bluuebunny/crossref_metadata_2025 huggingface dataset:
Heat Transfer to Air, Carbon Dioxide and Helium Flowing through Smooth Circular Tubes under Conditions of Large Surface/Gas Temperature Ratio
Authors: Barnes J. F. , Jackson J. D.
Published: February 2007

In this paper, experiments are described on the transfer of heat from a heated tube to a gas flowing through it. Three gases were used: air, helium and carbon dioxide. The difference in temperature between the tube and the gases was large and the main objective of the work was to study the effects of radial variations of the gas properties with temperature. The conditions under which the experiments were performed were (1) essentially fully developed velocity and temperature profiles, (2) approximately uniform wall heat flux and (3) low subsonic turbulent flow.

Some analysis has been developed to cover the present experimental work. Predicted Nusselt number-Reynolds number relations for the constant properties case are found to be in reasonable agreement with the experimental data for Reynolds numbers above about 10 000, provided the ratio of eddy diffusivities is assumed to vary from about 1·0 at Re = 104 to about 1·2 at Re = 105. The effects of variations of surface/gas temperature ratio, predicted by the analysis, are found to be in quite good agreement with the experimental data of both this and earlier investigations.
Buckling of Circular Conical Shells under Axisymmetrical External Pressure
Authors: Singer Josef
Published: February 2007

The stability equations for thin conical shells derived by Seide are solved for loading under hydrostatic pressure and lateral pressure varying in the axial direction. The solution implies slightly relaxed boundary conditions for the u and v displacements, but for the w displacements the usual conditions of simple supports are enforced rigorously. The stability equation in the radial direction is rederived in a modified form similar to that given by Batdorf for cylindrical shells and is solved by the Galerkin method. Typical cases are analysed. The results for hydrostatic pressure loading are compared with results found by other investigators and with those obtained by Hoff and the author in an analysis restricted to small cone angles.
Hydrodynamic Lubrication in Wire Drawing
Authors: Tattersall G. H.
Published: February 2007

Part I. It was shown by Christopherson and Naylor that hydrodynamic lubrication in wire drawing could be provided by supplying lubricant at the entry of the die at a pressure comparable with the yield stress of the wire. The necessary pressure could be conveniently generated by causing the wire to approach the die through a tube of a diameter slightly larger than the wire diameter, sealed on to the inlet side of the die. They carried out experiments with oil as the lubricant, on wires of copper and mild steel, and developed a theory which accounted for their experimental results but suffered from the defect that all their equations contained two dependent variables, P the pressure developed and q the quantity of lubricant flowing.

In the present paper a theory is developed by considering all regions up to that in which the wire deforms, and equations are obtained by means of which P and q are expressed in terms of independent variables. The calculated values of pressure for Christopherson and Naylor's conditions show good agreement with their experimental results but the theoretical values of lubricant flow are too high by a factor of two to three. The probable reason for this discrepancy is that the breakdown of the oil under shear has been ignored.

Part II. In Part I of this paper a theory is developed for hydrodynamic lubrication in wire drawing with oil as the lubricant, and the calculated values of P the lubricant pressure and q the lubricant flow are compared with values taken from previously published experimental work. Part II is concerned with the case when the lubricant is a soap.

Experiments were carried out, in which P and q were measured as a function of wire speed u for a series of accurately made tubes (or nozzles) of a range of dimensions, and for about a dozen soaps of widely varying rheological properties. It is shown that there is a maximum value of both P and q and that this result can be explained in terms of the theory with the additional condition that the apparent viscosity of the soap is an exponential function of wire speed of the type μ = μ0 exp (– Bu).

The wire speed at which the maxima occur is the same for P and q and appears to be independent of nozzle dimensions but dependent on soap properties. It is equal to I/ B.

For a given soap with different nozzles the value of the maximum pressure Pmax is proportional to l/h2 where l is the length of the parallel portion of the nozzle and h is the clearance over the wire diameter, provided the thickness of the lubricant film is small compared with 1/2 h. For a given soap with different nozzles Pmax is proportional to μ0/ B.
Effect of Metallic Contact on the Pitting of Lubricated Rolling Surfaces
Authors: Dawson P. H.
Published: February 2007

The degree of metallic contact, expressed as the ratio of the surface roughness to the oil film thickness, is found to play an important part in determining the pitting behaviour of lubricated rolling surfaces. In particular under a repeated contact stress of about twice the nominal pitting endurance limit, experiments have shown that the life of the surface before pitting occurs is governed by this ratio. At the same high stress there is some evidence that, in the complete absence of metallic contact, pitting does not occur at all.
Dynamic Behaviour of a Rigid-Plastic Steel Beam
Authors: Rawlings B.
Published: February 2007

The estimation of permanent damage caused to steel structures from such effects as bomb blast, earthquakes, or collisions from moving objects is a problem which has attracted the attention of engineers, especially over the past decade.

