Changes In Cross-sectional Shape Research Articles

The Steady Expiratory Pressure-Flow Relation in a Model Pulmonary Bifurcation

Experiments were conducted over a range of Reynolds numbers from 50 to 8000 to study the pressure-flow relationship for a single bifurcation in a multi-generation model during steady expiratory flow. Using the energy equation, the measured static pressure drop was decomposed into separate components due to fluid acceleration and viscous energy dissipation. The frictional pressure drop was found to closely approximate that for an equivalent length of curved tube with the same curvature ratio as in the model bifurcation. The sensitivity of these results to changes in airway cross-sectional shape, non-planar configuration, and flow regime (laminar-turbulent) was investigated. In separate experiments using dye visualization and hot-wire anemometry, a transition to turbulent flow was observed at Reynolds numbers between 1000 and 1500. Transition had very little effect on the pressure-flow relation.

On acoustical models for sound propagation in rigid frame porous materials and the influence of shape factors

The propagation of sound in rigid-frame porous materials saturated with air is studied experimentally and theoretically. Two existing theoretical models, the Attenborough and the Biot–Allard models, are first evaluated using measured characteristic impedances and propagation constants for samples of ceramic material. The Biot–Allard model is found to give good agreement to the measured data if a single, frequency-independent shape factor is introduced. The Attenborough model, though, requires a shape factor that has a significant frequency dependence. To provide a more stringent test, we have constructed a model porous material that has large variations in pore cross-sectional area. This sample contains 373 straight cylindrical pores whose diameters alternate between 0.025 and 0.154 cm along their lengths. Both the Biot–Allard and Attenborough models are unable to describe the measured acoustical properties for this sample. A simple theoretical model is proposed that describes the propagation of sound through pores whose cross-sectional area and shape change along the course of each pore in a known fashion. Very good agreement between experimental results and the theoretical predictions for the two-diameter model is found. It is demonstrated that the dynamic density function (that describes the viscous effects) is associated more with the narrow sections of the pores and the dynamic bulk modulus (describing the thermal effects) is associated more with the wider sections of the pores. This theoretical model for arbitrary materials can then be generalized. Two different shape factors are required, in general, to describe both the viscous and thermal effects.

Quantitation of right ventricular shape changes after left ventricular assist device implantation.

Complex effects of left (LV) and right ventricular (RV) interaction account for changes in RV function during LV assist device (LVAD) support. It has been hypothesized that changes in RV cross-sectional shape (RVS) may be a contributing factor in the development of RV dysfunction during LVAD support. To test the hypothesis that the RVS would become more circular as a result of septal shift during LVAD support, 13 patients were studied before and after LVAD implantation. The shape of the RV was quantified using a shape factor (SF) that was equal to (4 x pi x area)/P2, where P is the perimeter of RVS. The RV area and perimeter were measured from digitized images of the RV obtained by transesophageal echocardiography in patients before and after LVAD implantation. The group SF increased considerably after LVAD (SFpre = 0.78 +/- 0.12 versus SFpost = 0.88 +/- 0.07, p < 0.05). Patients were divided into three groups: 1) patients whose RV exhibited a low SF pre-LVAD that increased significantly, 2) those with a moderate SF pre-LVAD that increased slightly, and 3) those who had high pre-LVAD SF (< 0.90) that did not change. The decompression of the LV caused by LVAD implantation results in a shift of the septum from right to left, increasing SF. This increase is more pronounced in some patients. Quantitation of the degree of RV SF change may help predict the development of RV failure during LVAD support.

Effect of Tube Ovalling on Pressure Wave Propagation Speed

For physiological and other flows it is often assumed that the pressure pulse wave speed is given by the classic Moens-Korteweg expression and this may be used, for example, to assist in the determination of in vivo blood vessel wall incremental Young's modulus. A number of physical factors affecting the value of this wave speed have been reviewed in the literature, but the effect of slight ovalling of the tube cross-section is rarely mentioned. The analysis for a tube of elliptic cross-section shows that even a very small degree of ovalling can cause quite substantial reductions in Young mode wave propagation velocities compared with the classic Moens-Korteweg expression. Bending-induced changes in cross-section shape with internal pressure increase the apparent elasticity of the tube wall. Experimental confirmation is provided by waterhammer wave speed measurements in a copper tube that has been ovalled by coiling. Even though the Young mode is not dominant in this case, as it would be for a physiological case, the measured wave speed is quite clearly less than the Moens-Korteweg theory and it can be shown that the small degree of measured tube ovality explains this.

Relation between transmural deformation and local myofiber direction in canine left ventricle.

