Constant Mean Pressure Research Articles

High-speed shock–boundary-layer interaction over deformed surfaces

This paper concerns the interaction of an oblique shock wave with a supersonic turbulent boundary layer over a thin panel surface, leading to shock–boundary layer interaction and panel buckling. We have performed high-order numerical simulations featuring various static two-dimensional surface deformations typically encountered in experiments. The deformation amplitudes we examined were at least half the height of the incoming turbulent boundary layer thickness. The results show that along the panel midspan, where the maximum deformation amplitude is located, the mean and root mean square pressure are affected by about 10%. Cases for which the pressure at the shock–boundary layer interaction was increased relative to the planar case showed to decrease downstream, and vice versa. Despite the weak response to the mean pressure amplitude, the mean pressure surface contour plots reveal that the streamwise, particularly the spanwise distribution, is affected more noticeably. For example, the surface deformation modes are shown to disrupt the spanwise constant mean pressure, forming higher (or lower) values at either the panel's midspan or edges, depending on the mode. Moreover, the surface curvature leads to a characteristic bending of the spanwise distribution, which can be concave or convex depending on the deformation mode. Analysis of the Reynolds stress anisotropy componentality at different heights from the buckled surface reveals a similar spanwise response of the turbulent velocity fluctuations. The results suggest that the deformation rate plays an important role alongside the deformation amplitude in the turbulent layer and shock–boundary layer interaction.

Impact of viscosity on creeping viscous fluid flow through a permeable slit: a study for the artificial kidneys

<abstract> <p>The idea of this study is to present the mathematical model of two-dimensional biofluid flow having variable viscosity along the height of the channel (proximal renal tube of artificial kidney). This research describes that flow resistance is dependent on the height of the channel (proximal renal tube of artificial kidney) which makes the high flow near the centre and slow near the wall. The goal of this research is to provide the formulas to find the flow speed, average pressure, outflow flux and filtration rate of the viscous fluid having variable viscosity. The complex mathematical problem is solved by the Inverse method and results for axial velocity are plotted at the opening, central and departure region of the conduit. The numerical values for constant reabsorption and mean pressure are calculated against the filtration rate for the constant and variable viscosity. The numerical results of pressure rise show that when the viscosity of biofluid varies from centre to the boundary, then high change in pressure is required as compared with the biofluid having constant viscosity along the height of the slit. These mathematical formulas are very useful for the bioengineers to design the portable artificial kidney which works as a mechanical tool to filter the biofluid.</p> </abstract>

The Numerical Prediction of The Flow Pattern under a Stationary Hovercraft.(Dept.M)

This paper presents a numerical solution procedure for the prediction of the flow pattern created under a stationary hovercraft using the irrotational flow model. A finite difference computer program using a rectangular grid was employed in this study. Three flow patterns are investigated. These flow patterns are the flow pattern at constant mass flow rate M, flow pattern at constant skirt height and the flow pattern at constant mean pressure along the underside of the hovercraft floor. It, also, determines the dependence of the pressure distribution on the relative height of the skirt and the mass flow rate. The relation between the mass flow rate and the skirt height, at constant average pressure along the underside of the hovercraft, was also obtained. The results show that the flow pattern changes with the variation the skirt height, while there is no change in the flow pattern with the increase of the mass flow rate, if the skirt . height is kept constant. It also explains the practical limitation of the unability of a hovercraft to operate over very rough seas.

Critical state constitutive models and shear loading of overconsolidated clays with deviatoric hardening

Abstract This paper presents an enhanced constitutive model integrating deviatoric hardening with a modified yield surface for overconsolidated clayey soils in a general framework of Cam-clay type models. Its performance was assessed with the simulation of drained and undrained triaxial tests on three clays at different consolidation states in comparison to two critical state models. The proposed model satisfactorily estimates the shear resistance, while capturing the smooth nonlinearity of the soil response. Shear triaxial tests at constant mean pressure were performed on an overconsolidated marl to study the shear response. Their simulation attests the importance of deviatoric hardening integration.

