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In a previous report [2] the author presents a new theory for V-belt drives. In that work special attention is directed to the motion of the belt. Stress variation in the cord of the belt is treated in another report (3). In the present report the earlier theory is extended and the main interest here is how the power loss is influenced by different belt and drive properties. The contribution to the power loss can be divided into two main parts viz: losses due to external friction (sliding between belt and pulley) and internal friction (sliding between molecules-hysteresis). The former losses are treated theoretically and the latter experimentally. A further separation is also made and power losses due to external friction arising when the belt enters and leaves the pulley are specially treated. Different types of contribution to the power loss are calculated by Gervas and Pronin (4) and in another paper (5) Gervas measures the internal friction losses caused by the bending (flexure) of the belt. However, the experimental method used didn’t separate the losses due to external and internal friction. In a chapter on optimum tensioning of a belt drive, different types of losses are combined and the efficiency reaches a maximum for a certain combination of transmitted power and pretension.

The problem of transient thermal stresses in a solid, elastic, homogeneous, and isotropic sphere is solved for uniform and nonuniform, local surface heating. The temperature solutions are obtained by using separation of variables and integral transformation. The corresponding thermal stresses are derived by superposing a particular displacement potential function on Boussinesq solutions. Numerical solutions for two particular cases of localized heating of a typical brittle spherical solid have been obtained and presented. The results indicate a tensile stress concentration in the interior of the solid below the heated zone.

An analytical model for flow-induced vibration of a tube row in a cross flow is formulated. A criterion for the onset of instability is developed. The tubes are modeled with different stiffnesses and damping normal and parallel to the free stream to simulate effects which arise in heat exchangers. The critical reduced velocity required for the onset of instability is shown to increase sharply with the separation of natural frequency between tubes. The effect of an adjacent wall and rows composed of a small number of tubes is explored. The model reduces to an experimentally validated criterion for symmetrically supported tubes.

The phenomenon on the tubes in a tube row, which vibrate alternately along the row in the transverse and stream-wise directions, will be explained by a vortex model. This model consists of the symmetrical vortex pair trains behind the stream-wisely vibrating tubes, and the Karman vortex streets behind the transversely vibrating tubes. It will be shown in the paper that the coupling between these two groups of vortex systems can excite the tube arrays to perform this fluidelastic vibration. A criterion for the onset of this orbital movement will be given with the expression ξ = R/Sxt. This criterion predicts a strong fluidelastic vibration for tubes with low transverse tube spacings and low natural flexible frequencies in a high speed flow. The theory leading to this criterion is based on the phenomenon of the variation in the position of the separation point for the free shear layer during the cylinder vibration. A switching of the jet for maintaining the fluidelastic vibration is then a result of this variation.

A three-dimensional incompressible isothermal laminar separation of a Newtonian fluid in transient and steady flow was investigated. The geometry chosen for this study was an annular expansion-contraction chamber with a rotating inner cylinder. It was found that an adaptation of a numerical solution first proposed by Fromm gave converged solutions for all Reynolds numbers in the laminar range. Theoretical computer plotted streamline patterns were superimposed on time exposure photographs of air bubbles in transparent oil. Measured static pressure differentials were compared with laminar theory. Turbulent flow was studied experimentally.

An analytical method for predicting the perturbed aerodynamic reactions of a harmonically oscillating flat plate airfoil with time dependent point of separation is presented. It is shown that this method in conjunction with an empirical knowledge of the time history of the separation point can predict stall-flutter. Numerical results are presented and compared with existing theoretical and experimental results with special emphasis on torsional mode of oscillation.

The initial value problem of waves generated by an oscillatory pressure distribution moving uniformly on the free surface of a two-layer fluid is solved. The integral representations of the waves both on the free surface and on the surface of separation are obtained. By a passage to the limit t → ∞, the steady-state solution of the problem is derived through an asymptotic evaluation of these integrals at large distances. It is noticed that stratification sharply changes the number and the character of the progressive waves and also introduces two critical speeds instead of one as found in homogeneous fluid. At these speeds the solution becomes singular.

