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A decanter centrifuge of novel design was developed for the dewatering of fine-solids slurries having micron-range particles that form paste-like, flowable, hard-to-dewater cakes. The design combines a compound beach with a cake-flow control structure that allows expressed liquid from the cake in the dry beach region to be returned back to the liquid pool while maintaining high solids throughput. In order to provide optimal performance with various operating parameters (feed rate, centrifugal gravity, pool, differential speed, concentration of feed solids, and different slurry types), the cake-flow control is adjustable. The second part of the beach is preferably at zero angle. Tests showed that the new design allows increases in both solids dryness and solids throughput.

Two new technologies - an adjustable gate to control the cake flow, and an efficient feed accelerator - combine to improve the classification of fine-particle slurries in decanters. This article discusses the concepts of both technologies.

Analysis of the hub-type feed accelerator commonly used in decanter centrifuges reveals serious deficiencies. It delivers to the surface of the pool a tangential speed far below the value of ωR , with a consequent loss of G -level and separation effectiveness. Although the G -level corresponding to the rotation speed is ultimately reached, this occurs by an undesirable ‘churning’ action of the conveyor that causes re-suspension and mechanical wear on the conveyor face. Moreover, the feed exiting the accelerator plunges into the pool with a high radial speed and in a circumferentially non-uniform manner. A novel, more effective accelerator is described here. This has vanes situated between parallel discs whose faces are normal to the axis of the machine. The vanes are forward-curved, and thus produce overspeeding . Downstream of the vanes is a conical smoothener , which smears out the jets from the vanes into a nearly uniform conical sheet. Model tests in the laboratory, using water, were used to develop the improved technology, which is equally adaptable to solid-bowl and screen-bowl decanters and also to pusher centrifuges. Many tests in the field, on both decanters and pushers, have verified that the new technology produces significant improvements in capacity and performance.

The simple cone-type feed accelerator commonly used for solid-bowl and screen-bowl decanter and pusher centrifuges delivers to the surface of the decanter pool or the pusher basket a tangenial speed far below the value of Ω R (the rim speed of the cone), with consequences adverse to performance. A novel, more effective cone accelerator is described. This has forward-curved vanes that produce overspeeding and a final unvaned section of cone — called a smoothener — which smears out the jets from the vanes into a nearly uniform conical sheet. Model tests in the laboratory were used for developing the new accelerator technology. Operation in the field has verified the expected improvements in capacity performance.

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.

The stability and initial growth rate of disturbances on an annular film lining a cylindrical tube have been the focus of several previous works. The further development of thsse disturbances as they grow to form stable unduloids or liquid bridges is investigated by means of a thin-film integral model. The model is compared both with perturbation theories for early times, and a numerical solution of the exact equations (NEKTON) for later times. The thin-film model gave results that were in good agreement with solutions of the exact equations. The results show that linear perturbation theory can be used to give good estimates of the times for unduloid and liquid bridge formation. The success of the model derives from the dominant influence of narrow draining regions that feed into the growing unduloid, and these regions remain essentially one-dimensional throughout the growth of the instability.The model is used to analyse the evolution of the liquid layer lining the small airways of the lung during a single breath. The timescales for formation of unduloids and liquid bridges are found to be short enough for the liquid layer to be in a virtually quasi-equilibrium state throughout the breathing cycle. This conclusion is only tentative, however, because the model assumes that the surface tension of the airway liquid lining does not change with changes in interfacial area despite the known presence of pulmonary surfactant.

