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 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.
Harnessing the freely available source of energy from the sun offers a number of additional benefits. Not least of these benefits is the fact that solar energy is an environmentally sustainable alternative. A four-wing compound parabolic concentrator (CPC) was designed as a modification of the regular non-imaging CPC concentrator that has a widespread use as solar collector. The design is intended to increase the angle of acceptance as well as concentration of energy from the sun. The conceptual design, mathematical formulation as well as construction and initial trial results have been presented in this paper. Pilot trials of the four-wing concentrator used for sanitizing both liquid and waste products produced satisfactory results. Improvements in terms of design as well as material used for construction and better preservation of heat can be considered further in the future research.
Achieving hygiene through hand washing is an important intervention in interrupting the cycle of transmission of communicable diseases. A hand washing facility named "Press Tap" has been developed and was successfully tested in different user environments. The hand washing device -which is simple and low cost -works on a foot pressing mechanism and integrates the usage of soaps using the same mechanism. This paper presents the conceptual development of the Press Tap including the governing hydraulic equations of flow that form the theoretical basis for the design of the hand washing facility. The paper also gives the construction features of the different components as well as useful operation aspects that were realized during the pilot trials of the device in different user environments.
Control of odour from urinal installations is an important task from considerations of health, hygiene and acceptability or use of these installations. Because of the problems associated with cost, technology and proprietary nature of many of the marketed technologies for odour control, there is a need to develop simple, easily adaptable and low cost technologies for odour traps in urinal installations. A research work was carried out for the development of simple and low cost odour control using devices that work on the principles of either buoyant force or gravity push combined with elastic band extension. The conceptual development of the odour trapping device arrangement and of the odour trapping mechanism is presented. The scientific model for determining the optimum elastic band extension for effective odour control is developed. Experiments were performed to verify the theoretical model relating force required for opening the odour trap with the optimum elastic band extension length. The experimental results were also used to determine the model parameters through regression. Different types of odour control devices were developed and installed to adapt to differing urinal installations including household level urinals, urine diversion dry toilets (UDDT) and community urine collection storage tanks. The devices, besides being simple and low cost, have more or less been found to work satisfactorily and effectively control odour from the urinal installations that they have been provided to.
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