Analyses of the response of complete framed structures to dynamic loads have, to date, been very idealized, representing the structure as a simple mass-inelastic spring system. Some more precise analyses have, however, been made of the behaviour of specific types of beams under particular loading conditions, but the results have remained unco-ordinated. In the present paper an attempt is made to unify these by considering the mechanics of behaviour of a flexural element under general time-dependent loading conditions, the effects of high strain-rate sensitivity being ignored. The equations derived will then form a basis for analysis of framed structures, by satisfying joint equilibrium and compatibility requirements.

A number of examples are given, and the limitations of the method are discussed.
Thermal Stresses in Elastic Axially Symmetrical Bodies
Authors: Baines B. H. , Hoyle R. D.
Published: February 2007

The thermal stresses in axially symmetrical elastic bodies with irregular boundaries can only be obtained using finite difference techniques. Hoyle demonstrated that a solution can be computed by using the two-diagram technique but the two stress functions used have proved to be difficult to handle. These difficulties are analysed and two other stress functions are suggested which have several advantages, one of which is that these functions converge satisfactorily when completely relaxed alternately. The boundary conditions which these functions must satisfy have been rationalized and a new approach to boundaries developed which removes the worst of the difficulties formerly associated with curved boundaries.
Elastic Restraints in the Flexure of Circular Plates
Authors: Duncan J. P. , Taylor T. E.
Published: February 2007

A method is presented for predicting the flexural behaviour of circular plates supported in elastic mountings. When loaded, such plates acquire a boundary condition intermediate between a simply supported and encastré condition. If, is as often the case, a relation Mr / dw/dr= A exists between the moment exerted on the mounting by the plate, Mr, and the slope produced in the mounting, dw/dr, the plate deflects like a simply supported plate having an ‘effective Poisson's ratio’ equal to Aa/D+ρ where ρ is the natural Poisson's ratio. This has been demonstrated both theoretically and experimentally and related to the existence of points of inflection in simply supported plates.
Damping of Torsional Vibrations by Dry Friction
Authors: Williams D.
Published: February 2007

The problem of damping out structural vibrations by the use of dry (Coulomb) friction, already discussed in relation to beam-like structures in a previous paper (1)†, is here considered in relation to the torsional vibrations of shafts.
Photoelastic Study of Stresses near Cracks in Thick Plates
Authors: Fessler H. , Mansell D. O.
Published: February 2007

Uniform tension was applied to 1-in. thick 6-in. wide plates which contained edge cracks normal to the direction of loading. After stress freezing, slices normal to the plane of the crack were cut and analysed. The results were compared with theoretical solutions by Westergaard (1)‡ and Williams (2). In general, both solutions were found satisfactory, but the hydrostatic tension predicted for the line of the crack was not found. The slight inequality of the stresses changed the directions of the principal stresses radically near the line of the crack.
An Optimization of the Principal Design Parameters of Stirling Cycle Machines
Authors: Walker G.
Published: February 2007

A Stirling engine is a mechanism used to convert heat into power or vice versa and operates on a closed regenerative thermodynamic cycle with compression and expansion of the working fluid at different temperatures.

According to the classical theory the performance of a Stirling cycle machine is a function of six independent parameters, namely:

speed, pressure of the working fluid, ratio of the temperatures in the compression and expansion spaces, ratio of the swept volumes in these two spaces, phase angle by which volume variations in the expansion space lead these in the compression space, volume of the heat exchangers and regenerator.

The four parameters (3)–(6) must be selected at the design stage of the machine. The paper describes the procedure and presents the results of computations carried out to establish the optimum combinations of these four parameters for

maximum engine output for the machine acting as a prime mover, maximum heat lifted for the machine acting as a refrigerator,

over a combined temperature range from 30 to 3000°K. The output of a Stirling cycle machine can be expressed in terms of non-dimensional power or heat lifted in several different ways. Four methods were studied in detail, the parameters optimized and design charts prepared. Wide variations in the optimum parameter combinations were obtained and a partial explanation of this phenomenon is offered.

Pressure-volume diagrams for machines of the same size were prepared for the four different parameter combinations. Maximum output was obtained from the machine designed on a basis of limited maximum pressure and total swept volume. The two charts relating to the case for prime mover and refrigerator optimized with regard to the maximum cycle pressure and total swept volume are recommended for use in future design work.
Large Deflection of an Encastré Rigid-Plastic Grid
Authors: Martin J. B.
Published: February 2007

The large deflection analysis of a rigid-plastic encastré beam carrying a point load obtained by Haythornthwaite is extended to cover beams carrying uniformly spaced equal point loads. It is shown how the principles revealed in the extended analysis may be used to draw the flow line for an idealized encastré three beam by three beam grid loaded at all node points. Experimental results are presented to show what significance may be attached to the analysis.
Torsional Stress Concentrations at Rounded Corners of Rectangular Hollow Sections
Authors: Byrne J. G. , Carré B. A.
Published: February 2007