The effect of section size on the room-temperature notch strength of H-11 steel, 2014-T6 and 7075-T6 aluminum alloys, and Plexiglas was investigated in three different series of notched cylindrical tensile specimens and notched rectangular bend specimens. The three test series permit the separation of the influences of the geometrical parameters, which determine the stress field near the base of the notch, on the notch strength as the size of the specimen increases. The notch strength decreases with increasing size for all series investigated. The decrease in strength is most pronounced for the sharp machine-notched and fatigue-cracked specimens but it is also observed, to a much smaller degree, in the other series of notched specimens for all materials. An analysis of the results of this study indicates that the loss in strength with increasing section size is due to at least two factors: An increase in stress concentration factor and an increase in critically stressed volume with increasing size. With a superposition of stress concentration and volumetric effects, a loss in strength with increasing size greater than that predicted by existing fracture concepts for a brittle material may be anticipated and was actually observed for sharply notched H-11 steel specimens. Insight into the size effect and experimental scatter observed in notched specimens of real materials is gained from a consideration of the behavior of a model of an inhomogeneous material in the presence of external notches. The constant-fracture stress concept applied to this model yields a size-effect prediction on notch strength and an expression for experimental scatter in terms of the interflow spacing and the notch root radius.

Using solutions obtained by separation of variables, the set of singular solutions of the shallow cylindrical shell equation is completed by finding a particular integral of a second-order problem. These new solutions are investigated, and those for concentrated forces and for all displacement dislocations are identified. The stress function and the components of the displacement vector are given for all these solutions.

The formal solution of the problem of defraction of a plane, time-harmonic, compressional wave by a group of cavities in a thin elastic plate is obtained by the method of multiple scattering. The cavities are circular and their geometry of distribution is arbitrary. Numerical results of two identical holes at a finite separation are presented in detail.

On the basis of the new flexural theory of elastic sandwich plates recently developed [1–3], the problem of general forced flexural vibration of sandwich plates in the plane-strain case is solved. The classical method of separation of variables combined with the Mindlin-Goodman procedure [4] for treating time-dependent boundary conditions is used. As an example, the results are made use of in solving the problem of a simply supported sandwich plate in plane strain with one of the two end sections prescribed a transverse deflection varying with time.

The effect of container capacitance on the thermal response of plane walls, infinite cylinders, and spheres subjected to sudden changes in ambient temperature is analyzed. A series solution is presented for each geometry which can be obtained by the method of separation of variables. The first three eigenvalues necessary for the numerical evaluation of the series are tabulated for each configuration. Analytical curves are presented which enable the engineer to determine whether the exact solution must be used or whether an additional approximation can be made which allows a simplification to results commonly found in heat transfer textbooks.

An evaluation is made of non-Hertzian contact stresses occurring during partial separation between a smooth elastic spherical inclusion and a surrounding infinite medium subjected to two independent axisymmetric stress components at infinity. Modifications of an analysis by another author for a special case involving a rigid inclusion and uniaxial tension applied at infinity are discussed, and an alternate method of solution is given. Extensive numerical results are presented for circumferential and normal stresses on the cavity corresponding to 12 different combinations of loading and elastic parameters which yield contact surfaces defined by either an equatorial spherical band or two polar spherical caps.

The pressure distribution in the contact zones and the radii at which flat and smooth axisymmetric, linear elastic plates will separate were computed for several thicknesses as a function of the configuration of the bolt load by the finite element method. The radii of separation were also measured by two experimental methods. One method employed autoradiographic techniques. The other method measured the polished area around the bolt hole of the plates caused by sliding under load in the contact zone. The computational and experimental results are in agreement and these yield smaller zones of contact than indicated by the literature. It is shown that the discrepancy is due to an assumption made in the previous analyses.

