Local Pressure Gradient Research Articles

Pre-surgery planning tool for estimation of resection volume to improve nasal breathing based on lattice Boltzmann fluid flow simulations

PurposeState-of-the-art medical examination techniques (e.g., rhinomanometry and endoscopy) do not always lead to satisfactory postoperative outcome. A fully automatized optimization tool based on patient computer tomography (CT) data to calculate local pressure gradient regions to reshape pathological nasal cavity geometry is proposed.MethodsFive anonymous pre- and postoperative CT datasets with nasal septum deviations were used to simulate the airflow through the nasal cavity with lattice Boltzmann (LB) simulations. Pressure gradient regions were detected by a streamline analysis. After shape optimization, the volumetric difference between the two shapes of the nasal cavity yields the estimated resection volume.ResultsAt LB rhinomanometry boundary conditions (bilateral flow rate of 600 ml/s), the preliminary study shows a critical pressure gradient of −1.1 Pa/mm as optimization criterion. The maximum coronal airflow ΔA := cross-section ratio frac{mathrm{virtual surgery }}{mathrm{post}-mathrm{surgery}} found close to the nostrils is 1.15. For the patients a pressure drop ratio ΔΠ := (pre-surgery − virtual surgery)/(pre-surgery − post-surgery) between nostril and nasopharynx of 1.25, 1.72, −1.85, 0.79 and 1.02 is calculated.ConclusionsLB fluid mechanics optimization of the nasal cavity can yield results similar to surgery for air-flow cross section and pressure drop between nostril and nasopharynx. The optimization is numerically stable in all five cases of the presented study. A limitation of this study is that anatomical constraints (e.g. mucosa) have not been considered.

Transition prediction and sensitivity analysis for a natural laminar flow wing glove flight experiment

Natural laminar flow technology can significantly reduce aircraft aerodynamic drag and has excellent technical appeal for transport aircraft development with high aerodynamic efficiency. Accurately and efficiently predicting the laminar-to-turbulent transition and revealing the maintenance mechanism of laminar flow in a transport aircraft’s flight environment are significant for developing natural laminar flow wings. In this research, we carry out natural laminar flow flight experiments with different Reynolds numbers and angles of attack. The critical N-factor is calibrated as 9.0 using flight experimental data and linear stability theory from a statistical perspective, which makes sure that the relative error of transition location is within 5%. We then implement a simplified eN transition prediction method with a similar accuracy compared with linear stability theory. We compute the sensitivity information for the simplified eN method with an adjoint-based method, using the automatic differentiation technique (ADjoint). The impact of Reynolds numbers and pressure distributions on TS waves is analyzed using the sensitivity information. Through the sensitivity analysis, we find that: favorable pressure gradients not only suppress the development of TS waves but also decrease their sensitivity to Reynolds numbers; there exist three special regions which are very sensitive to the pressure distribution, and the sensitivity decreases as the local favorable pressure gradient increases. The proposed sensitivity analysis method enables robust natural laminar flow wings design.

Analysis of the turbulent flow patterns generated in isotropic porous media composed of aligned or centered cylinders

The analysis of the turbulent flow inside porous media composed of infinite arrangements of cylinders with square and circular cross sections disposed in aligned or centered configuration is presented. The porosity (ϕ) was varied from 0.3 to 0.8, at a pore Reynolds number Rep=105, representing fully turbulent flow conditions. The flow cases were solved numerically by using the low-Reynolds Abe-Kondoh-Nagano version of the k-ε model. New correlations are provided for the domains composed of aligned particles in terms of ϕ for the volume averaged turbulence kinetic energy (k), its dissipation rate (ε), and macroscopic pressure gradient (MPG). These correlations are especially useful when it is not possible to model the local details of the porous media in macroscopic turbulence modeling. The highest energetic losses in terms of volume averaged k, ε, and MPG was found for the centered square arrangement. In all cases, these parameters increased abruptly as ϕ decreased, as the pore-scale local pressure gradients and turbulent kinetic energy dissipation rate levels increased. Depending on the case, they were triggered by a combination of sudden expansion-contraction of the flow channels, flow impingement, and the decrease of the effective flow area by flow recirculation. In all cases, the pore-scale local pressure gradients and turbulent kinetic energy dissipation rate levels increased abruptly as ϕ decreased, and consequently the energy losses increased. The tracer dispersion presented similar low homogeneity times for the centered cylinder arrangements. At each porous media, the variations of turbulence intensity, effective flow area, and tortuosity levels in terms of ϕ were not as significant as those observed for the local pressure gradient and dissipation rate. This effect may be considered to improve mixing and reduce pressure drops in devices such as static mixers, heat exchangers, cooling fins arrays, and other devices composed of slender tubes.