Values are presented for torsional stress concentration factors and stresses at the centre of the outer side of rectangular hollow sections of finite thickness with rounded inner corners. The results were obtained for four different ratios of the corner radius to the thickness of the section, initially for square sections, but in such a way that it was possible to deduce results for all rectangular sections with the same corner radii for which the ratio of wall thickness to breadth of section was less than one eighth. The results for the square sections were obtained by solving the finite difference analogues to Laplace and Poisson equations by the Young-Frankel successive over-relaxation method. The results agree extremely well with such exact analytical results as are available, but a comparison with some previously published results obtained by the Southwell relaxation method shows a serious discrepancy, which is explained.
Alternating Stress Required to Propagate Edge Cracks in Copper and Nickel-Chromium Alloy Steel Plates
Authors: Frost N. E.
Published: February 2007

Fatigue tests at zero mean load have been carried out on copper and nickel-chromium alloy steel plate specimens containing two small coplanar edge cracks. For a wide range of crack lengths it was found that whether or not a crack grew depended on the value of ρ3 l, where ρ is the semi-range of the alternating stress and l is the edge-crack length. If ρ3 l is greater than C a crack will grow, if ρ3 l is less than C a crack will remain dormant. C had a value of 0·6 for copper and of 5·5 for the alloy steel when ρ was in ton/in2and l in inches.
Analytical Determination of the Discharge Characteristics of Cylindrical-Tube Orifices
Authors: Hall G. W.
Published: February 2007

Rational expressions for the incompressible discharge characteristics of square-edged cylindrical-tube orifices having axial lengths of the order of one diameter or greater are derived by the application of boundary layer theory to a simplified model of the flow mechanism. The theoretical predictions of discharge coefficient value and of cavitation inception in the case of liquids are shown to accord well with available experimental data. The effects of chamfered and radiused entry are discussed. This new analysis is intended as a step towards the goal of establishing the means of deriving optimal orifice designs in the fields of flow measurement, servomechanisms, fuel injection, pneumatic gauging, and in other domains.
Solution of Navier-Stokes Equations for the Non-Linear Hydrodynamic Slider by Matrix Algebra Methods
Authors: Woodhead R. W. , Kettleborough C. F.
Published: February 2007

The equations of viscous flow, the Navier-Stokes equations, are difficult to solve because they are non-linear, multi-variable, partial differential equations. For isothermal two-dimensional flow three equations have to be solved simultaneously, the momentum equation for each direction and the continuity equation. The usual numerical method is to replace the continuous system with the discrete representation at a number of points by the finite difference approximations to these equations, assuming that the solution to the discrete system approximates and converges with increasing point representation to the continuous solution. An iteration process, whereby the non-linear terms provide corrections to the solution of the linear portion of the equations, would tax many digital computers from the viewpoints of both storage and time.

The use of matrix methods discussed in this paper enables considerable simplification and savings in both computer storage and time. Further non-linear terms present no difficulty whatsoever and are*** readily incorporated in the method of solution. This approach permits ready generalization not only to other problems in hydrodynamics but also to other non-linear differential equations. The only knowledge required is that associated with normal matrix methods and finite difference formulae applicable to numerical differentiation and integration. It is thought that the simplicity of the method will appeal to engineers in general.

The first part of the paper examines the basic equations by the usual order of magnitude approach and reduces them to their simplest form with the dominant inertia terms retained. The numerical results are shown to be in good agreement with a single perturbation solution.

The second part describes the numerical solution of the equations.
Design of Rectangular Tubeplates for Large Heat Exchangers
Authors: Blake C. S. , Paton A. D.
Published: February 2007

A method is proposed for dealing with large rectangular and circular tubeplates, in which edge loading and deflection is absorbed by a bellows or a diaphragm. The simple design procedure is based on curves derived from a theory which considers a strip at the edge of the tubeplate. Specimen curves and a recommended design procedure are included.

Reference is made to the ratios known as deflection and ligament efficiencies and results of tests are given which suggest that the values of these are in fact lower than those in general use. In an example it is shown that a significant saving can result by the use of a diaphragm in place of the more conventional bellows. Finally a description is given of a test rig, designed to check the values of stress and deflection in a given system of loading.
The Determination of Modal Shapes in Resonance Testing
Authors: Pendered J. W. , Bishop R. E. D.
Published: February 2007

An experimental study is described which shows the elementary ‘peak-amplitude’ technique of resonance testing to great disadvantage. On the basis of that method the experimentally determined ‘modal shapes’ are completely misleading. While the Kennedy and Pancu method would produce acceptable modes it would demand a much greater effort. An alternative technique is described which gives excellent results at the cost of much less labour. While the new method appears to have an added advantage over the Kennedy and Pancu method when there is strong coupling between the modes, it may well prove to be less accurate when there are close natural frequencies.
Response of a Non-Linear System to Pulse Excitation
Authors: Ariaratnam S. T.
Published: February 2007