A three-dimensional axisymmetric elasticity problem pertaining to the contact stresses between a smooth rigid sphere and an infinite elastic solid with a smooth spherical cavity of the same diameter has been considered. Uniaxial loading is applied to the solid at infinity, resulting in a separation along a portion of the boundary between the sphere and the solid. The problem has been considered as a mixed boundary-value problem of elasticity. The angle of contact and the stress distributions along the contact surface are determined by solving a set of dual-series equations associated with Legendre polynomials. Numerical results are presented.

A theoretical framework for predicting the steady-state operational characteristics of two-component heat pipes is established. The laws of conservation of mass and energy as well as thermodynamic phase equilibrium relations are applied to the system, and the governing relations between the various system parameters are specified. Measurements of the operational characteristics of a water–ethanol heat pipe indicate that complete separation into two pure components did not occur in any of the experiments. The observed degrees of separation and other operational characteristics agree well with the predictions.

The Zero Power Plutonium Reactor (ZPPR) is a fast experimental reactor that operates at very low power levels and is used to simulate proposed fast power plutonium reactors in the 1000-MW range. The reactor is built on two large tables, one stationary and one movable, with numerous roller bearings on the underside for ease of travel. Half of the reactor is built on each table, and then the tables are brought together before the reactor can go critical. The tables are each designed to support at least 120 tons of fuel and structural material. Load tests were conducted to prove the system and to determine deflections in the foundation and runways. Many safety devices are built into the table drive system, such as an electric feed-rail system that disconnects the power supply to the drive motor if a relay fails, three speeds of table closing to control reactivity-addition rates, and two independent table-separation systems. Fuel control rods are used for reactivity changes; fuel and poison safety rods are used for shutdown control. Core material is loaded into 2 × 2 × 23-in. drawers, and the drawers are slid into matrix tubes stacked 10 feet high on the tables. Matrix tubes and drawers and the tables were aligned to obtain a minimum gap at the interface.

An analysis is made of the suction holding power of a device in which a fluid flows radially outward from a central hole between two parallel circular plates. The holding power and the fluid flow rate are determined as functions of the plate separation. The effect of changing the proportions of the device is investigated. Experiments were made to check the analysis.

Flow around a sphere for Reynolds numbers between 2 × 105 and 6 × 104 has been observed by measuring the pressure distribution around a circle of longitude under a variety of conditions. These include the effects of laminar and turbulent boundary layer separation, tunnel blockage, various boundary layer trip arrangements and inserting an object to disrupt the unsteady, recirculation region behind the sphere.

The shape of the film-vapor interface is found for a thin liquid film separating from a stationary surface and being swept away on an opposing moving surface. The analysis is for two-dimensional Newtonian flow, and includes the effects of gravity, inertia, and surface tension. The principal assumption is that of a quadratic tangential velocity distribution across the film. The solution shows that the entire separation phenomenon is completed in a distance of about one plate clearance from the stagnation point. Stagnation points occur on the vapor-liquid interface at the separation point and at a film height of 3h∞ (three times the film height on the moving plate far downstream). For a fixed separation height, the asymptotic film thickness h∞ is shown as a function of three dimensionless parameters. The results are in good agreement with published experimental data.

Revisions of the Denavit-Hartenberg symbolic notation are proposed which extend its use to the entire domain of rigid link mechanisms. The extended notation provides a clear separation of the pair variables and the invariant parameters of a mechanism and thus provides a framework in which higher pairs can be systematically modeled. The new symbolism can be used directly with the existing matrix methods of kinematic analysis, and a numerical scheme is presented to reduce the task of data collection for these methods.

A simple equation expressing the wake momentum thickness as a primary function of the suction-surface diffusion ratio (ratio of maximum surface velocity to outlet velocity) of coaventional low-speed cascade blades is derived from boundary-layer theory in conjunction with simplifying approximations. The derived equation is utilized to gain an insight into qualitative effects on stalling diffusion ratio of such factors as Reynolds number, transition location, and extent of local laminar separation. Use of parameters suggested by the analysis is shown to result in generalized experimental loss and stall correlations and in means for estimating total-pressure loss and unstalled range of operation for commonly used blades.