To determine the relation between local myofiber anatomy and local deformation in the wall of the left ventricle, both three-dimensional transmural deformation and myofiber orientation were examined in the anterior free wall of seven canine left ventricles. Deformation was measured by imaging columns of implanted radiopaque markers with high-speed, biplane cineradiography (16 mm, 120 frames/sec). Hearts were fixed at end diastole and sectioned parallel to the local epicardial tangent plane to determine the transmural distribution of fiber directions at the site of strain measurement. The principal direction of deformation associated with the greatest shortening was compared with the local fiber direction in the outer (21 +/- 8% of the wall thickness from the epicardium) and inner (65 +/- 9%) halves of the wall. Although the fiber direction varied substantially with depth from the epicardium, the principal direction did not. In the outer half of the wall, fiber direction averaged -8 +/- 24 degrees, while the principal direction averaged -33 +/- 24 degrees from circumferential (counterclockwise angles are positive). In the inner half, fiber direction averaged 69 +/- 10 degrees, while the principal direction averaged -22 +/- 21 degrees. Therefore, while fiber and principal directions were not substantially different in the outer half, the greatest shortening occurred orthogonally to the fiber direction in the inner half. Normal and shear strains measured in a cardiac coordinate system (circumferential, longitudinal, and radial coordinates) were rotated (transformed) to "fiber" coordinates in both halves of the wall. In the outer half, normal strains observed in the fiber (-0.09 +/- 0.04) and cross-fiber (-0.04 +/- 0.04) directions were not significantly different (paired t test, p less than 0.05). In the inner half, more than twice as much strain occurred in the cross-fiber (-0.17 +/- 0.03) than in the fiber direction (-0.06 +/- 0.06). Moreover, the only shear strain that remained substantial after transformation was transverse shear in the plane of the fiber and radial coordinates. These results suggest that both reorientation and cross-sectional shape changes of myofibers or the interstitium may contribute to the large wall thickenings observed during contraction, particularly in the inner half of the ventricular wall.

Liquid metal MHD flow in a duct whose cross section changes from a rectangle to a trapezoid

This paper treats the liquid-metal MHD flow in a semi-infinite rectangular duct and a semi-infinite trapezoidal duct, which are connected by a finite-length transition duct. There is a strong, transverse, uniform magnetic field. The walls parallel to the magnetic field (sides) remain parallel, while the walls intersecting the magnetic field are twisted in the transition duct to provide the change in cross-sectional shape. The left side has a constant height, while the height of the right side increases or decreases in the transition duct. This geometry gives a skewed velocity profile with a high velocity near the left side, provided that the right side is relatively thick. All walls are thin and electrically conducting, but the sides are considerably thicker than the other walls. Junctions of different ducts with walls parallel to the magnetic field are treated for the first time. In expansions, contractions and other geometric transition ducts, as well as in straight ducts with axially varying magnetic fields, the fluid flow and the electric currents are concentrated in boundary layers adjacent to the sides and in the sides. At a junction with a straight duct with a uniform magnetic field, the flow and current must transfer from the boundary layers and sides to the core regions. These transfers at junctions play a key role in any three-dimensional flow.

Web flexibility and I-beam torsional oscillation

Two recent theories on torsional oscillation of general doubly-symmetric non-circular cross-section beams incorporate a second order effect, that of in-plane shear deformation involving a change in cross-sectional shape, and are found to give excellent agreement with exact results for an elliptical section rod. For “technical” torsional oscillation theories of I-section beams this in-plane shear has previously been considered within the flanges only; in the present work the greater effect of shear distortion of the web is included, having previously been considered only in static analysis. The theory predicts three modes of wave propagation, one of which is essentially torsional in character; a second mode may be identified with predominatly flange bending according to the second branch of Timoshenko beam theory whilst a new mode involves individual flange torsion with asymmetric web deformation, and has the lowest phase velocity except at the longest wavelength. An alternative symmetric web deformation is also considered.

The morphology and grain size of Nb3Sn filaments in in situ prepared multifilamentary Nb3Sn-Cu composite wire

Multifilamentary Nb3Sn-Cu wire was prepared from chill-cast Cu-20 wt% Nb ingots by drawing 12.5 mm ingots to 0.15 mm diameter wire, plating with 9 vol% Sn and reacting at temperatures ranging from 450 to 725° C. The morphology and grain size of the as-cast Nb filaments and the Nb3Sn filaments formed on heat treatment were characterized by TEM and SEM studies, and the Sn diffusion process was evaluated using electron microprobe analysis. The as-drawn Nb filaments had a cross-section typically 50 A by 2500 A and were generally convoluted in the wide direction. Tin diffusion produced Nb3Sn filaments with an essentially equi-axed cross-section having diameters of around 800 A for the 550° reaction temperature and grains extending across the diameter. It was shown that the change in cross-sectional shape is produced largely by coarsening of the thin Nb filaments prior to diffusion of Sn to form the Nb3Sn. Optimum Jc values at both 1 and 8 T were found to occur for diffusion temperatures of 550° C and times of 3 to 6 days where the grain size was 750 to 800 A.