Ion temperature gradient control using reinforcement learning technique

Plasma with an internal transport barrier (ITB) is desirable for a steady-state tokamak reactor because of its high confinement quality and high bootstrap current fraction. However, the local pressure gradient tends to be steep and the plasma often becomes unstable. In this study, an ion temperature gradient control system based on neutral beam injection (NBI) is developed using the reinforcement learning technique. The response characteristics of an ion temperature gradient to NBI are non-linear and sensitive to experimental conditions, which makes it difficult to develop a robust control system. Our control system is trained for plasmas with a wide range of ITB strengths. Using the reinforcement learning technique, the system acquires a robust control feature through several thousand iterations of trial and error in an integrated transport simulation hosted by TOPICS. The control system is composed of neural networks (NNs) whose input variables are the ion temperature gradient, the current NBI power, and the NBI powers for several previous control time steps. The trained system can determine a control output which is suitable for the response characteristics inferred from the input variables. The trained control system is tested in the TOPICS simulation using plasma models based on two experimental plasmas of JT-60U with different ITB strengths. It is shown that the ion temperature gradient can be appropriately controlled for both plasmas, which supports the expectation that this system is applicable to real experiments.

Modeling Gaseous CO2 Flow Behavior in LayeredBasalts: Dimensional Analysis andAquifer Response.

Particular attention is paid to the risk of carbon dioxide (CO2 ) leakage in geologic carbon sequestration (GCS) operations, as it might lead to the failure of sequestration efforts and to the contamination of underground sources of drinking water. As carbon dioxide would eventually reach shallower formations under its gaseous state, understanding its multiphase flow behavior is essential. To this aim, a hypothetical gaseous leak of carbon dioxide resulting from a well integrity failure of the GCS system in operation at Hellisheiði (CarbFix2) is here modeled. Simulations show that migration of gaseous carbon dioxide is largely affected by formation stratigraphy, intrinsic permeability, and retention properties, whereas the initial groundwater hydraulic gradient (0.0284) has practically no effect. In two different scenarios, about 18.3 and 30.6% of the CO2 that would have been injected by the GCS system for 3 days could be potentially released again into the atmosphere due to a sustained leakage of the same duration. As the gaseous leak occurs, the aquifer experiences high pressure buildups, and the presence of a less conductive layer further magnifies these. Strikingly, the dimensional analysis showed that buoyant and viscous forces can be comparable over time within the predicted gaseous plumes, even far from the leakage source. Local pressure gradients, buoyant, viscous, and capillary forces all play an important role during leakage. Therefore, neglecting one or more of these contributions might lead to a partial prediction of gaseous CO2 flow behavior in the subsurface, giving space to incorrect interpretations and wrong operational choices.

Heat Transfer Coefficient, Pressure Gradient, and Flow Patterns of R1234yf Evaporating in Microchannel Tube

Abstract This paper presents the heat transfer coefficient, pressure gradient, and flow pattern of R1234yf in a microchannel tube. Both heat transfer coefficient and pressure gradient are presented against real saturation pressure, while flow pattern captures at the exit of data points are presented in the same plot. The experiment was conducted on a 24-port microchannel tube with an average hydraulic diameter of 0.643 mm. The experiment covers mass flux from 100 to 200 kg m−2s−1, heat flux from 0 to 6 kW m−2, vapor quality from 0 to 1, and inlet saturation temperature from 10 to 30 °C. Comparing the correlations to the HTC measurements at very low quality (about 0.1), Gorenflo, D., and Kenning, D. (2010, Pool Boiling, in: VDI Heat Atlas, 2nd ed, Springer, pp. 757–788) agree with the results. As vapor quality increases, pressure gradient increases. The adiabatic pressure gradient is a strong function of mass flux and saturation pressure (temperature). Flow patterns of R1234yf are also affected by mass flux and saturation pressure. The heat transfer coefficient is a strong function of mass flux and heat flux. The saturation temperature has a smaller effect on HTC in the condition range (10 – 30 °C). Under the test range, the accelerating pressure drop is insignificant compared to friction. Comparing to the results, Mishima, K., and Hibiki, T. (1996, “Some Characteristics of Air-Water Two-Phase Flow in Small Diameter Vertical Tubes,” Int. J. Multiph. Flow, 22(4), pp. 703–712) and Muller-Steinhagen, H., and Heck, K. (1986, “A Simple Friction Pressure Drop Correlation for Two-Phase Flow in Pipes,” Accessed March 1, 2018)., 20, pp. 297–308.) have small mean absolute error (MAE) to predict local pressure gradient. For the heat transfer coefficient, Sun, L., and Mishima, K. (2009, “An Evaluation of Prediction Methods for Saturated Flow Boiling Heat Transfer in Mini-Channels,” Int. J. Heat Mass Transf, 52(23–24), pp. 5323–5329) and Gungor, K. E., and Winterton, R. H. S. (1986, “A General Correlation for Flow Boiling in Tubes and Annuli,” Int. J. Heat Mass Transf, 29(3), pp. 351–358) have an MAE less than 30%.

