William C. Lennox

A pore-scale investigation of mass transport from dissolving DNAPL droplets

Spheres and pendular rings of trichloroethylene and tetrachloroethylene are observed dissolving in an artificial porous medium consisting of a single layer of glass beads. Given the simple geometry of the droplets, pore-scale mass transfer coefficients are calculated. For dissolving spheres, mass transfer coefficients are found to be constant over time. However, coefficients for pendular rings are found to decrease as the rings shrink in size. This is consistent with the concept of diffusion-controlled mass transfer in low-flow zones. Sherwood numbers measured at Reynolds numbers between 0.0033 and 8.33 show a similar trend to empirical relationships established by previous researchers using other techniques. As in previous experiments, considerable scatter in mass transfer rates is observed at a given mean flux. It is hypothesized that this variation in local mass transfer rates is caused by variations in local pore velocity.

A Control Volume Model of Solute Transport in a Single Fracture

A control volume model of solute transport through a single fracture in a porous matrix is developed. Application to problems of contaminant transport through fractured clay demonstrates several strong features of the method. The control volume approach inherently conserves mass and treats dispersivity at interfaces in a physically correct manner. By employing an upstream weighting scheme, based on the exact solution to the one-dimensional steady state advection-dispersion equation, the model proves to be more efficient than previous single-fracture models. The significance of matrix diffusion in the direction parallel to the fracture axis is investigated. For the transport of a nonreactive tracer through a 20-micrometer-wide fracture in clay material, analytical solutions based on one-dimensional matrix diffusion are erroneous for flow velocities of less than 1 m/day. The influence of boundary conditions on two-dimensional matrix diffusion is considered, and the clean-up of a contaminated fracture is simulated.

Solution to the practical problem of moments using non-classical orthogonal polynomials, with applications for probabilistic analysis

Abstract A method is presented for solving the “practical” problem of moments to produce probability density functions (PDFs) using non-classical orthogonal polynomials. PDFs are determined from given sets of moments by applying the Gram–Schmidt process with the aid of computer algebra. By selecting weighting functions of similar shape to desired PDFs, orthogonal polynomial series are obtained that are stable at high order and allow accurate approximation of tail probabilities. The method is first demonstrated by approximating a χ2 PDF with an orthogonal series based on a lognormal weighting function. More general orthogonal expansions, based on Pearson type I and Johnson transform distributions, are then demonstrated. These expansions are used to produce PDFs for maximum daily river discharge, concrete strength, and maximum seasonal snow depths, using limited data sets. In all three cases the moments of the high order series are found to closely match those of the data.

Moment operations on random variables, with applications for probabilistic analysis

Abstract A general method is developed for conducting simple operations on random variables, avoiding difficult integrals and singularities, which must be overcome when obtaining exact solutions. For sum, difference and product operations, and combinations thereof, exact moments are first determined from the moments of the constituent variables. The method of orthogonal expansion, developed in the previous paper [Probabilistic Engineering Mechanics 2000;15:371–379], is then used to produce approximate probability density functions (PDFs). The quotient operation is also considered; it requires knowledge of the negative moments of the denominator variable. The quotient and difference operations are used in a first example to establish PDFs for the hazard quotient and excess wind loading on a concrete chimney. A second example demonstrates how the proposed method may be used as an alternative to Monte Carlo simulation for simple probabilistic risk calculations; a PDF for predicted contaminant concentration at a groundwater well compares favorably with a histogram obtained by simulation.

Screening model for the contamination of a well in a uniform flow field

Explicit solutions are developed for the steady state concentration of a contaminant at a water supply well, because of a continuous source within the capture zone. The solutions are based on the streamline equation for a well in a uniform flow field [Todd, 1959] and account for the dilution of contaminated waters at the well where streamlines are converging. Integration along a streamline also yields expressions for the travel time and distance to the well, which may be used to calculate the concentration of an exponentially decaying contaminant. In a sensitivity analysis with fixed source location, travel times decrease with higher values of hydraulic conductivity down to a minimum value. This minimum is given by a hydraulic conductivity just under the limiting value that places the source on the capture zone boundary.

Effect of survey size on student ratings of teaching

Questionnaires filled in by students have become increasingly important due to the part they play in decisions about the tenure, promotion and merit pay of faculty. Since it is rare to get a complete return, it is important to determine what reliance to place on various completion rates. Using data from the faculty of engineering in one university the authors conclude that if class size is 30 or more, a 50% response rate gives an acceptable indication of rating. In a small class, less than 30, something like an 80% return is needed if the same degree of confidence is to be achieved.

Measurement of Quality of Teaching and Courses by a Single Question Versus a Weighted Set.

SUMMARY Results are examined arising from use of two alternatives for evaluating the quality of teaching and courses, namely a linear combination of a number of questions versus a single, global question. The relationship between the global question and the combination of individual questions is shown to be highly correlated, but not with a slope of 45 degrees.

Issues of teaching effectiveness as observed via course critiques

Responses to student questionnaires utilized at the University of Waterloo are examined with respect to the willingness of students to complete the questionnaire, the variability of professor ratings over time and the utility of the obtained responses to the University administration. Perhaps the greatest value of a questionnaire from an administrative viewpoint is the “flagging” of courses and/or professors that are in difficulty.

Incorporation of Computer Algebra into an Undergraduate Course in Open Channel Hydraulics

SUMMARY Modern computer algebra systems have wide-ranging mathematical capabilities and user-friendly interfaces, which make them ideal tools for research and education. To demonstrate the applications of computer algebra for teaching, this paper reports on its successful incorporation into a senior, undergraduate, civil engineering course in open-channel hydraulics. Computer algebra is particularly useful for this course, since many hydraulics problems are non-linear and have traditionally required laborious solution techniques. The advanced capabilities of computer algebra systems also make them ideal tools for the design of hydraulic structures.

Evaluation of Streamflow Forecasting Models

For application purposes, it is no longer a sound investment to develop a streamflow forecasting model from basics. Currently, streamflow forecasting models are available for nearly every scenario one can imagine. A model could be stochastic or conceptual; lumped parameter or distributed parameter. The task of developing a model has been transferred to one of evaluation and selection since no single model can be applied universally without sacrificing some element of its performance. Therefore, it is necessary to have some kind of consensus as to how forecasting models are evaluated and selected for each individual application. In the past, the evaluations were often conducted by comparing the forecasted and the observed streamflows with numeric and/or graphic criteria with little consideration given to the specific application. However, in this study, forecasting models are evaluated through simulated real-time applications to investigate which one maximizes the system performance.