Solutions to the Navier-Stokes equation set for spiral pipes

The research presented herein embodies three subject area specifically aimed at the investigation and application of the spiral geometry. These areas are: the derivation of a spiral coordinate system in E2; the formulation of a new metric suitable for spiral pipe structures; the numerical simulation of an incompressible viscous fluid flowing through spiral pipe structures. The spiral coordinate system is first derived and then proven admissible using differential geometry. Validation is achieved using the spiral coordinate system as an alternative transformation for mapping from Cartesian to Polar coordinates for the solution domain of the general wave equation from a square to a circular elastic membrane. Problems associated with curves that do not possess natural-parameterisation in terms of arc-length, and as such cannot use the standard form of the Frenet-Serrat formulae, are solved with the derivation of a generalized metric. This metric is presented and proven for use on an arbitrary shaped pipe of class 'n' and is especially suited for spiral pipe structures. The associated Christoffel symbols of the second kind are also derived and presented in association with the generalized metric for use with the tensorial form of the Navier-Stokes and continuity equations. Finally, the spiral coordinates system is extended into E3 for two types of pipe; the spiral conic and the spiral parabolic. The Continuity and Navier-Stokes equations are numerically solved for an incompressible viscous Newtonian fluid for these pipe structures with various inlet conditions and geometric constraints. A correlation is made with these solutions and solutions found for the helical pipe structure, the nearest equivalent to the spiral found in the open literature

A Comparison of Length, Complexity & Functionality as Size Measures for Predicting Web Design & Authoring Effort

Software practitioners recognise the importance of realistic estimates of effort to the successful management of software projects, the Web being no exception. Estimates are necessary throughout the whole development life cycle. They are fundamental when bidding for a contract or when determining a project’s feasibility in terms of cost-benefit analysis. In addition, they allow project managers and development organisations to manage resources effectively. Size, which can be described in terms of length, functionality and complexity, is often a major determinant of effort. Most effort prediction models to date concentrate on functional measures of size, although length and complexity are also essential aspects of size. The first half of this paper describes a case study evaluation in which size metrics characterising length, complexity and functionality were obtained and used to generate effort prediction models for Web authoring and design. The second half describes the comparison of those size metrics as effort predictors by generating corresponding prediction models and comparing their accuracy using boxplots of the residuals. Results suggest that in general all categories presented a similar prediction accuracy. 1