Mechanistic foam flow model with variable flowing foam fraction and its implementation using automatic differentiation

Foam injection is an effective method for modifying gas mobility in subsurface flow applications making it ideal for environmental remediation applications. Remediation of contaminated soils/aquifers of nonaqueous phase liquids using foamed surfactant solutions is a viable option but a predictive foam model is needed that is flexible to the addition of more accurate physical descriptions. Such a model is essential to ensure successful operations in soil remediation applications. The objective of this paper is to develop a full-physics, mechanistic transient foam flow model and integrate it into the multiphysics, modular AD-GPRS framework (Automatic Differentiation–General Purpose Research Simulator). We chose AD-GPRS because it allows rapid prototyping and addition of complex physics and modeling strategies. We develop the model ground-up from pore-scale observations and implement a new flowing foam fraction constitutive relation that depends on the local pressure gradient, local permeability, and flowing bubble density. Our model predicts the two flow regimes commonly observed in steady-state pressure gradient measurements: the low-quality regime and the high-quality regime. Additionally, the model is used to match transient experimental results of homogeneous and slightly heterogeneous cores with a wide range of permeability values. The implementation of this model within AD-GPRS allows testing of ideas and modeling strategies as well as inclusion of more complex physics or foam generation kinetics.

Natural and anthropogenic effects on microplastic distribution in a hypersaline lagoon

Information on the transport and distribution of microplastics in coastal lagoons is scarce. This study provides the first evaluation of microplastic distribution in a hypersaline coastal lagoon and explores natural and anthropogenic factors that drive their location and transport. The study combines different field strategies: spatial distribution of microplastics in sediments, for September 2017 (wet season and peak use of the lagoon) and February 2018 (winter season, characterized by intense Northerly winds and least use of the lagoon); spatial distribution of microplastics in the water column in the winter season; ocean-lagoon exchanges of water and microplastics at the lagoon entrance during tidal cycles. Also, one-year records of water level variations along the lagoon provide connections between local pressure gradients and water fluxes. Statistical analyses indicate relationships between temporal variations of microplastic concentrations and human activities. Results show marked seasonality in sources and transport agents. During the summer, microplastics concentration was related to human activities. After this season, the accumulated precipitation in the continental karst region leads to an increase in the water level at the head of the lagoon. The resulting pressure gradient promotes seaward flushing of hypersaline water and of microplastics. At tidal (diurnal) time scales, measurements at the mouth of the lagoon revealed that more particles were collected in ebb than in flood. This variability underscores the need to resolve tidal variability for microplastic sampling in coastal lagoons and estuaries.

Using Geomembrane Liners to Reduce Seepage through the Base of Tailings Ponds—A Review and a Framework for Design Guidelines

Geomembranes are used worldwide as basin liners in tailings ponds to decrease the permeability of the foundation and prevent further transportation of harmful contaminants and contaminated water. However, leakage into the environment and damage to the geomembrane have been reported. This paper reviews available literature and recommendations on geomembrane structures for use as a basal liner in tailings ponds, and presents a framework to achieve early involvement and an integrated approach to geomembrane structure design. Cohesive planning guidelines or legislative directions for such structures are currently lacking in many countries, which often means that the structure guidelines for groundwater protection or landfill are applied when designing tailings storage facilities (TSF). Basin structure is generally unique to each mine but, based on the literature, in the majority of cases the structure has a single-composite liner. The type of liner system used depends mainly on the material to be used on top of the structure, local hydraulic pressure gradient, and climate conditions. More practical information and scientific knowledge on the use of base liners in various cases are needed. A sustainable approach could be risk-based design, where the life cycle of the basin is taken into consideration. To this end, this paper proposes geomembrane-lined tailings pond to be assessed as a stakeholder. Emphasis on this, early enough, can ensure critical factors for tailings ponds to be considered from the outset in the design of mines and reduces the environmental footprint of the mining industry. More holistic project management and early involvement and integration are recommended to improve construction quality during the entire life cycle of the pond. In the long term, use of dry stacking or other alternative methods should be encouraged, despite the higher costs for operators.