The response of a single-degree-of-freedom non-linear system of the Duffing type to two forms of pulse excitation is examined by the Poincaré-Lighfhill perturbation method. The analytical results obtained are compared with numerical solutions calculated on a digital computer. The significance of the results in stability problems in certain multi-degree-of-freedom non-linear systems is discussed.
Critical-Flow Nozzle Meter and Its Application to the Measurement of Mass Flow Rate in Steady and Pulsating Streams of Gas
Authors: Kastner L. J. , Williams T. J. , Sowden R. A.
Published: February 2007

Simple theory indicates that when critical flow of a gaseous fluid is established in a given passage, the rate of mass flow becomes dependent only on the absolute pressure and temperature upstream, and changes in downstream conditions no longer have any influence. In practice, some modifications of the theoretical conclusions may sometimes be necessary. The discharge coefficient of a simple plate orifice, for instance, is greatly dependent on the amount of jet contraction, and this may be influenced by changes in downstream pressure even under critical-flow conditions. However, a properly shaped flow nozzle is not affected in this way, and is well suited for flow measurement under critical conditions.

In the experiments described, a large number of small-diameter nozzles with quadrant entrances was tested, and the effects of nozzle length/throat diameter ratio and entry radius/throat diameter ratio were carefully examined. A range of simple cylindrical nozzles was also tested. Such nozzles are easily reproduced and are to be recommended in cases where a rather low discharge coefficient is not a disadvantage.

The above experiments were made with smoothed steady flows but in addition a number of trials with pulsating flows was carried out and it was found that the observed coefficients of discharge for pulsating flow differed very little from those applying to steady-flow conditions. In view of the acknowledged difficulty in metering unsteady flows, this is a most valuable property, and it is thought that critical flow meters are very suitable for measuring the output of reciprocating compressors, free piston gasifiers and other plant delivering gas at high pressure.
Effect of Pre-Strain on Yield Surfaces in Copper
Authors: Mair W. M. , Pugh H. Ll. D.
Published: February 2007

An investigation into the effect of both tensile and torsion pre-strain is reported. A thin-walled tube was pre-strained in either tension or torsion, unloaded, and then subjected to a combination of tension and torsion to establish the yield locus in the tensile-stress-shear-stress plane corresponding to the particular pre-strain. The results for torsion pre-strain in particular support a hardening theory, proposed by Hodge, that an inflation of the yield surface is accompanied by a translation.

It is shown that the method of defining yield is of prime importance. Different conclusions can be drawn about the general behaviour of the yield surfaces for a work-hardening material, depending on the definition of yield used.
Analytical Design for Time Optimum Transient Response of Hydraulic Servomechanisms
Authors: Davies R. M.
Published: February 2007

A design is proposed and analysed for an hydraulic control system whose valve is operated in such a way as to provide time optimum system response to step inputs of various magnitudes for various inertial loads. It is attempted to operate initially with maximum acceleration, followed by maximum deceleration within the constraints imposed in avoiding cavitation. Analytical solutions are found for the non-linear equations of motion describing this operation of the system. The theoretical limitations and practical implications of the work are discussed.
Residual Vibration in Modal Balancing
Authors: Parkinson A. G. , Bishop R. E. D.
Published: February 2007

Details are given of a practical technique that has been developed for the balancing of large flexible rotors. The special conditions that arise when such a rotor is borne in bearings from which vibration readings are taken are described. A modal balancing technique may be used for all modes through whose critical speeds the shaft runs, and then an averaging technique can account for the remaining modes.
Analytical Study of Systems for Bifurcated Power Transmission
Authors: Macmillan R. H. , Davies P. B.
Published: February 2007

The evolution and advantages of three previously described bifurcated power transmission systems are outlined. Three new systems are then described, analysed, and compared. Four of these systems, though different, are shown to possess identical characteristics. The analysis used may be applied to other problems, and curves for design use are presented.
Effect of High-Strain Fatigue Cycles on the Brittle-Ductile Transition of Two Mild Steels
Authors: Harris D. J. , Benham P. P.
Published: February 2007

Low endurance fatigue curves were obtained for grades A and D mild steel under the following axial conditions:

reversed load cycling—plain specimens; repeated tensile load cycling—plain specimens (grade A only); reversed strain cycling—plain material; reversed strain cycling—notched material.

Some results were also obtained for reversed strain cycling in bending of notched specimens. The fatigue results were generally as expected, the grade D steel showing a slightly superior fatigue strength.

