Component Of Gravity Research Articles

Pedestrian walking safety system based on smartphone built‐in sensors

People watching smartphones while walking causes a significant impact to their safety. Pedestrians staring at smartphone screens while walking along the sidewalk are generally more at risk than other pedestrians not engaged in smartphone usage. In this study, the authors propose Safe Walking, an Android smartphone-based system that detects the walking behaviour of pedestrians by leveraging the sensors and front camera on smartphones, improving the safety of pedestrians staring at smartphone screens. More specifically, Safe Walking first exploits a pedestrian speed calculation algorithm by sampling acceleration data via the accelerometer and calculating gravity components via the gravity sensor. Then, this system utilises a greyscale image detection algorithm to detect the face and eye movement modes based on OpenCV4Android to determine if pedestrians are staring at the screens. Finally, Safe Walking generates a vibration by a vibrator on smartphones to alert pedestrians to pay attention to road conditions. The authors implemented Safe Walking on an Android smartphone and evaluated pedestrian walking speed, the accuracy of eye movement, and system performance. The results show that Safe Walking can prevent the potential danger for pedestrians staring at smartphone screens with a true positive rate of 91 % .

Quantitative assessment of parkinsonian tremor based on a linear acceleration extraction algorithm

Abstract Tremor detection plays a crucial role in Parkinson’s disease (PD) treatment and symptom monitoring. The current gold standard for the clinical assessment of parkinsonian tremor is the evaluation using the standard clinical rating scales, which is performed by the well-trained neurologists. However, this assessment approach relies mainly on the subjective judgment of the evaluator. This study, on the basis of the Movement Disorder Society-Sponsored Revision of the Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) criteria, proposed a custom quantitative assessment system for parkinsonian tremors. It adopted an attitude estimation-based gradient descent algorithm to separate the linear acceleration (caused by pure translational motion) from the accelerometer output, which combines gravity component. Signal features extracted from the linear accelerations and angular velocities during the tremor tasks were fitted to the clinicians’ ratings with a multiple regression model. Clinical experiments with 34 PD patients and 14 age-matched controls demonstrated that the prediction accuracy was improved by using the decomposed linear acceleration for the extraction of tremor features, which has promoted assessment accuracy compared with the relevant literature (r2 improved from 0.89 to 0.95 for rest tremor, and from 0.90 to 0.93 for postural tremor). In addition, the prediction accuracy was worse when using only the linear accelerations for regression analysis (r2 reduced from 0.95 to 0.87 for rest tremor, and from 0.93 to 0.84 for postural tremor), which means that the effect of rotational motion cannot be ignored in tremor quantification.

Study on the heat exchange efficiency of ITER GS thermal anchor

Thermal anchor is a key component of ITER gravity supports and serves to maintain them a temperature for the normal operation of superconducting coils. Two rows of thermal anchor pipes introduced by 80 K helium gas are connected with supports to reduce the heat transferred from pedestal ring to magnet. TIG welding is chosen as the connecting method for the attachment of thermal anchor. A prototype of GS flexible plate with thermal anchor attached is manufactured by TIG welding. And heat exchange efficiency test is done on the prototype with its thermal anchor being introduced by liquid nitrogen under a circumstance similar to ITER. Temperature of the area next to thermal anchor on the plate is about 100 K with only one pipe until temperature variation is not obvious. As helium is a quite expensive coolant for the cooling down of plate, computer simulations with 80 K helium gas being introduced into thermal anchor is performed instead. The finite element model is built and revised as per the test results. And the test results and simulations are discussed and analyzed to make sure the conductive heat from pedestal ring could be dissipated by using helium gas.

Quartet-Metric Gravity and Dark Components of the Universe

In the report there are presented the general frameworks for the quartet-metric gravity based on the two main principles. First, there exist in space-time the distinct dynamical coordinates, given by a scalar quartet, playing the role of the Higgs fields for gravity. Second, the physical gravity fields arising due to the spontaneous symmetry breaking serve as the dark components of the Universe. It is argued that the mere admixture to metric of the scalar quartet may give rise to an extremely wide spectrum of the emergent gravity phenomena beyond General Relativity (GR). Further developing the proposed frameworks to find out the next-to-GR theory of gravity is a challenge.

