A variable chlorine decay rate modeling of the Matsapha town water network was developed based on initial chlorine dosages. The model was adequately described by a second order rate function of the chlorine decay rate with respect to the initial chlorine dose applied. Simulations of chlorine residuals within the Matsapha water distribution network were run using the EPANET 2.0 program at different initial chlorine dosages and using the variable decay rate as described by the second order model. The measurement results indicated that the use of constant decay rate tended to underestimate chlorine residuals leading to potentially excess dosages with the associated chemical cost and side effects. The error between the two rate models varied between 0% and 15%. It is suggested that the use of water quality simulation programs such as EPANET be enhanced through the extension programs that accommodate variable rate modeling of chlorine residuals within distribution systems.

The feasibility of household level treatment of grey water with activated charcoal was performed using laboratory batch adsorption testing on locally available charcoal media. The study results indicated that the potential for removal of organic matter was significantly high for the high pH cloth wash water compared to the low pH kitchen wastewater which also contained non-adsorbed organics. The addition of ash considerably improved the removal and projected life length of adsorption media for kitchen wastewater treatment. The adsorption isotherms obtained were all modeled adequately using the Freundlich isotherm while the isotherm shapes display different types of adsorption for the different streams of grey water because of the heterogeneous nature of the adsorbates in grey water. The replacement life length of activated charcoal for single drum household level treatment ranged between 7 and 15 months. For family daily flow rates up to 400 lit/day, the replacement costs of a single drum charcoal per cubic meter of grey water treated were calculated to be below the current tariff levels for acquiring water in cities in Swaziland. A considerable part of the grey water pollutant can be removed through pretreatment by sorption alone such as by filtration through sand or other cheap media before adsorption. For complete household level treatment of grey water, a three-step treatment consisting of sand pre-filtration, activated charcoal adsorption and sand post-filtration are recommended.

An iterative formula based on Newton's Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method has super quadratic convergence of order 2.414 (i.e., 1+ √ ). Newton method is said to fail in certain cases leading to oscillation, divergence to increasingly large number or off-shooting away to another root further from the desired domain or off shooting to an invalid domain where the function may not be defined. In addition when the derivative at the iteration point is zero, Newton method stalls. In most of these cases, hybrids of several methods such as Newton, bisection and secant methods are suggested as substitute methods and Newton method is essentially blended with other methods or altogether abandoned. This paper argues that a solution is still possible in most of these cases by the application of Newton Method alone without resorting to other methods and with the same computational effort (two functional evaluations per iteration) like the traditional Newton method. In addition, the proposed modified formula based on Newton method has better convergence characteristics than the traditional Newton method.

The germicidal properties of some metals and metal compounds were investigated in relation to their electro-chemical properties that may play a role in the inactivation of E. coli bacteria. These properties included the atomic and ionic radii, ionization energy, oxidation state, energy of formation with hydro-sulfide groups, and the redox potential of the metals. Cultures of E. coli bacteria with predetermined numbers of colony-forming units (CFU's) were brought in contact with the metals as well as metal compounds, using Eosin methylene blue agar medium and sterilized, distilled water. The rate of inactivation was determined by counting the CFU's at predefined intervals of time after inoculation. The experimental results showed that the rate of inactivation increases with increasing ionization energy of the metals. While the rate of inactivation increases with decreasing atomic radii for some of the transition metals, there is no apparent relationship between ionic radius and rate of inactivation for the metal compounds. In addition, non-transition group III metals such as aluminum and indium showed higher rates of inactivation that are comparable to the action of silver. This is probably due to the increase in coagulation potential and the resulting adsorption of bacteria, because a larger number of ions are able electrons carried by these atoms. In general, there is a difference between the atoms and the ions in terms of their rate of inactivation. This difference increases amongst the transition metals that have lower oxidation potential, lower ionization potential as well as larger ionic radius. The results also showed that for the metals, adsorption through coagulation is an important fact or that is responsible for inactivation of E. coli. For the metal compounds, additional mechanisms such as direct reaction through complex formation, physico-chemical distortion of the cell structure through direct entry of the ions into the cell, may contribute towards greater inactivation.

A model for relating the time-dependent variable rate of reaction to the decay of chlorine residual in water is developed based on the initial chlorine dose, molar concentrations of reactants, and the rate constant itself. The mathematical model, while retaining its second order nature, simplifies the solution as the residual chlorine and aggregate parameters such as molar concentration of reactants can be estimated. The model is based on molar-averaged reaction rates involving arithmetic and harmonic means of reactants that eliminate the individual reaction rates that are difficult to determine. Part of the mathematical assumption used in the derivation of the equations using molar averaging is tested for its validity through theoretical as well as Monte Carlo simulation of the error term over wide ranges of assumed reaction rates and molar concentration of reactants. The second-order variation of the rate of reaction with respect to the initial chlorine concentration has been verified through experimental tests of bulk chlorine decay carried out at different chlorine doses.