Experimental results on flow-field statistics are presented for turbulent oscillatory flow in a circular pipe for the range of Reynolds numbers Reδ = U0δ/ν (U0 = amplitude of cross-sectional mean velocity, δ = (2ν/ω)½) = Stokes layer thickness) from 550 to 2000 and Stokes parameters Λ = R/δ (R = radius of the pipe) from 5 to 10. Axial and radial velocity components were measured simultaneously using a two-colour laser-Doppler anemometer, providing information on ensemble-averaged velocity profiles as well as various turbulence statistics for different phases during the cycle. In all flows studied, turbulence appeared explosively towards the end of the acceleration phase of the cycle and was sustained throughout the deceleration phase. During the turbulent portion of the cycle, production of turbulence was restricted to the wall region of the pipe and was the result of turbulent bursts. The statistics of the resulting turbulent flow showed a great deal of similarity to results for steady turbulent pipe flows; in particular the three-layer description of the flow consisting of a viscous sublayer, a logarithmic layer (with von Kármán constant = 0.4) and an outer wake could be identified at each phase if the corresponding ensemble-averaged wall-friction velocities were used for normalization. Consideration of similarity laws for these flows reveals that the existence of a logarithmic layer is a dimensional necessity whenever at least two of the scales R, u*/ω and ν/u* are widely separated; with the exact structure of the flow being dependent upon the parameters u*/Rω and u2*/ων. During the initial part of the acceleration phase, production of turbulence as well as turbulent Reynolds stresses were reduced to very low levels and the velocity profiles were in agreement with laminar theory. Nevertheless, the fluctuations retained a small but finite energy. In Part 2 of this paper, the major features observed in these experiments are used as a guideline, in conjunction with direct numerical simulations of the ‘perturbed’ Navier–Stokes equations for oscillatory flow in a channel, to identify the nature of the instability that is most likely to be responsible for transition in this class of flows.

The stability of oscillatory channel flow to different classes of infinitesimal and finite-amplitude two- and three-dimensional disturbances has been investigated by direct numerical simulations of the Navier–Stokes equations using spectral techniques. All infinitesimal disturbances were found to decay monotonically to a periodic steady state, in agreement with earlier Floquet theory calculations. However, before reaching this periodic steady state an infinitesimal disturbance introduced in the boundary layer was seen to experience transient growth in accordance with the predictions of quasi-steady theories for the least stable eigenmodes of the Orr–Sommerfeld equation for instantaneous ‘frozen’ profiles. The reason why this growth is not sustained in the periodic steady state is explained. Two-dimensional infinitesimal disturbances reaching finite amplitudes were found to saturate in an ordered state of two-dimensional quasi-equilibrium waves that decayed on viscous timescales. No finite-amplitude equilibrium waves were found in our cursory study. The secondary instability of these two-dimensional finite-amplitude quasi-equilibrium states to infinitesimal three-dimensional perturbations predicts transitional Reynolds numbers and turbulent flow structures in agreement with experiments.

Using a theoretical model, we studied spreading of a bolus of insoluble surfactant deposited on a thin liquid layer of a model airway. Applications include instillation of exogenous surfactant as a treatment for neonatal respiratory distress syndrome, the use of surfactant carriers to deliver drugs via the lung, and the movement of liquid along the airway tree due to naturally occurring gradients of surface tension. The time-dependent governing equations were solved numerically for longitudinal axisymmetric surfactant spreading. We examined the influences of the resident liquid layer (thickness, viscosity, endogenous surfactant, airway radius), of the bolus (volume and surfactant content), and of gravity. The gradient in surface tension drives the flow toward the region of higher surface tension, ultimately creating a shocklike wave of nearly twice the initial lining thickness. Pressure gradients due to interfacial curvature (capillarity) have little effect on the rate of surfactant spread. The presence of an endogenous resident surfactant greatly augments the rate of spreading while inhibiting development of the shock. In all cases studied, the effect of circumferential curvature was negligible, indicating that the liquid layer can be treated as if it were spreading over a flat surface. Our results reveal that the surfactant spreads as time to the one-third power. Accordingly, a surfactant deposited in the trachea of a neonate would spread to the periphery in approximately 12 s.