Reducing spin-up time for simulations of turbulent channel flow

Spin-up of turbulent channel flow forced with a constant mean pressure gradient is prolonged because the flow accelerates due to an imbalance between the driving pressure gradient and total bottom stress. To this end, a method ensuring a time invariant volume-averaged streamwise velocity during spin-up is presented and compared to simulations forced with a mean pressure gradient for both linear and logarithmic initial velocity profiles. The comparisons are made for open-channel flow with a friction Reynolds number Reτ of 500. Additional simulations with Reτ ranging from 1 to 400 are also run to confirm validity of the method for a range of Reynolds numbers. While the method eliminates spin-up time related to approaching the target volume-averaged velocity, spin-up time is still required for the flow to transition to turbulence and reach statistical equilibrium. Therefore, the time evolution of turbulence in response to different initial velocity profiles and random perturbations is investigated. Simulations initialized with linear velocity profiles trigger turbulence and reach statistical equilibrium sooner than those initialized with logarithmic profiles given the same initial perturbations, a manifestation of the increased shear created by linear profiles. The results suggest that, combined with appropriate initial conditions, ensuring a time invariant volume-averaged streamwise velocity can reduce the computational time associated with spin-up of turbulent open-channel flows by at least a factor of five.

DEM analysis of the shear strength of cross-anisotropic sand with non-spherical particles

This paper aims to investigate the shear strength of cross-anisotropic Toyoura sand by three-dimensional (3D) discrete-element simulation with non-spherical particles. Twenty true triaxial tests with constant mean pressure, different intermediate principal stress ratio [b = (σ2 − σ3)/(σ1 − σ3)] and different bedding angle δ (the angle between the bedding plane and the horizontal plane) were simulated. The results show that an increase in b induces a decrease in shear strength when δ is fixed. As the major principal stress direction changes from perpendicular to parallel with respect to the bedding plane, the shear strength decreases. The shear strength was characterised by a modified Mohr–Coulomb strength criterion by considering the influence of the material fabric. The characteristic of peak shear strength decreasing with b and δ can be well captured by the modified criterion. A 3D failure surface in φ–b–δ space was obtained from the simulated results; the combined influences of b and δ on the friction angle were investigated in detail. These varying characteristics of friction angle with b and δ can be captured by the modified strength criterion.

An invariant representation of mean inertia: theoretical basis for a log law in turbulent boundary layers

A refined scaling analysis of the two-dimensional mean momentum balance (MMB) for the zero-pressure-gradient turbulent boundary layer (TBL) is presented and experimentally investigated up to high friction Reynolds numbers, $\unicode[STIX]{x1D6FF}^{+}$. For canonical boundary layers, the mean inertia, which is a function of the wall-normal distance, appears instead of the constant mean pressure gradient force in the MMB for pipes and channels. The constancy of the pressure gradient has led to theoretical treatments for pipes/channels, that are more precise than for the TBL. Elements of these analyses include the logarithmic behaviour of the mean velocity, specification of the Reynolds shear stress peak location, the square-root Reynolds number scaling for the log layer onset and a well-defined layer structure based on the balance of terms in the MMB. The present analyses evidence that similarly well-founded results also hold for turbulent boundary layers. This follows from transforming the mean inertia term in the MMB into a form that resembles that in pipes/channels, and is constant across the outer inertial region of the TBL. The physical reasoning is that the mean inertia is primarily a large-scale outer layer contribution, the ‘shape’ of which becomes invariant of $\unicode[STIX]{x1D6FF}^{+}$ with increasing $\unicode[STIX]{x1D6FF}^{+}$, and with a ‘magnitude’ that is inversely proportional to $\unicode[STIX]{x1D6FF}^{+}$. The present analyses are enabled and corroborated using recent high resolution, large Reynolds number hot-wire measurements of all the terms in the TBL MMB.

Voicing produced by a constant velocity lung source

An investigation is made of the influence of subglottal boundary conditions on the prediction of voiced sounds. It is generally assumed in mathematical models of voicing that vibrations of the vocal folds are maintained by a constant subglottal mean pressure pI, whereas voicing is actually initiated by contraction of the chest cavity until the subglottal pressure becomes large enough to separate the vocal folds. The problem is reformulated to determine voicing characteristics in terms of a prescribed volumetric flow rate Qo of air from the lungs-the evolution of the resulting time-dependent subglottal mean pressure p[overline]-(t) is then governed by glottal mechanics, the aeroacoustics of the vocal tract, and the influence of continued contraction of the lungs. The new problem is analyzed in detail for an idealized mechanical vocal system that permits precise specification of all boundary conditions. Predictions of the glottal volume velocity pulse shape are found to be in good general agreement with the traditional constant-pI theory when pI is set equal to the time averaged value of p[overline]-(t). But, in all cases examined the constant-pI approximation yields values of the mean flow rates Qo and sound pressure levels that are smaller by as much as 10%.