О построении гравитационной модели Земли и геоида

The article gives a way to construct the gravity model of the Earth and the geoid. The model is obtained by solving two successive well-posed problems having a unique solution reduced to solving (generalized) Fredholm integral equations of the second kind. The initial data for constructing of the model are the values of the gravity component of the weight force, independent of time, on the surface of a simply connected area containing the Earth body inside itself. The proposed algorithm, unlike most known ones, makes it possible to construct a real geoid, since it automatically takes into account the presence of masses outside of the quasigeoid. The accuracy of the construction of the gravity model in the form of a volumetric Newtonian potential is limited only by the accuracy of field measurements and can be checked at the computation stage, since the values of the density of this potential, corresponding to the values of the average density of the constituent components of the Earth, must be zero outside of the figure of the Earth. The density of atmospheric air is taken into account.

Analytical equation for outflow along the flow in a perforated fluid distribution pipe.

Perforated fluid distribution pipes have been widely used in agriculture, water supply and drainage, ventilation, the chemical industry, and other sectors. The momentum equation for variable mass flow with a variable exchange coefficient and variable friction coefficient was developed by using the momentum conservation method under the condition of a certain slope. The change laws of the variable momentum exchange coefficient and the variable resistance coefficient along the flow were analyzed, and the function of the momentum exchange coefficient was given. According to the velocity distribution of the power function, the momentum equation of variable mass flow was solved for different Reynolds numbers. The analytical solution contains components of pressure, gravity, friction and momentum and reflects the influence of various factors on the pressure distribution along the perforated pipe. The calculated results of the analytical solution were compared with the experimental values of the study by Jin et al. 1984 and Wang et al. 2001 with the mean errors 8.2%, 3.8% and 2.7%, and showed that the analytical solution of the variable mass momentum equation was qualitatively and quantitatively consistent with the experimental results.

Moho depth model for the Central Asian Orogenic Belt from satellite gravity gradients

AbstractThe main purpose of this study is to construct a new 3‐D model of the Central Asian Orogenic Belt (CAOB) crust, which can be used as a starting point for future lithospheric studies. The CAOB is a Paleozoic accretionary orogen surrounded by the Siberian Craton to the north and the North China and Tarim Cratons to the south. This area is of great interest due to its enigmatic and still not completely understood geodynamic evolution. First, we estimate an initial crustal thickness by inversion of the vertical gravity component of the Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) and DTU10 models. Second, 3‐D forward modeling of the GOCE gravity gradients is performed, which determines the topography of the Moho, the geometry, and the density distribution of the deeper parts of the CAOB and its surroundings, taking into account the lateral and vertical density variations of the crust. The model is constrained by seismic refraction, reflection, and receiver function studies and geological studies. In addition, we discuss the isostatic implications of the differences between the seismic Moho and the resulting 3‐D gravity Moho, complemented by the analysis of the lithostatic load distribution at the upper mantle level. Finally, the correlation between the contrasting tectonic domains and the thickness of the crust reveals the inheritance of Paleozoic and Mesozoic geodynamics, particularly the magmatic provinces and the orocline which preserve their crustal features.

Non-Abelian gauge fields as components of gravity in the discretized Kaluza–Klein theory

Discretized Kaluza–Klein theory in [Formula: see text] spacetime can be constructed based on the concepts of noncommutative geometry. In this paper, we show that it is possible to incorporate the non-Abelian gauge fields in this framework. The generalized Hilbert–Einstein action is gauge invariant only in two cases. In the first case, the gauge group must be Abelian on one sheet of spacetime and non-Abelian on the other one. In the second case, the gauge group must be the same on two sheets of spacetime. Actually, the theories of electroweak and strong interactions can fit into these two cases.

Mechanical Behaviors of Bottom Hole Assembly with Bent-Housing Positive Displacement Motor Under Rotary Drilling