The effect of curvature on longitudinal dispersion in an axially uniform toroidal tube during oscillatory flow is investigated. The regimes of dispersion and the rate of longitudinal transport are estimated by order-of-magnitude arguments. Experiments are reported for the range, 0.66 30, curvature causes a sharp increase in the effective diffusivity, relative to that for a straight tube, by a factor of about 6 at Dn2/α4 ≈ 2. The results from two numerical simulation methods are also presented. One, a Monte Carlo simulation (0.01 < Dn < 10, 0.01 < α < 0.32, Sc = 104), predicts the spread of a bolus in quasi-steady flow. The other, a spectral-element method (1 < Dn < 1000, 1 < α < 100, Sc = 0.68), is used to find the dispersion in unsteady oscillatory flow subjected to a constant longitudinal concentration gradient. Two mechanisms are identified by which axial transport is modified by curvature. First, the enhanced lateral transport due to secondary flow decreases axial transport by a factor of up to 5 for low β2 and increases axial transport by an even greater amount for high β2. Second, axial transport is enhanced owing to a form of resonance when the secondary flow circulation time is equal to the cycle period.

A hydraulic model of the circulatory system was used to study external cardiac assist (ECA) as a noninvasive, synchronous, counterpulsative aid to the failing heart. Four different modes of external pressurisation of the legs were compared. (1) In uniform compression, a spatially-uniform pressure is applied simultaneously to the entire length of the leg. (2) In graded compression, a decreasing pressure is applied simultaneously from foot to groin. (3) In sequential compression, a wave of compression is applied, at uniform pressure level, from foot to groin. (4) In graded-sequential compression, the gradation of pressure and wave-like application are combined. Depressurisation was either to atmospheric pressure or to a vacuum. For each mode tests were made with broad ranges of pressure and timing parameters. “Optimal” combinations of these were selected for comparisons among the modes. The effectiveness of cardiac assist was assessed in terms of (i) the augmentation of mean diastolic pressure, signifying increased coronary perfusion; and (ii) the lowering of mean systolic pressure, signifying reduced left ventricular oxygen requirements. Measurements of regional volume flow rates and of cross-sectional area of the leg artery provided additional insights. All four external cardiac assist modes produced substantial augmentation of mean diastolic pressure. The simplest mode, namely, uniform compression, was however the least effective in this respect. The graded, sequential, and graded-sequential modes were all better, in ascending order. These results are explained haemodynamically in terms of the tendency of a uniformly-pressurised collapsible vessel to form an occlusive flow-limiting throat at its downstream (proximal) end. Nonuniform compression is the means by which this phenomenon may be avoided. Application of vacuum during depressurisation further increased the diastolic augmentation for every external cardiac assist mode. The changes in mean systolic pressure produced by ECA were much smaller than the changes in mean diastolic pressure. In general, the modes with greater diastolic augmentation also had relatively higher mean systolic pressures. With depressurisation to atmosphere, application of external cardiac assist increased the mean systolic pressure slightly, relative to the unassisted condition. However, depressurisation to 6.7 or 13.3 kPa (50 or 100 mmHg) vacuum resulted in either a reduction or virtually no change of mean systolic pressure, relative to the unassisted condition.

The one-dimensional theory of steady flow in a thin-walled tube, partially collapsed by a negative transmural pressure difference, is developed in a general way. The mechanics of the flow is closely coupled to the mechanics of the tube. The latter is characterized by a “tube law”: the relationship between cross-sectional area and transmural pressure difference. Features analogous to those in gas dynamics and free-surface flow may manifest themselves: a characteristic wave propagation speed; opposite phenomena at flow speeds, respectively, less than and greater than the wave speed; choking; and shocklike transitions. There are many practical examples of such flows, mainly in physiology and medicine. The one-dimensional, steady analysis includes the effects of friction, lengthwise variations in external pressure, variations in elevation, resting area, wall stiffness, and mechanical properties. The speed index S (ratio of flow speed to wave speed), analogous to the Mach and Froude numbers, appears naturally in the results as a controlling parameter of behavior. Various practical ways of passing continuously from subcritical (S < 1) to supercritical (S > 1)speed are suggested. A preliminary theory of shocklike, dissipative transitions is developed, the results of which depend sensitively on the tube law. Explicit working formulas are developed for several simple types of flow (friction alone; changes in rest area alone; changes in external pressure or elevation alone) for a simple, approximate tube law. Various modes of flow behavior for a flow affected by both friction and gravity are explored.