Parametric instabilities of the radial motions of non-linearly viscoelastic shells under pulsating pressures

This paper treats the classical problem of radial motions of cylindrical and sphericalshells under pulsating pressures. The novelty in this work is that the shells are taken to be non-linearly viscoelastic(of strain-rate type). It is remarkable that this classical problem, which does not treat the loss of stability to non-radial motions (but which is essential for such treatments), has such a rich dynamics due to the often neglected effects of non-linear material response, to the role of prestress under the action of the mean pressure, and to the different effects of pressure on cylindrical and spherical shells. The study of radial motions near primary resonance (when the frequency of the pulsating pressure is near the natural frequency about an equilibrium state under a constant pressure) gives formulas ensuring that the motions are of hardening or softening type depending on the constitutive functions and whether the constant mean pressure is compressive or inflational. The method of multiple scales gives asymptoticformulas for the principal parametric instability regions (Mathieu tongues) and for the stable and unstable motions at twice the forcing frequency, which closely agree with those obtained by numerical continuation methods. The dependence of frequency on amplitude and the form of instability regions are critically influenced by deviations (even very slight deviations) of material response from that of linearly viscoelasticshells, by the constant mean pressure, and by the type of shell. This paper exhibits the rich diversity of postcritical periodic motions.

Unstable manifold computations for the two-dimensional plane Poiseuille flow

We follow the unstable manifold of periodic and quasi-periodic solutions in time for the Poiseuille problem, using two formulations: holding a constant flux or mean pressure gradient. By means of a numerical integrator of the Navier–Stokes equations, we let the fluid evolve from an initially perturbed unstable solution until the fluid reaches an attracting state. Thus, we detect several connections among different configurations of the flow such as laminar, periodic, quasi-periodic with two or three basic frequencies, and more complex sets that we have not been able to classify. These connections make possible the location of new families of solutions, usually hard to find by means of numerical continuation of curves, and show the richness of the dynamics of the Poiseuille flow.

Servo-controlled pneumatic pressure oscillator for respiratory impedance measurements and high-frequency ventilation.

The ability to provide forced oscillatory excitation of the respiratory system can be useful in mechanical impedance measurements as well as high frequency ventilation (HFV). Experimental systems currently used for generating forced oscillations are limited in their ability to provide high amplitude flows or maintain the respiratory system at a constant mean pressure during excitation. This paper presents the design and implementation of a pneumatic pressure oscillator based on a proportional solenoid valve. The device is capable of providing forced oscillatory excitations to the respiratory system over a bandwidth suitable for mechanical impedance measurements and HVF. It delivers high amplitude flows (> 1.4 l/s) and utilizes a servo-control mechanism to maintain a load at a fixed mean pressure during simultaneous oscillation. Under open-loop conditions, the device exhibited a static hysteresis of approximately 7%, while its dynamic magnitude and phase responses were flat out to 10 Hz. Broad-band measurement of total harmonic distortion was approximately 19%. Under closed-loop conditions, the oscillator was able to maintain a mechanical test load at both positive and negative mean pressures during oscillatory excitations from 0.1 to 10.0 Hz. Impedance of the test load agreed closely with theoretical predictions. We conclude that this servo-controlled oscillator can be a useful tool for respiratory impedance measurements as well as HFV.

Mechanical behaviour of powders using a medium pressure flexible boundary cubical triaxial tester