Analytical methods are developed for treating steady-state axisymmetric thermoelastic problems defined in bispherical coordinates. Possible geometrical configurations include the infinite space with two spherical cavities of arbitrary radii and separation distance, the half-space with a spherical cavity, and the thick-walled shell having eccentric spherical boundaries. Thermal conditions must be prescribed at the surface of the body such that the temperature distribution is uniquely determined. The surfaces of the body are traction free. Numerical results for a half-space containing a spherical cavity heated to constant temperature with zero temperature on the plane and at infinity are presented in graphical form for representative geometrical variations.

This paper describes quantitatively one stage of the flow development process in equipment working with two-phase mixtures. The kinetics of a Taylor bubble, as it rises behind a series of other bubbles in a gas-liquid slug flow, have been determined. The rise velocity of a bubble is expressed as a function of separation distance from the bubble ahead of it. Using this information, the pattern of development of bubbles which initially enter a tube at regular intervals is determined by means of finite difference calculations. The density and, to a first approximation the pressure drop, of the developing flow are then calculated from continuity considerations. The density distribution in the entrance region is found to be a function of flow rates of the two phases, of distance from the inlet, and of initial bubble size. Density calculated by the present theory is compared with experimental measurements by the present and other investigators. Theory and experiments are in good agreement.

Hydraulic transients in a short horizontal pipeline resulting from the closure of a valve at the upstream end of the pipe were examined. Test conditions resulted in water column separation at the valve. Measurements of transient pressure and velocity changes for a number of tests are presented. Calculated results based on the method of characteristics are compared with the measurements. Special attention was devoted to the evaluation of the dynamic behavior of the valve.

Direct measurements of the distributions of normal and frictional stresses on a rake face under cutting conditions have been considered to be practically impossible. However, as reported in this paper, the stress distributions have been successfully obtained photoelastically by using a tool made of a photoelastic material. According to the authors’ experiment, the frictional stress on the rake face is distributed uniformly over a wide range of the tool-chip contact length, but it decreases rapidly near the point of chip-separation on the rake face. As to the normal stress, it has a peak near the cutting edge, being rather stationary in the middle part of the contact length and decreasing gradually toward the point of chip-separation.

A complex envelope f(t) is used to replace the traditional sine and cosine envelopes of the response of a sinusoidally forced, slightly nonlinear system, so that the response is y(t) = Re [f(t)ejw0t]. By setting Im [f(t)ejw0t] equal to the Hilbert transform of y(t), simple equations for the derivative of f(t) are easily obtained by the method of averaging. The approximations implicit in the method of averaging are shown to introduce broad-band filtering, whose effects can be eliminated by use of all harmonics. An example of an off-center rotary load shaken by a general elliptical motion shows how resonant modes of the device’s mount can be selectively energized at different frequencies, provided the modes have high Q and adequate separation of resonant frequency.

Based on an expression given by Cooke, an equation is derived for a three-dimensional “equivalent radius” for cones at a small angle of attack. This function when used in any of the available axisymmetric boundary-layer equations yields corresponding solutions for yawed cones. Expressions for the streamlines along which the above equations are to be integrated are also derived. The method yields a line of possible incipient separation or wake formation in addition to the boundary-layer properties in both the longitudinal and circumferential direction. Numerical solutions including heat transfer effects are presented for a wind tunnel model and compared with experimental results.

Recent work on the supersonic freestream-centered propulsive jet interaction problem has shown that minimum total afterbody drag can be achieved during power on flight with less than a full (zero annular base) boattail. In contrast to optimum power-on configurations, minimum total afterbody pressure drag for power-off (coast) flight requires, in general, a full boattail. Flow separation of the freestream on the boattail is known to occur for a wide range of flight conditions during power-on operation. This flow separation is shown herein to reduce total afterbody drag for nearly full boattails to values which approach the corresponding values for optimized configurations without separation. Thus, the possibility of reconciling flight-profile drag minimums for both power-on and power-off conditions by using afterbody separation is suggested and shown to be a feasible design consideration.