Abundant drilling activities had confirmed that the fully rotary drilling can improve the rate of penetration effectively. However, the fully rotary drilling has brought some challenges for the trajectory control ability of the bottom hole assembly (BHA). One of the reasons is the effect of drill-string rotation was ignored in the existing methods, where the bent-housing positive displacement motor (PDM) was regarded as the prebending beam. According to the D’Alembert principle, the dynamical centrifugal force, generated by drill-string rotation, was equivalent to a quasi-static problem. The mechanical model of BHA with bent-housing PDM was established based on the Timoshenko beam theory. The calculated formula of bit side force (BSF) and resultant steering force (RSF) was deduced. The influences of inclination, rotational speed of drill-string, bend angle, eccentricity, stabilizer, weight on bit (WOB) and elbow position on the average BSF and RSF were investigated. The results show that the rotational speed of drill-string has a significant influence on the steering ability. The average BSF increases with the rotational speed of drill-string, while the RSF increases firstly and decreases subsequently. The controlling factor is the transverse component of drill-string gravity in a low rotational speed, while it is the centrifugal force in a high rotational speed. The BSF climbs up and then declines with WOB and rotational speed of drill-string. When the rotational speed of drill-string exceeds 100 RPM or WOB is higher than 80 kN, the BSF will decrease, resulting in a decline in angle buildup. The present method can be utilized to optimize the drilling parameters, BHA configuration and structure of bent-housing PDM.

Sequestered oil pollution mapping, and tracking active oil breakouts in sensitive rivers, bays, and estuaries

ABSTRACT Oil on the water surface represents just the American Petroleum Institute API > 10 gravity component of any crude oil spill or well blowout, and is identified and tracked by conventional remote sensing means. However, the API ≤ 10 components of the hydrocarbons are not readily accessible by these means. UV sensors on underwater vehicles can sample just a few cubic centimeters at a time and are subject to fouling. Side-scan sonar, under certain conditions, can “see” gas bubbles on the near outer shell of a subsurface plume if they exist early on during a blowout, but cannot assess the entire volume. Oil sequestered in bed sediments in oceans or rivers is not visible to UV sensors, nor is it visible to divers. It is apparent that this sensing gap problem needed to be addressed. A new technology developed by the US Geological Survey, working closely with Williamson & Associates of Seattle, holds promise for rapid mapping and characterization of below-surface hydrocarbons. Crude oil drifting in the deep ocean water column, oil blanketing the seafloor, and oil sequestered in seafloor and river bottom sediments can now be quickly mapped in 3D. If drifting in the seawater column, dispersed oil can be tracked as its distribution evolves over time. This technology also is potentially useful for mapping combined storm-water overflow (CSO, or sewage) deposits, as well as Superfund sites in Puget Sound and other sensitive rivers, bays, and estuaries close to cities that pose serious hazards to both humans and wildlife. The technology is based on a surface-sensitive electro-physical property known as induced polarization (IP). This surface-sensitivity means that highly dispersed IP-reactive materials have more surface area exposed to surrounding water, and are thus more responsive than undispersed materials of the same mass. IP technology has been used successfully for many decades to map disseminated porphyry sulfide deposits on land, but has only been applied commercially at sea since 2007. Recent laboratory and Puget Sound experiments have verified that the IP response of oil dispersed in water and sequestered in sediments is unusually strong: at least 20 times greater than a strong “hit” in an IP survey for sulfide minerals on land. The marine IP system has been towed behind a small boat in as little as 1–2 meters water depth, while one version has been tested (using a towed sled) to 3,500 meters depth. Depending on the cable-streamer design, the depth of detection of chargeable materials in sediments can be greater than 20 meters. It can be used to monitor active drill platforms for leaks. Finally, IP is also strongly reactive to buried pipelines; in the Gulf of Mexico there are over 43,000 miles of poorly-located, often hidden, corroding pipe. We can now map it precisely.