A medium pressure (<21 MPa) flexible boundary cubical triaxial tester was designed to measure the true three-dimensional response of powders. In this study, compression behaviour and strength of a microcrystalline cellulose powder (Avicel® PH102), a spray-dried alumina powder (A16SG), and a fluid-bed-granulated silicon nitride based powder (KY3500) were measured. To characterize the mechanical behaviour, three types of triaxial stress paths, that is, the hydrostatic triaxial compression (HTC), the conventional triaxial compression (CTC), and the constant mean pressure triaxial compression (CMPTC) tests were performed. The HTC test measured the volumetric response of the test powders under isostatic pressure from 0 to 13.79MPa, during which the three powders underwent a maximum volumetric strain of 40.8 per cent for Avicel® PH102, 30.5 per cent for A16SG, and 33.0 per cent for KY3500. The bulk modulus values increased 6.4-fold from 57 to 367MPa for Avicel® PH102, 3.7-fold from 174 to 637 MPa for A16SG, and 8.1-fold from 74 to 597MPa for KY3500, when the isotropic stress increased from 0.69 to 13.79 MPa. The CTC and CMPTC tests measured the shear response of the three powders. From 0.035 to 3.45MPa confining pressure, the shear modulus increased 28.7-fold from 1.6 to 45.9MPa for Avicel® PH102, 35-fold from 1.7 to 60.5MPa for A16SG, and 28.5-fold from 1.5 to 42.8MPa for KY3500. In addition, the failure stresses of the three powders increased from 0.129 to 4.41 MPa for Avicel® PH102, 0.082 to 3.62 MPa for A16SG, and 0.090 to 4.66MPa for KY3500, respectively, when consolidation pressure increased from 0.035 to 3.45MPa. In addition, the shear modulus and failure stress values determined from the CTC test at 2.07, 2.76, and 3.45MPa confining pressures are consistently greater than those from the CMPTC test at the same constant mean pressures. This observation demonstrates the influence of stress paths on material properties. The CTT is a useful tool for characterizing the three-dimensional response of powders and powder mixtures.

Role of calcium-sensitive K(+) channels and nitric oxide in in vivo coronary vasodilation from enhanced perfusion pulsatility.

In vitro studies support K(+)(Ca) channel-induced smooth muscle hyperpolarization as underlying acetylcholine-mediated (or bradykinin-mediated) vasodilation that persists despite combined nitric oxide (NO) and PGI(2) inhibition. We tested the hypothesis that these channels are activated by enhanced pulsatile perfusion in vivo and contribute substantially to vasodilation from this stimulus. The canine left descending coronary artery was perfused with whole blood at constant mean pressure, and physiological flow pulsatility was set at 40 or 100 mm Hg by computer servo-pump. Cyclooxygenase was inhibited by indomethacin. Mean flow increased +18+/-2% (P:<0.0001) with enhanced pulsatility. This response declined approximately 50% by blocking NO synthase (L-NMMA) or K(+)(Ca) [charybdotoxin (CbTX)+apamin (AP)]. Combining both inhibitors virtually eliminated the flow rise. Inhibiting either or both pathways minimally altered basal coronary flow, whereas agonist-stimulated flow was blocked. Bradykinin-induced dilation declined more with CbTX+AP than with L-NMMA (-66% versus -46%, P:=0.03) and was fully blocked by their combination. In contrast, acetylcholine-induced dilation was more blunted by L-NMMA than by CbTX+AP (-71% versus -44%, P:<0.002) and was not fully prevented by the combination. Substituting iberiotoxin (IbTX) for CbTX greatly diminished inhibition of pulse pressure and agonist flow responses (with or without NOS inhibition). Furthermore, blockade by IbTX+AP was identical to that by AP alone, supporting a minimal role of IbTX-sensitive large-conductance K(+)(Ca) channels. K(+)(Ca) activation and NO comodulate in vivo pulsatility-stimulated coronary flow, supporting an important role of a hyperpolarization pathway in enhanced mechanovascular signaling. Small- and intermediate-conductance K(+)(Ca) channels are the dominant species involved in modulating both pulse pressure- and bradykinin-induced in vivo coronary dilation.

Variation of Interior Ballistic Parameters at a Constant Mean Pressure in the Postprojectile Space of a Gun Barrel

An analytical solution of the problem of determining the interior ballistic parameters in the postprojectile space of a gun under constant pressure is proposed. Simple formulas for temperature calculation are obtained. It is shown that the temperature can be as high as the thermodynamic value at constant volume, and it can be lower than the thermodynamic temperature at constant pressure. Under quasistationary conditions, the density and temperature of combustion products tend with time to values observed in the case where both the pressure and density are constant. The effect of the initial burning surface of the projectile on parameters corresponding to the beginning of the quasistationary state is estimated. The results obtained can be useful in solving design problems.

Reversal of glibenclamide-induced coronary vasoconstriction by enhanced perfusion pulsatility: possible role for nitric oxide.