A solution is obtained from a simplified approach for the problem of the motion of two fragments driven into a vacuum after rupture of a container filled with gas. Following rupture, the two container fragments are driven in opposite directions. From the separation developed between the moving fragments, the originally contained gas escapes to the vacuum, perpendicular to the direction of motion of the fragments, and with locally sonic velocity. The present solution removes two restrictions of an earlier similar approach: (1) the speed of the gas within the original volume (and consequently, by inference, that of the fragments) is small relative to the sonic escape velocity, and (2) the volume between the separating fragments while they are accelerating undergoes negligible change from the original volume.

A solution is presented for predicting the upstream separation point in a two-dimensional channel flow in which an obstacle is present. The paper considers only the separation of a laminar boundary layer but could also be applied to the turbulent boundary-layer case. The mathematical model considers free-streamline theory to get the pressure distribution ahead of separation. Go¨rtler’s series solution and Witting’s finite-difference method are then used to predict separation. The theory is checked experimentally.

The effects of square and reentrant entrances on flow regimes (no “appreciable” separation, large transitory stall, and fully developed two-dimensional stall) and local heat-transfer coefficients were determined with air flowing through a symmetrical, plane-wall, two-dimensional subsonic diffuser with one of the diverging walls heated and maintained isothermal. Flow and heat-transfer studies were made for the following ranges: 2θ = 0 to 45 deg, L/W = 6 to 18, and Rextut = 4 × 104 to 3 × 105. Results indicated that 2θ, L/W, and entrance configuration greatly affected the flow regime and heat transfer. Equations relating Um′ to Ut, Ur to Ut, and equations of the type Nu = C Pr0.6Rex0.8 are presented. For the configurations tested, heat-transfer rates were greater for reentrant than for square entrances.

The primary objective was to develop an exact solution to the simplest possible laminar boundary-layer problem for a curved rotating blade. It was formulated initially so that the results might be used to illuminate some of the characteristics of boundary-layer behavior on centrifugal impeller blades. The solution was obtained by a perturbation technique and the results compared to existing approximate solutions and related exact solutions. A primary result shows that rotation itself may induce laminar boundary-layer separation on a blade trailing face in the absence of free-stream, longitudinal adverse pressure gradients. This result is then interpreted to show that such a separation may become important for impellers of low ReD = uˆtD/ν; i.e., when ReD ≤ 900.

A theoretical and experimental investigation has been made of the two-dimensional, aerodynamic characteristics of flexible airfoils or sails with no thickness. Thin-airfoil theory has been used to calculate the shapes of the camber lines as a function of angle of attack and excess length of material over the chord length. It is found that for specific eigenvalues of a nondimensional chordwise tension parameter, specific shapes arise for which there is no stagnation point. Some eigenmodes also correspond to boundaries between stable and unstable airfoil shapes. Lift, center of pressure, shapes, and pressure distributions are determined for the entire practical range of angle of attack. An experimental investigation of the lift, drag, and moment of quasi-two-dimensional flexible airfoils has been made, and the measurements have been compared with theory. Certain of the aerodynamic characteristics are in good accord with theory, but certain others are not, principally because of fabric porosity and boundary-layer separation.

Measurements have been made of the mean flow in a two-dimensional, constant-width, ninety-degree miter bend and compared with predictions of available free-streamline theories. Agreement is quite favorable, especially with a model incorporating separation ahead of the concave corner. Reynolds number effects observed in real flows are argued to be associated with changes in the location of the outer-wall separation point. Requirements for relevancy of free-streamline models of internal flows separating at a salient edge are suggested and confirmed for cases examined.