The major part of the programme was then concerned with the effect of plastic strain cycling on the brittle fracture transition behaviour. Prior axial strain cycling initiated fairly blunt fatigue cracks after only a few cycles in all notched specimens and the Tipper test transition was lowered by about 10°C for the grade A steel, but there was little effect on the grade D material. The Charpy transition temperature was raised by various amounts (20°C maximum), depending on the cyclic strain range, number of cycles and type of steel.
Use of a Transcendental Approximation in Laminar Boundary Layer Analysis
Authors: Hanson F. B. , Richardson P. D.
Published: February 2007

The usefulness of an approximate boundary layer velocity profile which is an exponential function of an exponential function is examined. The momentum and energy integral equations for two-dimensional incompressible boundary layers are used to determine the parameters of the assumed profile for the classic example of wedge flows. The integrals involved are reduced to the exponential integral, which can be evaluated from existing tables. Comparison of the wall shear stress with Hartree's solution is remarkably good except near separation, and the agreement of the minimum critical Reynolds number with comparable results based upon Hartree's profiles is also very good. The profile function described here can be applied to further examples.
Digital Computation Methods for Evaluating Heat Flux in Condensers
Authors: Chisholm D. , Provan T. F. , Mitchell D.
Published: February 2007

Numerical methods of evaluating heat- and mass-transfer coefficients and local heat fluxes in surface condensers are outlined using the correlations for the vapour-side coefficients of Berman and Fuks, Chilton and Colburn, and Akers, Davis and Crawford. The procedures are particularly appropriate where a digital computer is used in solving the equations.
A Theoretical Basis for the Practical Simulation of Random Motions
Authors: Robson J. D. , Roberts J. W.
Published: February 2007

It is desirable to be able to impose on a given equipment random motions which are effectively equivalent to those observed in a similar equipment in service. Analysis of the response of a body to random excitation leads to the formulation of the conditions for exact spectral simulation in terms of normal co-ordinates. This is made the basis for the formulation of a simplified test in which at all points the predominant constituents of the motion are correctly reproduced. In systems where a single mode predominates at each of the significant frequencies of the motion, simulation may in principle be achieved in a test using a single vibrator.
Theoretical Investigation into the Effects of Close Natural Frequencies in Resonance Testing
Authors: Pendered J. W.
Published: February 2007

It is difficult (if not impossible) to find the principal modes, natural frequencies and levels of damping of a structure by means of a resonance test if the structure happens to possess two (or more) close natural frequencies. Under the assumption that this condition does exist, the ability of each of the various techniques for extracting the modes and frequencies from resonance test results is investigated.
Pressure Waves in Horizontal Liquid-Filled Flexible Tubes
Authors: Paidoussis M. P.
Published: February 2007

This paper deals with the velocity of propagation of waves in flexible liquid-filled tubes lying on a flat horizontal surface. The tubes considered are of sufficiently small rigidity that their cross-sectional shape is determined by the internal hydrostatic pressure, lying quite flat when empty.

It is shown that at low internal pressures very long waves propagate essentially as gravity waves in a canal. The wave velocity increases with the internal pressure and, at the same time, is increasingly affected by the extensibility of the tube wall. At very high pressures, long waves propagate essentially as axisymmetric waves in distensible circular cylinders. The calculated and measured velocities of propagation of very long waves are in substantial agreement.

The system is frequency dispersive and the wave velocity rapidly increases with the wave number. An approximate analysis is presented, applying only when the tube contains little liquid, establishing the mechanism underlying this behaviour. This is qualitatively supported by experimental observations.
Limited Life of Shells of Revolution Subjected to Severe Local Bending
Authors: Marcal P. V. , Turner C. E.
Published: February 2007

Tests were performed on axially loaded expansion bellows in order to obtain the relationship between maximum strain, load and deflection in the plastic region. A numerical method, previously proposed by the authors, was also used to investigate the behaviour of the bellows. The experimental and calculated results were found to be in reasonable agreement.

The strains measured at collapse did not exceed three and a half times the strain at first yield while the strains after collapse were of a higher order of magnitude.

The bellows were finally tested to failure in the low-cycle regime. The results agreed with fatigue tests on the parent material.

A simple model based on the behaviour of the bending of a beam is proposed for predicting the strains in a shell of revolution with severe local bending. This model is used to classify the types of loading which lead to different modes of failure in the plastic region. The proposed design procedures are then used in case studies of the limited-life design of bellows and pipe bends, and comparison made with the observed fatigue lives.
Combined Free and Forced Convection Heat Transfer for Laminar Flow in Horizontal Tubes
Authors: Brown A. R. , Thomas M. A.
Published: February 2007

This paper describes an investigation into combined free and forced convection heat transfer for laminar water flow in horizontal tubes. The experimental data obtained do not agree with existing correlations, which relate mainly to oils. A new correlation has been derived which fits the water data to within ±8 per cent.
Non-Steady Flow through a Gauze in a Duct
Authors: Benson R. S. , Baruah P. C.
Published: February 2007

By using steady flow relations including pressure loss coefficients a method is developed for calculating wave action in a duct with a gauze. Both steady and non-steady flow experiments for five gauzes are described. The results of the non-steady flow tests showed excellent agreement between the predicted indicator diagrams, using the steady flow pressure loss coefficients, and the measured indicator diagrams. The methods described in the paper may be used by engine designers to predict the effect of gauzes or similar devices on the wave action in exhaust systems of internal combustion engines.
Effects of Fluid Inertia and Compressibility on the Performance of Valves and Flow Meters Operating under Unsteady Conditions
Authors: McCloy D.
Published: February 2007