Dipole modes with depressed amplitudes in red giants are mixed modes

Context. Seismic observations with the space-borne Kepler mission have shown that a number of evolved stars exhibit low-amplitude dipole modes, which is referred to as depressed modes. Recently, these low amplitudes have been attributed to the presence of a strong magnetic field in the stellar core of those stars. Subsequently, and based on this scenario, the prevalence of high magnetic fields in evolved stars has been inferred. It should be noted, however, that this conclusion remains indirect. Aims. We intend to study the properties of mode depression in evolved stars, which is a necessary condition before reaching conclusions about the physical nature of the mechanism responsible for the reduction of the dipole mode amplitudes. Methods. We perform a thorough characterization of the global seismic parameters of depressed dipole modes and show that these modes have a mixed character. The observation of stars showing dipole mixed modes that are depressed is especially useful for deriving model-independent conclusions on the dipole mode damping. We use a simple model to explain how mode visibilities are connected to the extra damping seen in depressed modes. Results. Observations prove that depressed dipole modes in red giants are not pure pressure modes but mixed modes. This result, observed in more than 90% of the bright stars (mV ≤ 11), invalidates the hypothesis that depressed dipole modes result from the suppression of the oscillation in the radiative core of the stars. Observations also show that, except for visibility, seismic properties of the stars with depressed modes are equivalent to those of normal stars. The measurement of the extra damping that is responsible for the reduction of mode amplitudes, without any prior on its physical nature, potentially provides an efficient tool for elucidating the mechanism responsible for the mode depression. Conclusions. The mixed nature of the depressed modes in red giants and their unperturbed global seismic parameters carry strong constraints on the physical mechanism responsible for the damping of the oscillation in the core. This mechanism is able to damp the oscillation in the core but cannot fully suppress it. Moreover, it cannot modify the radiative cavity probed by the gravity component of the mixed modes. The recent mechanism involving high magnetic fields proposed for explaining depressed modes is not compliant with the observations and cannot be used to infer the strength and prevalence of high magnetic fields in red giants.

Inverse rigid-body dynamic analysis for a 3UPS-PRU parallel robot

Inverse rigid-body dynamic analysis for a 3UPS-PRU parallel robot are conducted in this research. The position, velocity, acceleration, jerk, and singularity are considered in the inverse kinematics analysis. The rigid-body dynamic model is developed by means of the principle of virtual work and the concept of link Jacobian matrices. The driving torque, driving power, and required output work of motors have been computed in the inverse rigid-body dynamics analysis. For the pre-defined trajectory, the required output work generated by the driving motor is achieved by numerical integration technique. The inverse kinematics and rigid-body dynamics have been investigated in an exhaustive decoupled way. The effects of the velocity of the moving platform on the components of the joint acceleration, joint jerk, driving torque, and driving power, which are related to the velocity of the moving platform, are investigated. There are linear relationships between the acceleration of the moving platform and the components of the joint acceleration, joint jerk, driving torque, and driving power, which are related to the acceleration of the moving platform. The total driving torques, the torques related to the acceleration, velocity, and gravity, the torques related to the moving platform, strut connected with the moving platform, strut connected with the base platform, and motor rotor-coupler are calculated. The total driving powers, the powers related to the acceleration component of torque, velocity component of torque, gravity component of torque, and the powers related to the moving platform, strut connected with the moving platform, strut connected with the base platform, and motor rotor-coupler are also achieved.

Gravity Compensation Method for Combined Accelerometer and Gyro Sensors Used in Cardiac Motion Measurements.

A miniaturized accelerometer fixed to the heart can be used for monitoring of cardiac function. However, an accelerometer cannot differentiate between acceleration caused by motion and acceleration due to gravity. The accuracy of motion measurements is therefore dependent on how well the gravity component can be estimated and filtered from the measured signal. In this study we propose a new method for estimating the gravity, based on strapdown inertial navigation, using a combined accelerometer and gyro. The gyro was used to estimate the orientation of the gravity field and thereby remove it. We compared this method with two previously proposed gravity filtering methods in three experimental models using: (1) in silico computer simulated heart motion; (2) robot mimicked heart motion; and (3) in vivo measured motion on the heart in an animal model. The new method correlated excellently with the reference (r 2>0.93) and had a deviation from reference peak systolic displacement (6.3±3.9mm) below 0.2±0.5mm for the robot experiment model. The new method performed significantly better than the two previously proposed methods (p<0.001). The results show that the proposed method using gyro can measure cardiac motion with high accuracy and performs better than existing methods for filtering the gravity component from the accelerometer signal.