Investigation on the unsteadiness of centrifugal compressor exposed to pulsating backpressure

Centrifugal compressor is exposed to pulsating backpressure due to the movement of intake valves in internal combustion engine. The performance of compressor deviates from the steady performance map, which affects the matching between turbocharger and engine. The behavior of compressor system at pulsation conditions are investigated via an in-house developed 1D unsteady code validated by experimental results. The influence of pulse frequency, magnitude and compressor characteristic curve on the compressor transient responses, including filling-emptying effect and wave dynamics, are analyzed. Results show that the strength of wave dynamics grows stronger with the increasing of pulse frequency, while the strength of filling-emptying effect increases first then decreases. The rise of pulse magnitude results in an almost linearly increasing of filling-emptying effect, while it can hardly affect the wave dynamics. Furthermore, the influence of pulsation magnitude and frequency represents the influence of local pressure gradient, and a correlation as quadratic curve can be evaluated between the pressure gradient and compressor unsteadiness. On the other hand, the influence of operating point, including the average mass flow rate and the slope of characteristic curve, is confirmed to be evidently smaller, comparing to the influence of pulsation frequency and magnitude. This study is helpful to estimate the behavior of compressor and the discrepancy of performance when operating at unsteady environment or matched with engine.

Modeling particle-fluid interaction in a coupled CFD-DEM framework

In this work, we present an alternative methodology to solve the particle-fluid interaction in the resolved CFDEM ® coupling framework. This numerical approach consists of coupling a Discrete Element Method (DEM) with a Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed particles in a fluid phase. As a novelty, our approach explicitly accounts for the body force acting on the fluid phase when computing the local momentum balance equations. Accordingly, we implement a fluid-particle interaction computing the buoyant and drag forces as a function of local shear strain and pressure gradient. As a benchmark, we study the Stokesian limit of a single particle. The validation is performed comparing our outcomes with the ones provided by a previous resolved methodology and the analytical prediction. In general, we find that the new implementation reproduces with very good accuracy the Stokesian dynamics. Complementarily, we study the settling terminal velocity of a sphere under confined conditions.

Modeling Drug Absorption from the Dermis after an Injection

A dermal absorption model for small and macromolecules was previously proposed by Ibrahim et al. This model estimated absorption of therapeutics from the dermal tissue based on their molecular size and protein binding through blood and lymphatics. Blood absorption followed a two-pore theory and the lymphatic absorption was limited by the constant lymphatic flow rate. Current work builds on this steady-state concept by modeling the absorption from the dermis immediately after an injection is given (unsteady state). An injection in the dermis creates a localized pressure gradient which resolves itself over time. This phenomenon is captured in the model to estimate the impact of injection volume on the absorption rate constant. Blood absorption follows the two-pore theory but is time-dependent and the lymphatic absorption is determined based on valve opening and pressure driven convective flow, returning to steady-state as the molecule is absorbed. A direct comparison of the steady-state analysis, experimental data and the current model is made. The results indicate that accounting for the localized time-varying pressure can better predict the experimental absorption rate constants. This work significantly improves the existing understanding of macromolecule uptake from the interstitial fluid following intradermal injection.

3D numerical modelling of braided channel formation

A numerical model was used to compute the formation of a braided channel system. The model calculated the water flow field from the fully 3D Navier-Stokes equations on a non-orthogonal unstructured adaptive grid. The sediment transport was computed from the Engelund-Hansen formula. A free surface algorithm based on local pressure gradients was used. The model was applied to an idealized geometry of an initially straight alluvial channel, where the evolution of the braided channel system over time was computed. The complex processes and geometry for this case made it very well suited for testing the numerical model. The purpose of the study was also to explain avulsion processes of a braided river in more detail. Figures are presented with water depth, velocity, water level and secondary currents during an avulsion. The effect of the water level changes and the secondary currents are shown. The geometry, sediment size and water discharge used in the numerical model was identical to a laboratory study. Reasonable agreement was found when comparing the active braiding intensity (BIA) computed by the numerical model with measurements from the flume experiment. Parameter tests include sediment transport formula, grid size, secondary current damping and grid parameters related to wetting/drying. The results using the Engelund-Hansen formula show a higher degree of braiding than the van Rijn or Mayer-Peter Müller formula. The secondary current strength is also shown to be very important for the braiding process and the BIA values.