Self-diffusion coefficients were determined experimentally for lateral dispersion of spherical and disk-like particles in linear shear flow of a slurry at very low Reynolds number. Using a concentric-cylinder Couette apparatus, recurrent observations were made of the lateral position of a particular radioactively labelled particle. The self-diffusion coefficientDwas calculated by means of random-walk theory, using the ergodic hypothesis. Owing to great experimental difficulties, the calculated values ofDare not of high accuracy, but are correct to within a factor of two. In the range 0 < ϕ < 0·2,D/a2ω increases from zero linearly with ϕ up toD/a2ω ≅ 0·02 (where ϕ = volumetric concentration of particles,a= particle radius, ω = mean shear rate of suspending fluid). In the range 0·2 < 0·5, the trend ofD/a2ω is not clear because of experimental scatter, but in this rangeD/a2ω ≅ 0·025 to within a factor of two. Within the experimental accuracy, spheres and disks have the same value ofD/a2ω.

In this companion paper to “Part I: Numerical Simulations,” we report in vitro experimental studies performed on a simple model leg consisting of a “vein” of thin-walled latex tubing surrounded by “tissue” of open-pore foam rubber. Three modes of periodic external compression were investigated: i) uniform compression; (ii) graded compression, decreasing from ankle to knee; and (iii) sequential compression, progressing from ankle to knee. The modes are compared on the basis of three hemodynamic criteria: degree of vessel collapse, level of fluid velocity, and level of shear stress. In uniform compression these measures of merit are distributed very nonuniformly along the length of the leg: they are high near the proximal end of the cuff but low elsewhere, a result due to the formation proximally of a partially occlusive throat. The latter does not form in either graded or sequential compression, with the consequence that favorable values of the three measures of merit occur more uniformly along the length of the pressurized region. It is concluded that either the graded or sequential mode of compression, or perhaps a combination of the two, would be more effective than uniform compression as a prophylaxis against deep vein thrombosis.

Ablation of human atheromas with laser pulses that had only a small effect on normal artery tissue was shown in vitro in air and under saline using 1-mu sec pulses at 465 nm from a flashlamp-excited dye laser. At this wavelength, there is preferential absorption in atheromas due to carotenoids. The threshold fluence for ablation was 6.8 +/- 2.0 J/cm2 for atheromas and 15.9 +/- 2.2 J/cm2 for normal aorta tissue. At a fluence of 18 J/cm2 per pulse, the ablated mass per unit of energy ranged from 161 to 370 micrograms/J for atheromas and from 50 to 74 micrograms/J for normal aorta tissue. Ablation products consisted of cholesterol crystals, shredded collagen fibers, and small bits of calcific material. Most debris was less than 100 micron in diameter, but a few pieces were as large as 300 micron. High-speed photography of ablation in air suggested explosive ejection of debris, caused by vapor formation, at speeds on the scale of 300 m/sec. Histological analysis showed minimal thermal damage to residual tissue. These data indicate that selective laser ablation of atheromas is possible in vitro.

Flows in thin-walled, collapsible tubes are of fundamental importance to various physiologic phenomena and clinical devices.A one-dimensional, unsteady theory is developed for flows generated either by externally applied pressures or by body forces. Part 1 deals with small-amplitude, linearized flows, part 2 with large amplitude, nonlinear flows. Experimental results for a tube collapsing under external pressure are given in part 3, together with theoretical interpretations and comparative results of numerical simulations.Several new and unanticipated phenomena are revealed. These are in part associated with the highly nonlinear ‘equation of state’ (transmural pressure versus area) for a partially collapsed tube, and in part with whether the flow speed is sub- or supercritical relative to the speed of area waves. For instance, a flow produced by a spatially uniform external pressure applied to a limited region becomes choked at a flow-limiting throat at which point the fluid speed reaches the local wave speed. This throat forms at the edge of the pressurized region. The critical velocity can be exceeded with the application of certain types of spatially graded external pressures.