A static model for predicting the input-output characteristics of direct and transverse impact modulators is presented. The model is based on the position and shape of the dividing streamsurface between the impacting jets. The streamsurface permits the separation and identification of the individual flow processes within the devices. Empirical relations are developed for each of the flow processes and combined to formulate the static model. Input-output characteristics calculated from the model are generally within 25 percent of measured characteristics. The pressure gain predicted by the model is shown to be highly sensitive to jet spreading characteristics and nozzle spacing.

A series solution is presented for the problem of the small deflections of a thin elliptical plate with the following boundary conditions: (a) The edge of the plate is supported and is given a small prescribed deflection in a direction perpendicular to the middle plane of the plate. (b) The external load applied to the plate consists of a general distribution of bending moments acting around the edge of the plate. Since the loading consists of moments distributed around the edge of the plate, the general Lagrange differential equation for the middle surface of the plate reduces to the biharmonic equation. Elliptic co-ordinates are used and the problem reduces to finding a solution of the biharmonic equation, in elliptic co-ordinates, which satisfies the boundary conditions. Solutions to this equation are of two types: (a) harmonic functions, and (b) biharmonic functions which are not harmonic. Functions of type (a) are found by the method of separation of variables in Laplace’s equation expressed in elliptic co-ordinates. Functions of type (b) are found by the use of complex variable theory.

The effect of noncondensable gas on laminar film condensation of a liquid metal on an isothermal vertical surface with forced vapor flow is analyzed. Where necessary the interfacial resistance due to thermodynamic nonequilibrium is included for a condensation coefficient σ = 1. A computer program has been developed to solve a finite-difference analog of the governing partial differential equations and is applied here to the mercury–air and sodium–argon systems. Heat-transfer results are presented for vapor velocities in the range 1 to 100 fps with mass fraction of gas varying from 10−5 to 3 × 10−2. The overall temperature difference ranged from 0.1 to 30 deg F while the temperature levels were 1200 and 900 deg R for mercury–air and 2000 and 1500 deg R for sodium–argon. The effect of noncondensable gas is most marked for low vapor velocities and high gas concentrations. At the lower pressure levels the inter facial resistance plays a dominant role, causing maxima in the curves of q/qNu versus x. For the mercury–air system the adverse buoyancy force causes vapor boundary-layer separation when the free-stream vapor velocity is low.

The contact of a hard sphere with a flat elastomer is examined both analytically and experimentally when adhesive stresses are present. Use of a transparent spherical indenter enables continuous measurement of contact size while the samples are pulled apart. For any combination of load and contact area, the superposition of a Hertz and a Boussinesq stress distribution separates the contact into a circular zone under compression and an outer annulus under tension. During separation, while the contact size decreases and the tensile annulus becomes a larger percentage of the total contact, the average tensile stress remains constant. This average adhesive is a material property which is easily measured and is shown to be invariant with respect to indenter radius and initial contact pressure. An application of this analysis to opaque indenters is described.

This paper presents stability data for a very long vertical pipe transmitting torque in a viscous medium. In addition to these factors, distributed pipe weight and hydrostatic-fluid pressure effects are included, distinguishing the problem from classic problems discussed in present literature. The additional factors of pipe weight and fluid pressure introduce terms having variable coefficients into the coupled differential equations. The coupled equations are combined into one equation by use of a complex dependent variable. The resulting equation is solved by separation of variables and power series methods.

This work presents an analytical investigation of a plastic mass being compressed between the ends of two elastic circular cylinders. A special function recently tabulated by the author is used to find the deformation of the elastic cylinders due to the pressure distribution caused by the compression of the plastic mass. Based on the deformed shape of the cylinders found by the iterative solution using the special function, the author presents a simplified approximate method for finding the pressure distribution on the cylinders when given the edge separation of the cylinders and the ratio of the shear strength of the plastic mass to the modulus of elasticity in shear of the cylinders.