Incompressible flow theory is used in the investigation of the effects of fluid inertia on unsteady flow through valves and flow meters. Two types of oscillatory disturbance are considered, one being due to valve oscillation at constant pressure drop and the other to pressure pulsation at constant orifice area. With the former type of disturbance it is shown that the mean flow rate decreases with frequency of oscillation. When the pressure drop pulsates the mean flow rate increases with frequency. These phenomena are shown to be of importance in hydraulic servomechanisms and in dynamic flow measurement.

Compressibility effects are considered and it is shown that cavitation can occur at the valve during oscillation.
Theoretical Estimation of the Frictional Energy Dissipation in a Simple Lap Joint
Authors: Earles S. W. E.
Published: February 2007

Some recent work on fretting fatigue in lap joints has shown that certain treatments of the joint contact surfaces greatly improve the fatigue life of the joint, and suggests that maximum benefit may be obtained by arranging for force transference within the joint to take place only by frictional resistance.

A simple theoretical analysis of a simple lap joint is here presented which estimates the frictional energy dissipation, and concludes that, for any pressure distribution imposed along the joint faces by the rivet clamping force, the damping capacity of the joint is a maximum when force transference is only by friction throughout the joint.
Resistance to Steady Laminar Flow of Pseudoplastic Fluids through Pipes and Valves
Authors: Ury J. F.
Published: February 2007

The well-known logarithmic friction factor diagram for laminar pipe flow can be extended in the following two respects:

For application to non-Newtonian fluids, by incorporating in the plot a modified form of the consistency curve for a given material. Methods are discussed of obtaining these curves, and of transforming them into the required shape. For prediction of flow resistance through valves and fittings, by use of an auxiliary diagram based on results of appropriate tests. The general procedure is outlined, and it is stressed that results cannot be relied on quantitatively, until test data are obtained for wider ranges of sizes and types than hitherto available.
Self-Induced Waves in open Channels
Authors: Binnie A. M.
Published: February 2007

When water is led from a reservoir through an open smooth contraction into an open horizontal channel fitted with a weir at outlet, a stream is produced which is apparently uniform. However, if the velocity is increased so that the Froude number is raised above about 1/2, a stationary wave train forms on the surface. In an attempt to overcome this disturbance, experiments were made with a tilting channel with and without a weir. To obtain a waveless stream, it was found essential to raise the Froude number somewhat above unity.
Self-Damped Pneumatic Isolator for Variable Frequency Excitation
Authors: Soliman J. I. , Tajer-Ardabili D.
Published: February 2007

The correct amount of damping is very important for the proper functioning of isolation systems. Isolation systems with a small amount of damping are unable to protect the equipment from damaging resonance build-up and excessive damping reduces the isolation effectiveness at high disturbing frequencies.

In this paper it is shown that when pneumatic isolators are used, damping can be provided simply by ‘transient pressure feedback’. The main advantage of this method of damping is that it is dependent on the disturbing frequency and, therefore, it is possible to have a large amount of damping at resonant frequency and a decreasing amount of damping as the frequency of vibration increases.
Structural Fatigue under Non-Stationary Random Loading
Authors: Roberts J. B.
Published: February 2007

In this paper the problem is examined of estimating the liability of structures to fatigue failure when subjected to non-stationary random loading processes. An analytic expression is deduced for the expected number of crossings per second with positive slope at any amplitude level for a normal non-stationary random process and this result is combined with the cumulative damage hypothesis to give an estimate of the mean damage in a given time for a structure with a normally distributed stress process. In the stationary case the expressions given here reduce to results already available in the literature.
Prediction of Turbulent Boundary Layer Development in Conical Diffusers
Authors: Carmichael A. D. , Pustintsev G. N.
Published: February 2007

Methods of predicting the growth of turbulent boundary layers in conical diffusers using the kinetic-energy deficit equation were developed. Three different forms of auxiliary equations were used. Comparison between the measured and predicted results showed that there was fair agreement although there was a tendency to underestimate the predicted momentum thickness and over-estimate the predicted shape factor.
New Equations for the Thermodynamic Properties of Saturated Water in Both the Liquid and Vapour Phases
Authors: Gibson M. R. , Bruges E. A.
Published: February 2007

Equations in the form of Chebyshev polynomials are presented which enable the thermodynamic properties of saturated water in its liquid and vapour phases to be calculated in a systematic manner. In the equations defining the pressure-temperature relationship the authors have made allowance for certain unpublished observations of the National Bureau of Standards and these are considered in the section relating to vapour pressure. It is believed that the assembly of equations specify for the first time the saturated liquid and vapour boundaries whose properties have previously only been available in tabular form.
Contact Fatigue on Soft Steel with Random Loading
Authors: Dawson P. H.
Published: February 2007

