A theoretical and experimental investigation of the character of in turbulent pipe flow has been carried out and some implications for the use of flowmeters considered. An extensive survey of Industrial users of flowmeters has been made, involving the participation of over 70 companies, which provides information about current industrial practice, attitudes and understanding. Axisymmetric perturbations of fully developed turbulent pipe flow been studied using the mixing-length model of turbulence. A linearised theory finds the character of small perturbations, decaying exponentially in the axial direction, in which the tangential and axial motion are independent. A non-linear similarity theory finds the flow field at a particular cross-section of the pipe assuming it to be determined by the specification of the Reynolds number, the pipe's roughness and the swirl number at that cross-section. Laser Doppler Anemometry was used to measure axial and tangential velocities on 4 equidistant cross-sections of a pipe following a double right-angle bend in two perpendicular planes. It was found the tangential velocity had the form of a solid body rotation decayed exponentially. The axial velocity profile after the bend asymmetrical, having the form of a horseshoe which rotated with swirl whilst returning to its fully developed form. Theoretical studies of the effect of the measured axial velocity profiles on the accuracy of electromagnetic and ultrasonic flowmeters presented. It is suggested that the decay of the level of swirl in turbulent flow after a double bend be modelled by the factor exp(-6fz/D) where f is the friction factor in fully developed flow and z/D the dimensionalised axial distance. The accuracy of flowmeters installed at particular locations downstream can then be predicted the appropriate error characteristics of flowmeters are known. Some indications of these characteristics are presented.

The study examines the behavior of pinned-end, centrally loaded columns of monosymmetric and asymmetric cross sections, with emphasis on angle shapes. The investigation covers flexural and flexural-torsional buckling in the elastic and inelastic ranges, which the aim of developing a rational method of predicting the buckling load for cross sections with low torsional rigidity and single or no axes of symmetry. The computer program that was developed takes into account the effect of residual stresses. The properties of the cross section were determined in the laboratory and utilized in the computer model. Full-scale column tests were run to verify the theoretical model. The results shows that equal-legged angles with low width-to-thickness ratio have flexural and flexural-torsional buckling loads that are less than 2% different. It is therefore suitable to continue using a flexural buckling solution for such shapes. This is also true for equal-legged angles with a high width-to-thickness ratio that fail in the elastic range, but in the inelastic range the flexural-torsional buckling load was about 11% less than the flexural buckling load. When the angle is unequal-legged, the flexural-torsional buckling load is always smaller than the corresponding flexural buckling load, in both the elastic and the inelastic ranges. The average difference between the flexural and flexural-torsional load for unequal-legged angle ranges from 3% in the elastic range to 10% in the inelastic range. The average ratio of the experimental results to the minimum of the theoretical results was 0.95 and the coefficient of variation was 0.053. Comparison with the results of other researchers show that it is possible to formulate an empirical formula that can be used in designing columns that are made of monosymmetric or asymmetric cross sections. However, due to the scarcity of data at this stage, it is recommended that the development of such a formula be postponed until additional test data are available. Moreover, in designing any cross section that does not have two axes of symmetry, it is advisable to check the possibility of flexural and flexural-torsional buckling.

An equivalent constant amplitude fatigue loading (Miner's stress) is developed for stationary random amplitude loadings. The effects of rainflow cycle counting and fatigue crack closure are included. A method for determining the opening stress in a random loading is also proposed. This research takes a fatigue damage factor approach. The damage factor is defined as the ratio of the wide band rainflow fatigue damage to the equivalent narrow band fatigue damage. The mathematical form of the damage factor equations is derived from theoretical derivations using the analytically tractable local range cycle counting method. Simulations of stationary Gaussian random processes are used to empirically derive the values of certain parameters dependent on the spectral shape for the rainflow cycle counting equations. There are five tasks in this research. (1) A simulation program for generating a Gaussian process has been written and is used to generate random loading histories for this study. (2) A previously proposed rainflow damage factor has been verified and refined with these simulations, without considering crack closure. (3) Using a sinusoidal approximation, the joint probability density functions between peaks, valleys and rises counted by the local range method are derived. (4) The resulting joint probability distributions are used to determine the theoretical damage with crack closure; simulations are again used to calibrate the parameters for rainflow stress cycles. (5) A procedure for finding an equivalent constant fatigue crack opening stress for stationary random loadings is described. An example application of the procedures and equations is given.