Particle acceleration and pressure gradient in a solitary wave traveling over a horizontal bed

This study presents experimental data on the hydrodynamic features of a nonlinear solitary wave of height H0 = 2.9 cm propagating over a horizontal bed in otherwise still water depth h0 = 8.0 cm. High-speed particle image velocimetry is used to quantify the local and convective particle accelerations and pressure gradients under the solitary wave. It is found that the magnitudes of the horizontal and vertical particle local accelerations are invariably larger than their convective counterparts, highlighting the important contribution of local acceleration to the pressure gradient in a solitary wave. The dimensionless pressure gradient in the horizontal direction is favorable, zero, and adverse for time before, at, and after the wave crest passes the section of interest. The dimensionless adverse pressure gradient exhibits a maximum for the dimensionless time T[=t(g/h0)1/2, where g is the gravitational acceleration and t is the time with respect to the crest passing the section] = 1.39, at which the dimensionless local acceleration has a negative maximum. Subsequently, flow reversal takes place above the bed surface. The relationship is elucidated between flow reversal at the bed surface and the evolution of the adverse pressure gradient in the near-bed zone, where uniform horizontal/free stream velocity exists.

Surface Curvature Effects on Film Cooling Performance for Shaped Holes on a Model Turbine Blade

Abstract Surface curvature has been shown to have significant effects on the film cooling performance of round holes, but the literature include few studies of its effects on shaped holes despite their prevalence in gas turbines. Experiments were performed using two rows of holes placed on the suction side of a scaled-up turbine blade in a low Mach number linear cascade wind tunnel with low freestream turbulence. The rows were placed in regions of high and low convex surface curvature. Geometries and flow conditions for the rows were matched to those from previous flat plate studies. Comparison of the adiabatic effectiveness results from the high curvature and flat plate rows revealed the same trends as those in the literature using round holes, with increased performance for the high curvature row at lower blowing ratios and the opposite at higher ones. The low curvature row had similar performance to the flat plate row at lower blowing ratios, suggesting the mild convex curvature had little beneficial effect. At higher blowing ratios, the low curvature row had inferior performance, which was attributed to the local freestream adverse pressure gradient that generated additional turbulence, promoting jet-to-mainstream mixing and decreasing performance.

Unsteady Coanda effect and drag reduction for a turbulent wake

Abstract

Foam Propagation at Low Superficial Velocity: Implications for Long-Distance Foam Propagation

Summary Since the 1980s, experimental and field studies have found an anomalously slow propagation of foam (Friedmann et al. 1991, 1994; Patzek 1996), a phenomenon that cannot be fully explained by surfactant adsorption. Friedmann et al. (1994) conducted foam-propagation experiments in a cone-shaped sandpack and concluded that foam, once formed in the narrow inlet, was unable to propagate at all at lower superficial velocities near the wider outlet. They concluded that long-distance foam propagation in radial flow from an injection well is in doubt. Ashoori et al. (2012) provide a theoretical explanation for a slower and/or nonpropagation of foam front at decreasing superficial velocity. By linking foam propagation to the minimum superficial velocity utmin (or minimum pressure gradient ∇Pmin) required for foam generation in homogeneous porous media (Rossen and Gauglitz 1990; Gauglitz et al. 2002), the study reveals that the minimum velocity for maintaining the propagation of foam is far less than that for creating foam but greater than the minimum velocity for maintaining foam in place. Lee et al. (2016) and Izadi and Kam (2019) find a minimum velocity for foam propagation from analysis of a similar population-balance model but associate it with the minimum velocity for foam stability. In this study, we extend the experimental approach of Friedmann et al. (1991) in the context of the theory of Ashoori et al. (2012). We observe dynamic propagation of foam in a cylindrical core with stepwise increasing diameter such that the superficial velocity decreases from inlet to outlet (in a ratio of 16:1). Previously (Yu et al. 2019), we mapped the conditions for foam generation (at large superficial velocities) in a Bentheimer sandstone core, in relation to surfactant concentration and injected gas fraction (foam quality). In this study, we enrich the map with the conditions for downstream propagation of foam (at significantly smaller superficial velocities). We also interpret our results for both foam generation and propagation in terms of local pressure gradient (following the implications of Ashoori et al. 2012), which plays a dominant role in the mobilization and creation of foam. Our results suggest that the minimum superficial velocities for both foam generation and propagation increase with increasing foam quality and decreasing surfactant concentration, in agreement with theory (Rossen and Gauglitz 1990). In addition, the minimum velocity for propagation of foam is much less than that for foam generation, as has been predicted by Ashoori et al. (2012). Implications of our laboratory results for field application of foam are briefly discussed.