Experimental results are presented for steady, supercritical flow of a liquid in a thin-walled compliant tube which is in a state of partial collapse due to a negative transmural pressure. Particular attention is paid to the effects of longitudinal tension.With a constant external pressure, friction acts to increase the area in the down-stream direction. With the tube tilted downward, friction may be so balanced by gravity forces as to result in an asymptotic approach to an equilibrium situation in which the area and velocity remain constant. When the downstream pressure is increased sufficiently, shock-like transitions to subcritical inflated states, with positive transmural pressure, occur. The longitudinal length scale of the shock is on the order of one to several tube diameters. The pressure rise across the shock lies between that for loss-free pressure recovery and that given by the Borda-Carnot sudden-expansion theory.The presence of longitudinal tension causes a train of standing waves of area to appear upstream of a local area disturbance, such as a shock-like transition. The standing waves are superimposed upon the more gradual area changes associated with friction and gravity. The wave amplitude grows in the downstream direction. Theoretical interpretations of the observations are presented in the companion paper (part 2).

Effective gas exchange can be achieved in normal dogs by ventilation at frequencies of 4–20 Hz using stroke volumes (SV) smaller than the anatomic dead space. CO2 elimination is largely a function of tracheal SV-frequency product (Vosc) in anesthetized, paralyzed dogs with normal lungs. To determine the effect of constriction of small airways on gas exchange during such high-frequency ventilation (HFV), we ventilated five anesthetized, paralyzed, and vagotomized dogs via a tracheal cannula before and during intravenous histamine infusion. Vosc was varied by varying the frequency while keeping SV constant. For low Vosc, CO2 elimination (VCO2) increased directly with Vosc during control and histamine experiments. At high Vosc, VCO2 continued to increase directly with Vosc during the control study, but during histamine infusion VCO2 was lower than control values. Eucapnia could be maintained in each dog during HFV, even during airway constriction. During histamine infusion the frequency-dependent mechanical properties of the lung influence the delivery of the HFV SV to the respiratory zone, and this may explain the lower VCO2 observed.

A simple, continuous, one-dimensional model for the geometry and structure of the bronchial airways is used for the analysis of fluid flow patterns which have been observed in forced expiration maneuvers. Various phenomena within the conducting system associated with flow limitation are investigated: (a) the conditions in which a “choke” (flow limitation) can occur in a compliant system; (b) theoretical flows that are physically impossible; (c) the possibility of having elastic jumps downstream of the choke point; (d) perturbations in the physical parameters of the conducting system.

The amount and rate of blood expelled with different modes of intermittent external pneumatic compression applied to the lower leg were studied on a regional basis in a series of experiments on healthy human volunteers. Radionuclide imaging of the labelled blood pool, with acquisition of counts synchronised to the pressurisation cycle, provided data on regional blood volumes in the leg in relation to time. To determine the changes in blood volume of the lower leg resulting from external pneumatic compression labelled red blood cell counts were determined during 10 different types of compression cycle. Since venous stasis is considered to be a major cause of venous thrombosis the red blood cell counts were used to calculate regional values of the fraction of blood ejected as well as comparative indices proportional to regional flow rate, regional velocity, and regional wall shear stress. All these indices should be maximised for optimal prophylaxis against deep vein thrombosis. The four compartment cuff in each compression mode applied a mean pressure of 45 mm Hg, but different combinations of values were used for intercompartmental pressure gradation (delta p) and for intercompartmental time sequencing to the onset of compression (delta t). Uniform compression (delta p = 0; delta t = 0) was substantially inferior to cycles with gradation and sequencing. The optimal values of delta p were in the range 5-10 mm Hg and of delta t in the range 0-0.5 seconds.

