Application of the Conjugate-Gradient Method for Analysing the Optimum Thrust Force for the Pico-Hydropower

A water thrust from the nozzle is the main factor for the optimizing of the pico-hydropower system.The previous study indicated that the optimal water trust resulting from the balance between the forebay tank and penstock pipe.The study of the balances has been conducted by governing of Bernoulli equation that is related to the discharge and thrust of water.The Bernoulli equation is solved using numerical analysis namely conjugate gradient methods as an algorithm for optimizing the target function by determining the values of independent variables.The main target in the numerical calculation is to obtain the maximum values of water thrust from the nozzle for rotating the turbine.The independent variables considered in this computational process are the diameters of both forebay tank and penstock pipe, in conjunction with both elevations.The values obtained in this numerical analysis indicated that the dimension of both the forebay tank and penstock pipe has a significant effect in enhancing the water thrust from the nozzle.Besides, the elevations of both are indispensable in increasing the water thrust for rotating the turbine of the picohydropower system.Considering these results and literature study, a simple scheme of forebay tank and penstock pipe with nozzle is proposed, completed by size and dimension.The diameter and height of the forebay tank are about 2.5 and 3.0 m, respectively.An ideal diameter for the penstock pipe is 0.10 m while the nozzle is 0.05 m.The system is possible to produce a driving force approximately 11-12 N. The theoretical estimation with 50% of loss power indicates that the system is possible to generate 3.0-6.0kW.The power may bigger than this estimation if the loss of power lower than 50% and an efficient system of more than 70%.