by inference other metals, was derived from a crustal source. The lead source may have been detritus from the Sierra Nevada batholith that comprises the Great Valley sequence, or alternatively, it may have been derived from a thorough mixture of radiogenic lead and nonradiogenic lead that occurred prior to mineralization.

A dynamic theory of hydrocarbon migration

This paper presents a new analysis of secondary migration of hydrocarbon that does not require capillary forces for trapping, but instead uses the method of characteristics and wave theory. The waves change speed and either reflect or refract (or partially reflect and partially refract) as they contact with layers of different flow capacities. Reflection of a certain wave from a boundary starts hydrocarbon accumulation below that boundary. The method is easy to use and conforms readily to graphical solution. For the sake of simplicity there is only two-phase flow. The application of this method gives new insights into the physics of migration and entrapment of oil. The method gives realistic times for oil accumulation and points to oil generation rate as the most sensitive variable. Oil and water densities, viscosities, and permeability are also important. We find that at the very small generation rates usually assumed the time required to develop a given column thickness is insensitive to the distance from the source rock. In general, the method also predicts a non-uniform saturation in the oil column caused by an interaction between buoyancy and viscous forces. Being based on the dynamic interactions of viscous and buoyancy forces, our theory is considerably at odds with hydrostatic approaches. We assume no capillary pressure, one-dimensional flow, and no regional groundwater flow, conditions which are not realized in actual migration. The theory should be viewed therefore as an end member of a more general theory; nevertheless, the largely graphical solutions give fundamental insights that are difficult to obtain by other techniques.

Definition of surface tension at a non-spherical interface

The thermodynamic characteristics of a non-spherical interface are considered. Two definitions of surface tension and their relationship are analysed. It is shown that the classical Gibbs definition has a clearer physical meaning. The hydrostatic approach to the determination of the surface tension and to the first and second bending moments of an interface is applied. Within the framework of this approach the generalized Laplace equation is obtained and the strict definition is applied to the surface of tension.

Hydrostatic approach to capillarity

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTHydrostatic approach to capillarityL. Boruvka, Y. Rotenberg, and A. W. NeumannCite this: J. Phys. Chem. 1986, 90, 1, 125–127Publication Date (Print):January 1, 1986Publication History Published online1 May 2002Published inissue 1 January 1986https://doi.org/10.1021/j100273a028RIGHTS & PERMISSIONSArticle Views77Altmetric-Citations17LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (339 KB) Get e-Alerts

Nonlinear Analysis of Liquid-Filled Tank

Recent developments related to the analysis and design of liquid storage tanks are surveyed. Different aspects of the problem are examined. Background for finite element formulation is also outlined. A numerical tank model which accounts for the lateral pressure loading is developed to provide an understanding of this effect on the behavior of liquid storage tanks. This lateral pressure loading is simulated via an equivalent hydrostatic approach in which the follower force effect is accounted. Results show that the tank model collapses at a critical load 20% lower than the classical prediction. It also shows that the axial stress is basically dominated by cos θ mode. Higher order modes, are significant in the hoop stress profile which is nonlinear in character. The observed “elephant-foot buckle” and the “ovalling” response of liquid storage tanks in many tank failures during earthquakes can be predicted with these nonlinear methodologies.

Pressure solution lithification as a mechanism for the stick‐slip behavior of faults

Many major faults, including a large fraction of the San Andreas, appear to be virtually quiescent between great earthquakes. The locked sections of the San Andreas near San Francisco and Los Angeles have little or no seismic activity on the primary fault trace, although secondary faults may be active. Stick‐slip behavior on a fault can be explained in terms of a static coefficient of friction, which is larger than the dynamic or sliding coefficient. In this paper we propose a modification of the friction hypothesis in which chemical lithification (cementation) occurs on the fault between earthquakes. As the stress on the fault increases it becomes large enough to break the cemented bonds between particles causing slip on the fault. We treat this problem quantitatively, assuming that pressure solution is responsible for the cementation. An advantage of this model is that the hydrostatic pressure approaches the lithostatic pressure during cementation so that low fault strengths are predicted.