The mechanics of the lung parenchyma is studied using models comprised of line members interconnected to form 3-D cellular structures. The mechanical properties are represented as elastic constants of a continuum. These are determined by perturbing each individual cell from a reference state by an increment in stress which is superimposed upon the uniform stretching forces initially present in the members due to the transpulmonary pressure. A force balance on the distorted structure, together with a force-deformation law for the members, leads to a calculation of the strain increments of the members. Predictions based on the analysis of the 3-D isotropic dodecahedron are in good agreement with experimental values for the Young’s, shear, and bulk moduli reported in the literature. The model provides an explanation for the dependence of the elastic moduli on transpulmonary pressure, the geometrical details of the structure, and the stress-strain law of the tissue.

Theories are developed to explain the experimental observations of steady, supercritical flow in compliant, partially collapsed tubes, presented in the companion paper (part 1).It is shown that the measured curves of area vs. distance are governed by a combination of (i) friction and gravity, which produce mean gradients of area, and (ii) longitudinal bending and tension forces, which produce standing waves of area superposed upon the mean gradients. The experiments confirm the one-dimensional theory for the mean gradients: (i) in the absence of gravity, friction causes a pressure rise and a positive mean gradient of area; (ii) a downward slope can cancel gravity and lead asymptotically to a uniform state having zero gradients of pressure and area.The inviscid dispersion relationship for area waves due to longitudinal bending and tension is developed, based on a simple, approximate model for the mechanics of the tube. The phase velocity increases as the wavelength decreases, hence the group velocity exceeds the phase velocity. Consequently, in steady flows that are supercritical with respect to the infinite-wavelength phase velocity, energy can propagate upstream and standing waves of area may appear.In the experiments of part 1, longitudinal tension predominated over longitudinal bending. The measured wavelengths of standing waves were found to be in general agreement with the dispersion relationship for tension-induced area waves. The observed streamwise growth of standing area waves is interpreted physically as the attenuation of waves radiating upstream from a source of disturbance such as a shock-like rapid increase of area. The rate of wave attenuation indicates that the skin-friction coefficient has a large out-of-phase oscillatory component. The observed steepness of shock transitions agrees with an approximate theory based on treating the forward portion of the shock as the rearward part of the standing wave train that the shock drives upstream.

Es wird ein expliziter Ausdruck fur die Wirbelstarkeω hinter einem gekrummten Verdichtungsstoss fur den Fall der zweidimensionalen Stromung eines idealen Gases in Termen der Geschwindigkeit der ungestorten StromungV∞, ihrer Mach-ZahlM∞, des Stosswinkelsσ und des Krummungsradiusrs des Verdichtungsstosses im betrachteten Punkt aufgestellt.

The method of characteristics for two-dimensional supersonic flow is reviewed and summarized. A characteristics chart is presented for use with the graphical procedure of Prandtl and Busemann. A new numerical procedure is described which eliminates graphical operations and which allows of more accurate solutions. To facilitate the numerical method, a table of useful functions is included.

Elsewhere in this issue are presented analytical procedures for handling complicated problems involving the simultaneous effects of area change, wall friction, drag of internal bodies, external heat exchange, chemical reactions, change of phase, mixing of injected gases, and changes in molecular weight and specific heat. Tables of functions are given herewith to facilitate the numerical solution of such problems for regions of flow where the stream properties change continuously.

Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which the relevant Reynolds number is small enough for inertial effects to be negligible and the wavelength to diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axisymmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values.Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward (‘reflux’) time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid-mechanical peculiarity with physiological implications is that of ‘trapping’: under certain conditions an internally circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave.

The flow generated by the rotation of a flexible disk next to a wall is analyzed for small Reynolds numbers. A nonlinear differential equation for the radial variation of the pressure and the gap width is solved simultaneously with the equation governing the deflection of a spinning circular membrane under axial pressure load. Optical methods are used to measure the gap width experimentally. The theory agrees well with the measurements.