The distribution of saturated clusters in wetted granular materials

The hydro-mechanical behaviour of partially saturated granular materials is greatly influenced by the spatial and temporal distribution of liquid within the media. The aim of this paper is to characterise the distribution of saturated clusters in granular materials using an optical imaging method under different water drainage conditions. A saturated cluster is formed when a liquid phase fully occupies the pore space between solid grains in a localized region. The samples considered here were prepared by vibrating mono-sized glass beads to form closely packed assemblies in a rectangular container. A range of drainage conditions were applied to the specimen by tilting the container and employing different flow rates, and the liquid pressure was recorded at different positions in the experimental cell. The formation of saturated clusters during the liquid withdrawal processes is governed by three competing mechanisms arising from viscous, capillary, and gravitational forces. When the flow rate is sufficiently large and the gravity component is sufficiently small, the viscous force tends to destabilize the liquid front leading to the formation of narrow fingers of saturated material. As the water channels along these liquid fingers break, saturated clusters are formed inside the specimen. Subsequently, a spatial and temporal distribution of saturated clusters can be observed. We investigated the resulting saturated cluster distribution as a function of flow rate and gravity to achieve a fundamental understanding of the formation and evolution of such clusters in partially saturated granular materials. This study serves as a bridge between pore-scale behavior and the overall hydro-mechanical characteristics in partially saturated soils.

Технология определения параметров гравитационного поля Земли по градиентометрическим измерениям. 5. Вычисление производных от компонент тензора градиента геопотенциала по уточняемым гармоническим коэффициентам

Технология определения параметров гравитационного поля Земли по градиентометрическим измерениям. 5. Вычисление производных от компонент тензора градиента геопотенциала по уточняемым гармоническим коэффициентам

DEM sourcing guidelines for computing 1 Eö accurate terrain corrections for airborne gravity gradiometry

In this paper we investigate digital elevation model (DEM) sourcing requirements to compute gravity gradiometry terrain corrections accurate to 1Eötvös (Eö) at observation heights of 80m or more above ground. Such survey heights are typical in fixed-wing airborne surveying for resource exploration where the maximum signal-to-noise ratio is sought. We consider the accuracy of terrain corrections relevant for recent commercial airborne gravity gradiometry systems operating at the 10Eö noise level and for future systems with a target noise level of 1Eö. We focus on the requirements for the vertical gradient of the vertical component of gravity (Gdd) because this element of the gradient tensor is most commonly interpreted qualitatively and quantitatively.Terrain correction accuracy depends on the bare-earth DEM accuracy and spatial resolution. The bare-earth DEM accuracy and spatial resolution depends on its source. Two possible sources are considered: airborne LiDAR and Shuttle Radar Topography Mission (SRTM). The accuracy of an SRTM DEM is affected by vegetation height. The SRTM footprint is also larger and the DEM resolution is thus lower. However, resolution requirements relax as relief decreases. Publicly available LiDAR data and 1arc-second and 3arc-second SRTM data were selected over four study areas representing end member cases of vegetation cover and relief.The four study areas are presented as reference material for processing airborne gravity gradiometry data at the 1Eö noise level with 50m spatial resolution. From this investigation we find that to achieve 1Eö accuracy in the terrain correction at 80m height airborne LiDAR data are required even when terrain relief is a few tens of meters and the vegetation is sparse. However, as satellite ranging technologies progress bare-earth DEMs of sufficient accuracy and resolution may be sourced at lesser cost. We found that a bare-earth DEM of 10m resolution and 2m accuracy are sufficient for achieving 1Eö accuracy in the terrain correction independent of relief or vegetation cover. For AGG systems operating at greater noise levels the 3arc-second SRTM is adequate for areas having tens of meters of relief and sparse vegetation and even for areas of greater relief and sparse vegetation if a constant elevation survey is flown at 80m above terrain peak.

Re-Os identification of glide faulting and precise ages for correlation from the Upper Jurassic Hekkingen Formation, southwestern Barents Sea

Re-Os geochronology of black shales provides absolute time pins in sedimentary successions and Os isotopic constraints on paleo-environmental conditions. Recognition and reconstruction of pre-faulting chronology within a visually monotonous shale section are critical to interpretation of the paleo-environmental record, and have relevance for fluid migration routes and basin modelling.Re-Os isochrons for five core intervals spanning 14m of black shale from the Hekkingen Formation on the northern margin of the Hammerfest Basin document within-unit reverse faulting, which is corroborated by detailed petrography, geochemical profiles, and the Os isotope record. The reverse fault is coincident with a beef-like carbonate vein. The five core intervals provide six isochrons with increasingly younger depositional ages of 153.3+4.1/−1.7Ma to 148.6+3.0/−4.1Ma, with increasingly higher initial 187Os/188Os ratios (0.475+0.025/−0.060 to 0.593+0.134/−0.098), consistent with original stratigraphic position. Our age data and inferred sedimentation rates suggest a vertical displacement of several meters across the fault. We suggest such compressional features are the distal (i.e., down-dip) components of gravity gliding structures.The rocks of the Hekkingen Formation at the studied locality record a period of water column euxinia. With the geochemical data in the correct stratigraphic order, we identify two periods of increased sulfide deposition with distinct trace-metal characteristics that reflect differences in the sharpness of the chemocline. These sulfide-producing events create complexity in cross-plots traditionally used to infer oceanographic conditions.Stratigraphically-corrected Os-isotope profiles allow us to correlate this stratigraphic interval of the Hekkingen Formation from the northern margin of the Hammerfest Basin with other sections in the Barents Sea and offshore Norway.