Direct Solution to Problems of Open Channel Transitions

Existing methods of solving problems of open channel transitions involve trials-and-error solution of higher degree equations and no direct solutions are available in technical literature. This paper presents unique dimensionless discharge-depth relationships for exponential, trapezoidal, and circular channels that facilitate direct solutions to various problems on horizontal, vertical, and combined horizontal-vertical transitions even with change in cross-sectional shape. Use of the proposed relationships is demonstrated with practical examples of culvert and aqueduct transitions.

Structure and Behavior of Spermatozoa of the Fire Ant Solenopsis saevissima (Hymenoptera: Formicidae)1

The length of the live spermatozoon of the fire ant Solenopsis saevissima (Fr. Smith), varies from 69µ to 73µ. The tail has a diameter of approximately 0.6µ and presents a double appearance, resolvable with the electron microscope into a great number of separate fibers and threads. The dorsal flagellar axis, comprising 9+1 fiber doublets and 9 further fibers around the periphery, is the locomotor component. The ventral moiety consists of 2 mitochondrial rods, bearing a series of obliquely sloping structures, repeating every 0.03µ. The sagittal plane of the cell proved to be perpendicular to the plane of locomotor flagellation. The relationship between these axes and the orientation of the central pair of axial fibers was elucidated. Locomotor waves are normally propagated rearwards from the neck region. Active specimens progress in saline up to 5.5µ/sec. During forward locomotion, spinning occurs about the long axis, up to 1 rev/2 sec, probably caused by a helical component in the superficially uniplanar flagellar movements. A trend shown by insect spermatozoa has been toward the extension of the mitochondrial nebenkern along the flagellum. This feature is considered in Solenopsis to be related to their more efficient employment in making energy available for flagellar work. Theoretical considerations by J. W. Flower, given in an appendix to the paper, make it clear that consequent changes in cross-sectional shape do not affect materially the fluid-dynamic efficiency of flagellation.

Meander spectra of the Angabunga River

Three sets of air photos spanning twenty-four years are used in an analysis of the dominant modes of meandering of the Angabunga River, in central Papua, using the method of the power spectrum. Spectra are constructed for successive reaches of the stream based on the auto-correlation of the direction of flow measured at equi-spaced points on the talweg of the channel. Such spectra display the meander intensity associated with each band of frequency, where frequency is the reciprocal of meander-wavelength, measured along the talweg. It is shown that the subjectively chosen characteristic meander wavelength used by previous workers is a poor indicator of the dominant frequencies of oscillation. All spectra show a number of stable peaks of meander intensity, of which the dominant one corresponds to a wavelength of the order of 90 times the root of the bankfull discharge, that is, about 50% longer than the expected “characteristic” wavelength. The most prominent spectral peaks are more stable in a downstream direction than are other parameters, such as channel width. The relative intensities of the various peaks, however, are subject to rapid change associated with change in channel cross-sectional shape. Parts of the channel with a lower width-depth ratio have relatively high intensity associated with high-frequency peaks, a fact which strongly influences the subjective judgement of meander wavelength.

Factors Controlling the Change of Shape of Certain Nemertean and Turbellarian Worms

ABSTRACT Nemerteans and turbellarians have an inextensible fibre system around them in the form of a lattice of left-and right-handed spirals. The effect of this system on the change of shape on these worms has been analysed theoretically and compared with the observed behaviour of nine species of turbellarian and nemertean from widely differing habitats. The following theoretical relationships have been studied: (a) Variation of the angle between the geodesics and the longitudinal axis of the worm during changes in length, and the role of the fibre system in limiting changes in length of the animal. (b) The change in cross-sectional shape during changes in length. (c) The extension of the fibres and the extensibility of the worms, assuming the fibres of the lattice to be elastic. The species investigated conform with the theoretical predictions to varying degrees and have been grouped accordingly : (a) Geonemertes dendyi and Rhynchodemus biUneatus have low extensibilities and fit the prediction well. They are nearly circular in cross-section at all lengths as a result of their low extensibility and this is related to their terrestrial habit and need for water conservation. (b) Amphiporus lactifloreus, Lineus gesserensis and L. longissimus are moderately flattened in the relaxed position and have extensibilities between 6 and 10. They are marine crawling forms using cilia for locomotion and so must present a fairly large ciliated surface to the substratum. The fibre system does not limit contraction; the compression of the epithelial cells causes the observed extensibilities to fall a little short of the theoretical values. (c) Cerebratulus lacteus, Malacobdella grossa, Polycelis nigra and Dendrocoelum lacteum are very flattened forms and have very high theoretical extensibilities, but very low observed ones. The factors causing this are the thickness of the body-wall musculature (Cerebratulus), the limiting effect of longitudinal and circular reticulin fibres in the muscle layers, and the presence of dorso-ventral and diagonal muscles. Their flattened form is correlated with ecological factors (with swimming in Cerebratulus, with its parasitic life in the mantle of bivalves in Melacobdella) or with physical ones in turbellarians where a permanently flattened form is necessary for these worms to move by ciliary action.