This paper considers the relationship between the resistances of small models of surface vessels as obtained in a towing tank, and the resistances of the corresponding full-size hulls. Tests of the bare model hulls are compared with tests of the same models roughened at the bow by applying narrow strips of comparatively coarse sand. The effects of the artificial stimulation of turbulence caused by this roughening, both in hastening the transition from laminar to turbulent friction and in altering the point of separation of the boundary layer, are discussed. Resistance curves for full-size hulls, as developed from tank tests of their models made with induced turbulence, are compared with direct measurements of full-size resistances, as obtained in open-water tests of the full-size hulls. The test results are presented graphically, and the work of other investigators in the field is included.

This study is concerned with the steady flow of a fluid of constant density and viscosity between two eccentric cylinders of fixed parallel axes. The inner cylinder has a constant angular velocity and the outer one is stationary. Approximate solutions of the Navier-Stokes equations were obtained for the two-dimensional flow. These solutions together with an experiment were utilized to study the appearance of an eddy with separation and reattachment points occurring at the outer cylinder.

The equation of motion in a laminar boundary layer on curved surfaces has been developed from the Navier-Stokes equations. After an order-of-magnitude analysis terms of highest and next order have been retained and a single ordinary differential equation of motion derived by the method of “similar solutions.” An iteration procedure has been used to determine effects of displacement thickness and surface curvature up to and including separation. The equation of motion has been solved by a digital computer using the Runge-Kutta step-by-step integration technique.

A free-streamline theory for an inclined flat plate in an infinite flow field, at an arbitrary angle of attack, is presented. Measurements of the location of the free-vortex layers, of the vortex-street frequency, and of the pressure behind an inclined sharp-edge plate are reported as a function of both the angle of attack of the plate and the lateral constriction of the flow. The separation between free-vortex layers is found experimentally to be essentially independent of lateral flow constriction. A form of the Strouhal number, using this separation distance as the characteristic flow dimension, is shown to be independent of lateral constriction of the flow and of the inclination of the plate.

This is an investigation of the distribution of the local rate of mass transfer from 4.2-in-diam naphthalene cylinders to air at ordinary temperature and pressure, flowing normal to the axis. The air speeds are near and within the critical zone of the drag. The results in the laminar region are compared with approximate boundary-layer calculations of H. Schuh and of H. J. Merk and with corresponding heat and mass-transfer experimentation in the literature. It is shown that the calculations after Merk are reliable from the point of stagnation to the predicted point of separation.

Separation and stall of an impulsively started elliptic cylinder at an angle of attack are investigated through the method of inner and outer expansions. The assumptions are large Reynolds numbers and small times. The interactions between the boundary layer and the outer inviscid flow are taken into consideration. Uniformly valid solutions are obtained for general two-dimensional cylinders. The movements of the separation points on an elliptic cylinder are calculated. Stall is found to be strongly dependent on the thickness ratio and the angle of attack of the cylinder but to be weakly dependent on the Reynolds number.

A method is presented for calculating the efficiency of a diffuser for two-dimensional, steady, incompressible flow without separation. The method involves a combination of organized boundary-layer data and frictionless potential-flow relations. The potential velocity and pressure are found after the boundary-layer growth is determined by a trial-and-check calculation.

Results of field measurement of transients in two pump discharge lines show that the pressures were greater than had been predicted during design, and a theory and method of analysis are developed which explains the time-history of the transients measured. The field measurements were undertaken because of the complexity of the phenomena and because very little measured data were available. Results are presented graphically along with analytical solutions. Conclusions drawn were: (a) The inherent difficulty of prediction of water-column separation effects is further complicated by the uncertainty about complete pump operating characteristics and actual moment of inertia of pumps and motors; (b) the effects of air and gases entrained in solution in the water must be considered in the analytical solution; and (c) entrained air can have a detrimental effect on the water-hammer transient, i.e., larger pressure surges in the discharge line and higher reverse speeds of the pumps can be caused by its presence.