Contributions intended for publication as Research Notes should be limited in length to 1000 words and two illustrations, and should be addressed to the Editor of Proceedings at the Institution Headquarters in London.
Comparison of Constant-Load and Constant-Stress Tensile Creep Data for an Aluminium-0.07 Percent Titanium Alloy at 250°C
Authors: Fairbairn J.
Published: February 2007

Constant-stress tensile creep data were obtained from an aluminium-0.07 per cent titanium alloy at 250°C and correlated using a power law of the form:

To obtain a better fit to the experimental data in the higher strain regions a modified time function was selected and the experimental data correlated using an equation of the form:

This equation was used to obtain theoretical constant-load curves which are compared with experimental constant-load data previously obtained from the same billet of material.
Theoretical Analysis of the Stresses in Pipe Bends Subjected to Out-of-Plane Bending
Authors: Smith R. T.
Published: February 2007

Most of the experimental and theoretical work on the flexure of pipe bends has concerned bending in the plane of the bend but comparison of the results of some experiments using out-of-plane bending with calculations based on existing theories indicated a need for a more exact theoretical analysis of this form of loading. In this paper a comprehensive theoretical treatment of the elastic flexure of curved tubes already published for in-plane bending has been adapted to deal with out-of-plane bending. The equations for both forms of loading have been programmed for solution by a digital computer and a design procedure is suggested to find the maximum stresses due to combined in-plane, out-of-plane and torsional bending moments.
Full Journal Bearings in Turbulent and Laminar Regimes
Authors: Szeri A. , Powers D.
Published: February 2007

An equation in lubricant pressure is derived, based on Prandtl's mixing-length theory, under general loading conditions. This non-homogeneous partial differential equation is amenable to reduction by separation of variables. One of the resulting ordinary equations is integrated directly, while the other is solved by a direct method. The solution is subject to zero pressure boundary conditions; for the long bearing both the pressure and its gradient vanish at the trailing edge. The approximate eigenfunctions are given as truncated sine series and the eigenvalues are bounded. Design figures are presented for journal bearings under static loading in both laminar and turbulent regimes.
Gyroscopic Whirl of a Rotating Bobbin Mounted on a Swing-Arm
Authors: Beddoe B.
Published: February 2007

A bobbin mounted transversely at one end of a flexible arm which is pivoted at the other end, is represented by four degrees of freedom. The frequency equation is derived in non-dimensional form and changes in the frequencies of free vibration due to gyroscopic effects are discussed. Four of a possible 20 sets of frequency curves are illustrated.

The analysis was prompted by vibration of a machine for winding synthetic yarn.
The Railway Wheelset and Suspension Unit as a Closed-Loop Guidance Control System: A Method for Performance Improvement
Authors: Benington C. K.
Published: February 2007

Using a simplified mathematical model, the conventional railway wheelset and suspension unit is shown to behave as a closed-loop guidance control system. The centre-line of the track corresponds to the input, and the lateral position of the centroid of the wheelset to the output. Analysis of the system shows that, while it may be made stable at up to high speeds, the performance in the stable region is unsatisfactory in certain respects. This is attributed to the large forces of interaction between the wheels and rails at the points of contact, arising, in the case of the conventional wheelset, from creepage.

These forces may be reduced and controlled by interposing a coupling having viscous characteristics between the wheels, in place of the rigid axle. The new arrangement is shown to be much more flexible, and capable of fulfilling a wide range of performance requirements.
Non-Dimensional Parameters in Isothermal Theories of Elastohydrodynamic Lubrication
Authors: Archard J. F.
Published: February 2007

Non-dimensional parameters used in the presentation of theories of elastohydrodynamic lubrication are here judged by the extent to which they can be given an acceptable physical meaning. A suitable basis for this is provided by considering the sequence of events as the load is increased.
Side Thrust Control by Secondary Gas Injection into Rocket Nozzles
Authors: Neilson J. H. , Gilchrist A. , Lee C. K.
Published: February 2007

Directional control of rockets can be achieved by using secondary gas jets for providing side forces. The present investigation is concerned with the fact that a greater side force can be achieved by expanding the secondary gas into the supersonic region of the main nozzle than by expanding it directly to atmosphere. A laboratory test rig using ambient temperature air for the primary and secondary flows is described. Axial thrust and side force were measured using strain gauge force transducers. The experiments were performed on a small axisymmetric main nozzle with a 10° semi-angle of divergence and with sonic injection through circular ports placed normal to the main nozzle axis. The investigations centred principally on the effects of (1) varying the secondary port size at a given axial location in the nozzle and of (2) varying the axial location of a port of constant diameter. Side force and axial thrust augmentation characteristics were obtained for a range of primary and secondary flow inlet pressures. The results show the relative importance of the parameters on which side force depends, the maximum side force that may be produced and the interdependence of axial thrust augmentation and side force.
Vibration of a Rotating Asymmetric Shaft Supported in Asymmetric Bearings
Authors: Black H. F. , McTernan A. J.
Published: February 2007