Experimental results are presented in the form of schlieren and interferometer photographs showing the interaction of oblique shocks with laminar and turbulent boundary layers on a flat plate in a supersonic stream. The effects of variations in shock intensity and boundary-layer thickness were studied through a Mach number range of 2.0 to 2.5. A greater variety of shock boundary-layer interactions was discovered than had hitherto been suspected. The nature of the interaction was found not to be solely dependent upon whether the boundary layer is laminar or turbulent. A laminar layer proved to be more greatly affected by an incident oblique shock than a turbulent layer. With relatively intense shocks the boundary layer was influenced far upstream of the point of incidence. Injection of a high-speed air stream into a turbulent boundary layer altered significantly the manner of reflection of an incident shock.

Unsteady, large-amplitude motion of a viscous liquid in a long elastic tube is investigated theoretically and experimentally, in the context of physiological problems of blood flow in the larger arteries. Based on the assumptions of long wavelength and longitudinal tethering, a quasi-one-dimensional model is adopted, in which the tube wall moves only radially, and in which only longitudinal pressure gradients and fluid accelerations are important. The effects of fluid viscosity are treated for both laminar and turbulent flow. The governing non-linear equations are solved analytically in closed form by a perturbation expansion in the amplitude parameter, and, for comparison, by numerical integration of the characteristic curves. The two types of solution are compared with each other and with experimental data. Non-linear effects due to large amplitude motion are found to be not as large as those found in similar problems in gasdynamics and water waves.

Recent developments in the fields of propulsion, flow machinery, and high-speed flight have emphasized the need for an improved understanding of the characteristics of compressible flow. A one-dimensional analysis for flow without shocks is presented which takes into account the simultaneous effects of area change, wall friction, drag of internal bodies, external heat exchange, chemical reaction, change of phase, injection of gases, and changes in molecular weight and specific heat. The method of selecting independent and dependent variables, and the organization of the working equations, leads, it is believed, to a better understanding of the influence of the foregoing effects, and also simplifies greatly the analytical treatment of particular problems. Examples are given first of several simple types of flow, including (a) area change only; (b) heat transfer only; (c) wall friction only; and (d) gas injection only. In addition, examples of flow with combined effects are given, including (a) simultaneous friction and area change; (b) simultaneous friction and heat transfer; and (c) simultaneous liquid injection and evaporation. A one-dimensional analysis for flow through a discontinuity is presented, allowing for energy, shock, drag, and gas-injection effects, and for changes in gas properties. This analysis is applicable to such processes as: (a) the adiabatic normal shock; (b) combustion; (c) moisture condensation shocks; and (d) steady explosion waves.

Tables of functions are given for solving problems in one-dimensional, compressible gas flow when energy effects, as represented by changes in stagnation temperature, are involved. The tables may be used for such typical processes as heat transfer at high gas speeds, combustion, moisture condensation shocks, flame fronts, and detonation waves. The Mach number is the independent argument of the tables, and there is one table for each of six specific-heat ratios, namely, 1.0, 1.1, 1.2, 1.3, 1.4, and 1.67.

A two-dimensional, semi-infinite tank, closed by a vertical wall at one end, is initially filled to a certain level with an in viscid liquid at rest. A gate in the lower part of the wall is suddenly opened to a region where the gas pressure is greater or less than the gas pressure over the free liquid surface in the tank. The liquid escapes (or moves inwardly) through the gate under the combined action of gravity and the driving pressure differential. The fluid motion, the shapes of the two free surfaces, and the discharge through the gate are calculated for small times after the opening.