The mixing of compounds in a highly viscous medium is important in many industrial settings; from food processing to the manufacturing of rocket fuel and drugs. Experts in mixing have long been aware of how things become mixed in a nonturbulent flow, but there has been little quantitative analysis of such mixing processes. As recent developments in chaos theory have found their way into the engineering literature, there have been some attempts to apply these ideas toward numerically quantifying nonturbulent mixing processes. Chaos theory is a new name for an old subject in mathematics, dynamical systems theory which includes ergodic theory. By examining the older literature of ergodic theory, one can determine what is necessary to quantify nonturbulent mixing processes. This has led to the methods which are suggested in this dissertation. After discussing some principles of ergodic theory, the design of a bladeless mixer is presented. The philosophy of this design is to adopt an abstract mathematically mixing system around which to design and build an actual machine. Ergodic theory is then used to develop methods for quantifying nonturbulent mixing processes by both experimental and numerical means. These methods are then applied to the bladeless mixer.

The displacements and stresses in layered rock above underground openings can be calculated using a beam model for the rock layers. The traditional approach assumes that interfaces between layers are frictionless and layers can slip past one another freely as they deflect. In contrast, the design of structural laminated beams has traditionally been based on the assumption that the interfaces between layers were welded, with no slip occurring there. In this work, the theory of composite laminated beams, which allows for partial slip on layer interfaces, is applied to the problem of predicting displacements and stresses in layered roof rock. The effects of rockbolt reinforcement are modeled by discrete shear and normal stiffnesses incorporated at locations in the model where the rockbolts cross layer interfaces. Published solutions and results for laminated composite beams are reviewed. Composite laminated beam theory provided a means of accounting for rockbolt reinforcement effects and provided a conceptual framework that was used to develop two FORTRAN programs; one, based on the force method of analysis, that automatically finds shear and tensile interface failures in the system, and the other a finite element program that employs beam elements, elastic interface elements, and rockbolt elements to model a rockbolted layered rock system. Published data together with results from these programs suggest that shear reinforcement may be more effective when placed near the ends of roof layers. The normal interaction between layers tends to be uniformly distributed unless rockbolt forces act on the layers or if partial delamination of layers has occurred. Both shear and normal reinforcement will cause stresses to be redistributed within the system of layers. Analysis of this redistribution of stresses requires that the sequence of interface failure be predicted which, in turn, requires that the properties of the individual layers, of the interfaces between layers, and of the rockbolts be properly taken into account. Laminated composite beam theory and programs based on this theory provide rational and efficient ways to study and analyze the behavior of layered roof rock.

Density functional theory of statistical mechanics in a square gradient approximation was used to study nucleation in confined systems such as a cylindrical pore and in-between two cylindrical disks. This approximation was further applied to study the evaporation and condensation in nanopores with finite lengths. Confinement effects induced nucleation phenomena that are not observed in more open systems. Density functional theory was also used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute was modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The results of this study indicate that local density augmentation and the solvation free energies are particularly sensitive to changes in solute and solvent particle geometry and solute/solvent anisotropic interactions. Density functional theory allowed us to systematically study the effect of a variety of geometric and interaction parameters on the properties and behavior of all the systems. Although more sophisticated, but computationally more demanding, theoretical approaches can be used, our results provide fundamental physical insights into the behavior of real systems and create a solid basis for the development of more realistic models.

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Typically, the problem of a plate on an elastic foundation has been approached by assuming that the foundation modulus (or modulus of subgrade reaction for a soil) remains constant as the plate deforms the foundation. If one were dealing with soil as the foundation material, it can be seen from a load-deformation plot for a particular soil, that this modulus would not be constant but would decrease as the deformations increase. The purpose of this thesis is to obtain an accurate solution that uses a more realistic model for the effect of the foundation behavior in the problem. When larger deflections of the plate are encountered, the results of the analysis using a non-linear model for the foundation differ substantially when compared to results using a linear model.