The parametrically excited vibrations of this system with assumed small asymmetry of the shaft cross-section are discussed in terms of the motion of a symmetric shaft having the mean cross-sectional flexibility, and the equations of motion are solved by the approximate perturbation-variation method of Hsu. Both features yield a more lucid appreciation of the motions expected than previous treatments: in particular, simpler explicit expressions for unstable bounds are given and forced vibrations due to mass unbalance are discussed with greater facility. The practically important case of nearly coincident natural frequencies is examined. The theoretical results are compared with analogue computation: good agreement with the approximate theory is found even for quite large shaft asymmetry.
Steady-Amplitude, Self-Excited Oscillations of Hydraulic Spool Valves
Authors: Foster K. , Kulkarni M. M.
Published: February 2007

The free oscillations of an inertia-loaded hydraulic spool valve are examined by obtaining first the theoretical conditions for a steady amplitude oscillation of a three-way valve working at low pressures where compressibility of the fluid is unimportant. The predictions are confirmed qualitatively, in experimental work on valves, but quantitatively there is some discrepancy between the experimental and theoretical negative damping forces for short valves.

This theory is then extended to the case where compressibility creates a distributed parameter effect in the inlet pipe, and it is shown that jumps in frequency and amplitude occur when the length of the inlet pipe is near to odd multiples of one-eighth of a wavelength. Another resonant system on the output of the valve also occurs when fluid compressibility combines with the inertia of a load on an output actuator, and again the agreement between the theory and experiment is good.

It is concluded from the work that a freely oscillating valve could be used as an oscillator, but the control over frequency of oscillation would be poor. Changing load conditions have a marked effect on both frequency and amplitude of oscillation.
Evaporation Rates of Liquid Droplets Evaporating in the ‘Spheroidal’ State on a Hot Surface
Authors: Satcunanathan S.
Published: February 2007

A theory is presented to show that for liquid droplets evaporating in the ‘spheroidal’ state on a hot surface, the evaporation rate may be expressed by the law:

Available experimental evidence verifies the above relationship.
Modal Curves of Pre-Twisted Beams of Rectangular Cross-Section
Authors: Dawson B. , Carnegie W.
Published: February 2007

An important aspect of the theoretical study of the vibrational characteristics of turbine and compressor blading is the prediction of the modal curves from which the stresses along the length of the blading can be determined.

The accurate prediction of the modal curves allowing for such factors as pre-twist, camber, size of cross-section, centrifugal tensile effects, aerodynamic effects, etc., is still not possible. However, a better understanding of the effects of some of these parameters can be obtained by a study of the modal curves of relatively simple idealized models. In this work the theoretical mode shapes of vibration of pre-twisted rectangular cross-section beams for various width to depth ratios and pre-twist angle in the range 0-90° are examined.

The theoretical results are obtained by the transformation method given by Carnegie, Dawson and Thomas (1)† and the accuracy of these results is verified by comparison with results obtained by Dawson (2) using the Ritz method. The theoretical results are compared to modal curves determined experimentally and good agreement is shown between them.

A physical explanation of the effects of the pre-twist angle upon the modal curves is given for the first three modes of vibration.
Visualization of Lateral Displacements of Vibrating Plates by the Shadow Moiréa Method
Authors: Hazell C. R.
Published: February 2007

The shadow moiré deflection-measuring method has been used successfully in the past to determine deflections in flat plates under static loading and to visualize nodal lines of vibrating plates. To demonstrate how this method may also be used to visualize the lateral displacements of vibrating plates, a circular plate with a free boundary was resonated and the resulting moiré patterns were recorded photographically. The lateral deflections represented by the moiré patterns were plotted and analysed. As long as the motion was periodic it was found that peak amplitudes of approximately 0·001 in or more could be measured.
One-Way Buckling of Elastically Restrained Columns
Authors: Allan T.
Published: February 2007

This paper is an extension of the author's work on one-way buckling phenomena. The effect of an elastic lateral restraint ( Ky) is considered in this paper and an analysis of a long thin beam subject to point loading and of a long thin column subject to axial loading is presented. This shows that the behaviour in such cases is similar and rather unique in that a single discrete wave or buckle forms in the member. This has a wavelength independent of the length of the member.

In the case of the column it is quite possible for several of these waveforms to appear along the column length, but they neither need to be joined to each other nor do they need to fill the whole length of the column. In practice, however, it is more usual for a single buckle wave to form. The axial load at which buckling occurs is shown to be independent of the amplitude of the buckle wave.

An experimental investigation is also reported which is in general agreement with the analysis.

By combining the ‘elastic’ and ‘constant load’† lateral restraint conditions, the author presents a strip column buckling analysis which will be found to be useful in appreciating the phenomena of certain shell buckling configurations.