ATP-sensitive potassium channels (K+ATP) prominently contribute to basal coronary tone; however, flow reserve during exercise remains unchanged despite channel blockade with glibenclamide (GLI). We hypothesized that increasing perfusion pulsatility, as accompanies exercise, offsets vasoconstriction from K+ATP-channel blockade, and that this effect is blunted by nitric oxide synthase (NOS) inhibition. In 31 anaesthetized dogs the left anterior descending artery was blood-perfused by computer-controlled servo-pump, with real-time arterial perfusion pulse pressure (PP) varied from 40 and 100 mm Hg at a constant mean pressure and cardiac workload. At control PP (40 mm Hg), GLI (50 micrograms/min/kg, i.c.) lowered mean regional coronary flow from 37 +/- 5 to 25 +/- 4 ml/min (P < 0.001). However, this was not observed at 100 mm Hg PP (41 +/- 2 vs. 45 +/- 4). NOS inhibition by NG-monomethyl-L-arginine (L-NMMA) did not alter basal flow at 40 mm Hg PP, but modestly lowered flow (-5%, P < 0.001) at higher PP (100 mm Hg), reducing PP-flow augmentation by -36%, and acetylcholine (ACh) induced flow elevation by -39%. Co-infusion of L-NMMA with GLI resulted in net vasoconstriction at both PP levels (-60% and -40% at 40 and 100 mm Hg PP, respectively). Unlike GLI, vasoconstriction by vasopressin (-43 +/- 3% flow reduction at 40 mm Hg PP) or quinacrine (-23 +/- 7%) was not offset at higher pulsatility (-44 +/- 4 and -23 +/- 6%, respectively). Neither of the latter agents inhibited ACh- or PP-induced flow responses, nor did they modify the effect of L-NMMA on these responses. Increased coronary flow pulsatility offsets vasoconstriction from K+ATP blockade by likely enhancing NO release. This mechanism may assist exercise-mediated dilation in settings where K+ATP opening is partially compromised.

Specificity of synergistic coronary flow enhancement by adenosine and pulsatile perfusion in the dog.

1. Coronary flow elevation from enhanced perfusion pulsatility is synergistically amplified by adenosine. This study determined the specificity of this interaction and its potential mechanisms. 2. Mean and phasic coronary flow responses to increasing pulsatile perfusion were assessed in anaesthetized dogs, with the anterior descending coronary artery servoperfused to regulate real-time physiological flow pulsatility at constant mean pressure. Pulsatility was varied between 40 and 100 mmHg. Hearts ejected into the native aorta whilst maintaining stable loading. 3. Increasing pulsatility elevated mean coronary flow +11.5 +/- 1.7 % under basal conditions. Co-infusion of adenosine sufficient to raise baseline flow 66 % markedly amplified this pulsatile perfusion response (+82. 6 +/- 14.3 % increase in mean flow above adenosine baseline), due to a leftward shift of the adenosine-coronary flow response curve at higher pulsatility. Flow augmentation with pulsatility was not linked to higher regional oxygen consumption, supporting direct rather than metabolically driven mechanisms. 4. Neither bradykinin, acetylcholine nor verapamil reproduced the synergistic amplification of mean flow by adenosine and higher pulsatility, despite being administered at doses matching basal flow change with adenosine. 5. ATP-sensitive potassium (KATP) activation (pinacidil) amplified the pulse-flow response 3-fold, although this remained significantly less than with adenosine. Co-administration of the phospholipase A2 inhibitor quinacrine virtually eliminated adenosine-induced vasodilatation, yet synergistic interaction between adenosine and pulse perfusion persisted, albeit at a reduced level. 6. Thus, adenosine and perfusion pulsatility specifically interact to enhance coronary flow. This synergy is partially explained by KATP agonist action and additional non-flow-dependent mechanisms, and may be important for modulating flow reserve during exercise or other high output states where increased flow demand and higher perfusion pulsatility typically co-exist.

石炭のガス透過性に関する間隙ガス圧および応力の影響

In this study the special tests of gas permeability of coal have been conducted in order to make clear the effect of internal crack pressure and external stresses on gas permeability of coal. Practically, gas permeation rate has been measured by changing the differential pressure as a parameter under a constant mean pressure and a constant hydrostatic stress.As the results of these tests, the relation between the gas permeation rate and the differential pressure had the linearity determined from Darcy's law. The gas permeability of coal decreased almost exponentially in response of an increase of the internal mean pressure and the external hydrostatic stress. From these considerations it became clear that the gas permeable cracks closed corresponding to the effective stress. Particularly, hydrostatic stress closed the permeable cracks irreversibly.