Experiments were conducted to determine the effect of viscosity on the pressure rise recorded by a blunt-nosed impact tube in incompressible flow. The results are presented in terms of the pressure coefficient (Cp ≡ 2Δp/ρV∞2) as a function of Reynolds number (Rey ≡ V∞α/ν), where Δp is the excess of stagnation-point pressure over free-stream static pressure, V∞ is the free-stream velocity, α is the radius of the impact tube, ρ is the fluid density, and ν is the kinematic viscosity of the fluid. Above Reynolds numbers of 1000, there is no effect of viscosity, and Cp is equal to unity. Between Rey ≌ 50 and Rey ≌ 1000, Cp is slightly less than unity, but has a minimum value of 0.99. For values of Rey less than 50, Cp is always greater than unity. When the Reynolds number is below unity, the pressure rise is independent of the fluid density, and the data may be represented approximately by the formula Cp ≌ 5.6/Rey. The results are compared with the experimental investigations of Barker and of Homann, and with the theoretical studies of Stokes and of Homann.

The mixing at constant pressure of a circular jet with an annular coaxial stream has been studied for conditions of nearly common density and temperature, but differing initial velocities. By using 10 per cent by volume of helium as a tracer in the inner stream, the mixing region was mapped with respect to both material and momentum transfer. It is concluded that material diffuses more rapidly than momentum; that the principal independent variable determining the shape of the mixing region is the velocity ratio of the streams; and that the integral method of Squire and Trouncer, using experimentally determined constants, is adequate for predicting approximate values of concentration and velocity in the mixing region of a jet flowing into a moving medium of the same density. Data for widely different experiments of various investigators show that the turbulent Prandtl and the Schmidt numbers are both within ±10 per cent of 0.70, independent of the nature of the experiment and the magnitudes of the laminar Prandtl and Schmidt numbers.

A theory of rounded-entrance flowmeters, based on a consideration of the potential and boundary-layer flows in a converging nozzle, is constructed. Curves are presented showing the discharge coefficient as a function of diameter Reynolds number, with the “total equivalent length-diameter ratio” of the nozzle as a parameter. The equivalent frictional length-diameter ratio of the contraction section of the ASME long-radius nozzle is presented. The theoretical curves of discharge coefficient versus diameter Reynolds number are in good agreement with experiment over a range of Reynolds number from 1 to 106. The theory provides a rational framework for correlating and extrapolating experimental results; it shows the effects of contraction shape and location of pressure taps; it furnishes values of discharge coefficient for untested designs; and it suggests precautions to be taken in design, installation, and operation.

The intra-aortic balloon, a device for providing mechanical assistance to the failing circulation, acts as an additional valveless ventricle in series with the heart. It consists of a gas-filled bag, mounted on a catheter, which is introduced into the aorta and caused to inflate and deflate under the action of a pressure source outside the body. A mathematical model of the arterial system called the “non-uniform elastic tube model” is developed consistent with physiologic measurements of hydraulic input impedance. In conjunction with a simple model of the balloon, the “pressure-node, flow source” model, any two of the four variables, heart pressure, heart flow, balloon pressure, and balloon displacement flow may be predicted as a function of time, given the remaining two. The model in fact applies to any counterpulsation scheme of heart assist involving the introduction and withdrawal of blood volume at a local point in the aorta. A principal conclusion is that the balloon should be both inflated and deflated during diastole for maximum benefit to the heart.

Flow patterns for compressible fluids at supersonic velocities are discussed, and it is shown that shock fronts form when neighboring Mach lines (envelopes of wave fronts originating from point disturbances) intersect. A criterion for divergence of Mach lines is developed for cases in which the passage is symmetrical in two or three dimensions and has a straight axis. This criterion is used as the basis for designing supersonic nozzles and diffusers. The analysis indicates that only a nozzle of infinite length can discharge a parallel stream into a tube of constant cross section without the formation of shock fronts. Methods are presented for designing nozzles of finite length, with the intensity of shock fronts reduced to as small a value as possible, and it is shown that nozzles of reasonable length may be designed so that shock fronts are insignificant. Experimental observations indicate that the proposed method of nozzle design is a practical one. With regard to supersonic diffusers having a straight axis, it is shown that shock fronts cannot be avoided, even though the diffuser is of infinite length. However, the methods of this paper may be used as an aid in determining the best diffuser design.