Pumping flow model for couple stress fluids with a propagative membrane contraction

A pumping flow model induced by propagative and non-propagative wall contraction is presented to examine the pumping and flow characteristics. A couple stress fluid model is considered to see the effect of couple stress parameter. An inelastic single membrane is used in upper wall of the channel with rhythmic contraction to produce unidirectional flow which can be applied in many physiological transports. Governing equations are derived using basic conservation principles of mass and momentum. Furthermore scaling analysis is made to introduce the lubrication theory (typical length scale δ=(H/λ)≪1 and low Reynolds number approximation). The influence of the couple stress parameter, propagative shape membrane, and the time variation on axial velocity, volumetric flow rate, local shear stress, pressure gradient, and streamline distribution are evaluated with aid of in-house code in Matlab. The significant stagnation line in the flow streamline with the membrane parameter is computed where the pressure gradient is zero. This study is relevant in the simulation of fluid dynamics of duodenum and intestine and other physiological systems. Novel smart biomimetic pumping devices are relatively easy to engineer using this pumping mechanism.

Circulation in a Short, Microtidal Submarine Canyon in the Alborán Sea

Serrano, M.A.; Diez-Minguito, M.; Valle-Levinson, A., and Ortega-Sanchez, M., 2020. Circulation in a short, microtidal submarine canyon in the Alboran Sea. In: Malvarez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1531–1535. Coconut Creek (Florida), ISSN 0749-0208.This study analyzes the circulation of a short, microtidal submarine canyon from observations and an analytical model. The Jolucar submarine canyon is located near the Carchuna beach (Granada, southern Spain) in the northern continental shelf of the Alboran Sea. Observations were analyzed with harmonic and spectral analyses techniques. Observations showed two layers flowing in opposite directions: down-canyon in the bottom layer and up-canyon in the upper layer. This suggest that the canyon might flush out dense materials form the nearshore. Moevoer, observed currents were mainly driven by tidal (10%) and, more significantly, by atmospheric forcing, i.e., by wind stress and local atmospheric pressure gradients, as shown by cross-spectral analysis. In order to explore the dynamics associated with these results, a classical analytical solution of wind-induced current profile in a non-homogeneous water column was extended to include the influence of pressure gradients. This result demonstrated that the circulation in Jolucar canyon could be influenced by atmospheric pressure gradients.

Using uncertainty to improve pressure field reconstruction from PIV/PTV flow measurements

A novel pressure reconstruction method is proposed to use the uncertainty information to improve the instantaneous pressure fields from velocity fields measured using particle image velocimetry (PIV) or particle tracking velocimetry (PTV). First, the pressure gradient fields are calculated from velocity fields, while the local and instantaneous pressure gradient uncertainty is estimated from the velocity uncertainty using a linear-transformation-based algorithm. The pressure field is then reconstructed by solving an overdetermined linear system which involves the pressure gradients and boundary conditions. This linear system is solved with generalized least squares (GLS) which incorporates the previously estimated variances and covariances of the pressure gradient errors as inverse weights to optimize the reconstructed pressure field. The method was validated with synthetic velocity fields of a 2D pulsatile flow, and the results show significantly improved pressure accuracy. The pressure error reduction by GLS was 50% with 9.6% velocity errors and 250% with 32.1% velocity errors compared to the existing baseline method of solving the pressure Poisson equation (PPE). The GLS was more robust to the velocity errors and provides greater improvement with spatially correlated velocity errors. For experimental validation, the volumetric pressure fields were evaluated from the velocity fields measured using 3D PTV of a laminar pipe flow with a Reynolds number of 630 and a transitional pipe flow with a Reynolds number of 3447. The GLS reduced the median absolute pressure errors by as much as 96% for the laminar pipe flow compared to PPE. The mean pressure drop along the pipe predicted by GLS was in good agreement with the empirical estimation using Darcy–Weisbach equation for the transitional pipe flow.