Contrasting effects of vasopressin and angiotensin II on rabbit aortic baroreceptors

Arginine vasopressin (AVP) reportedly enhances, whereas angiotensin II (ANG II) attenuates, baroreflex control of the circulation. Here we examine whether these responses can be attributed, in part, to local actions on myelinated baroreceptor (BR) afferents, either directly or via changes in vascular tone. An in vitro rabbit aortic arch/aortic nerve preparation was used to study regularly discharging presumably myelinated BRs under controlled static and pulsatile pressures. At constant suprathreshold pressures, AVP (10(-13) M to 10(-6) M) had no effect on arch diameter or BR frequency, whereas equimolar concentrations of ANG II evoked dose-dependent vasoconstriction and associated BR inhibition. Differences were not caused by limited diffusion to BR endings lying outside the media, since similar results were obtained with either luminal or adventitial applications. AVP also had no effect on diameter or discharge in arches preconstricted with norepinephrine, whereas acetylcholine (ACh) relaxed the arch and thereby increased BR activity. These results eliminate possible AVP-induced endothelium-dependent vasodilation or potentiation of adrenergic vasoconstriction that would not be evident in isolated arches lacking tone. Finally, AVP did not sensitize BRs to changes in pressure, since ramp-evoked pressure-discharge curves remained constant and pulsatile discharge in response to sine-wave pressure inputs was unaltered. ANG II, however, shifted pressure-discharge curves to higher pressures and, with pulsatile inputs at constant mean pressure, reduced peak and average discharge firing rates. In conclusion, AVP has no apparent peripheral effect on aortic myelinated BRs in rabbits that could contribute to amplification of the baroreflex when AVP levels are elevated. In contrast, ANG II can inhibit BR firing as a consequence of local vasoconstriction, which may contribute to attenuation of the reflex when ANG II levels are elevated.

Theory and predictions for finite-amplitude waves in two-dimensional plane Poiseuille flow

It has been found by Pugh and Saffman [J. Fluid Mech. 194, 295 (1988)] that in a two-dimensional channel, the stability of finite-amplitude steady waves to modulated waves can depend on the boundary conditions imposed on the flow. In particular, near the limit point in Reynolds number, stability can depend on whether the flux or the mean pressure gradient is prescribed for the flow. Here a continuous range of intermediate boundary conditions is defined and studied using bifurcation theory. Based only on previous numerical solutions to the Navier–Stokes equations at constant mean flux and constant mean pressure gradient, it is shown that the finite-amplitude steady waves must have a double-zero eigenvalue at some intermediate boundary condition. From this a unifying picture emerges for the dynamics near the limit point in Reynolds number and specific predictions are made for finite-amplitude solutions to the Navier–Stokes equations. These predictions include the existence of a homoclinic orbit and a degenerate Hopf bifurcation.

Flow/velocity characteristics of arterial bypass stenoses

In the carotid system with relatively constant blood flow, peak systolic velocity within a stenosis (PSVST) can characterize the degree of hemodynamic stenosis. We have studied flow/velocity characteristics in an in vitro model of stenosis within conduits of varying diameters in an attempt to quantify the degree of stenosis from flow/velocity profiles in peripheral vein bypasses. A Harvard pulsatile flow pump (70 BPM) pumped human blood (HCT, 35–45%) through thin-walled polytetrafluoroethylene (3–6 mm in i.d.) into a variable peripheral resistance maintaining a constant mean blood pressure of 80 mm Hg over a flow range of 0–500 ml/min. A Diasonics DRF400 duplex scanner with a 10-MHz imager and 4.5-MHz Doppler probe was used to image and Doppler the conduits and measure flow through them. Validation of Doppler flow measurements (DF) was performed comparing them with flow measured (MF) by timed collection. PSVST within and pressure drop across a 50% stenosis was measured for each of the conduit's sizes over a range of 0–500 ml/min MF. The results show a good correlation between DF and MF ( r = 0.99, P < 0.001) for the whole range of internal diameters. In each 50% stenosed conduit, PSVST correlated well with MF ( r = 0.95, P < 0.001). Curves were constructed of MF vs PSVST for each 50% stenosed conduit. We conclude that measurement of volumetric flow, conduit diameter, and peak systolic velocity within a vein bypass can objectively predict bypass stenoses of 50% or greater.