Improved accuracy of aboveground biomass and carbon estimates for live trees in forests of the eastern United States

Accurate estimation of forest biomass and carbon stocks at regional to national scales is a key requirement in determining terrestrial carbon sources and sinks on United States (US) forest lands. To that end, comprehensive assessment and testing of alternative volume and biomass models were conducted for individual tree models employed in the component ratio method (CRM) currently used in the US' National Greenhouse Gas Inventory. The CRM applies species-specific stem volume equations along with specific gravity conversions and component expansion factors to ensure consistency between predicted stem volumes and weights, and additivity of predicted live tree component weights to match aboveground biomass (AGB). Data from over 76 600 stem volumes and 6600 AGB observations were compiled from individual studies conducted in the past 115 years – what we refer to as legacy data – to perform the assessment. Scenarios formulated to incrementally replace constituent equations in the CRM with models fitted to legacy data were tested using cross-validation methods, and estimates of AGB were scaled using forest inventory data to compare across 33 states in the eastern US. Modifications all indicated that the CRM in its present formulation underestimates AGB in eastern forests, with the range of underestimation ranging from 6.2 to 17 per cent. Cross-validation results indicated the greatest reductions in estimation bias and root-mean squared error could be achieved by scenarios that replaced stem volume, sapling AGB, and component ratio equations in the CRM. A change in the definitions used in apportioning biomass to aboveground components was also shown to increase prediction accuracy. Adopting modifications tested here would increase AGB estimates for the eastern US by 15 per cent, accounting for 1.5 Pg of C currently unaccounted for in live tree aboveground forest C stock assessments. Expansion of the legacy data set currently underway should be useful for further testing, such as whether similar gains in accuracy can be achieved in estimates of regional or national-scale C sequestration rates.

USING THE ANALYTIC SIGNAL METHOD OF GRAVITY GRADIENT TENSOR (GGT) TO DETERMINE THE LOCATION AND DEPTH OF THE FAULTS IN THE PRE-CENOZOIC BASEMENT ROCKS OF THE RED RIVER TROUGH

USING THE ANALYTIC SIGNAL METHOD OF GRAVITY GRADIENT TENSOR (GGT) TO DETERMINE THE LOCATION AND DEPTH OF THE FAULTS IN THE PRE-CENOZOIC BASEMENT ROCKS OF THE RED RIVER TROUGH

Multiphase flow modelling in moderately rotating inclined porous media

ABSTRACTAdvective and diffusive multiphase flows through vertical porous media are well examined and discussed in the scientific literature. However, uncommon configurations with inclined porous media are examined to a lesser extent, while advanced configurations with superimposed motion have hitherto scarcely been addressed. An example of such configuration is the inclined rotating tubular fixed bed reactor, which is a novel intensified multiphase reactor for heterogeneous catalytic gas‐liquid‐solid reactions (H.‐U. Härting, R. Lange, F. Larachi, M. Schubert, Chem. Eng. J. 2015, 281, 931).For the prediction of liquid saturation and two‐phase pressure drop in inclined and moderately rotating confined porous media, a two‐fluid model is presented. The model is one‐directional, isothermal, and considers incompressible Newtonian fluids. To account for the interphase momentum transfer, adopted Ergun‐type closures are formulated taking the peculiarities of stratified, dispersed, and annular flow into account. The effects of inclination and rotation are incorporated as additional body forces, whereby inclination is taken into account by the longitudinal gravity component and a semi‐empirical closure for the complex effects of the rotational velocity is presented. The applicability of the model is validated against experimental liquid saturation and two‐phase pressure drop data.