Graphical exploration for an economic diameter of penstock pipe: A case study of the Middle Kali Gandaki Hydropower Project, Nepal

Abstract

The design and cost of penstock pipes are significant in hydropower plants with medium to high heads. The empirical formulas for designing practice often rely on simplifying assumptions that are not grasped in all situations for implementation. The economic diameter is an optimum size on the graph where the sum of the overall cost of shaft construction and the cost of energy loss is minimal. This study reports a novel approach to optimize the diameter of the penstock, integrating the cost of energy loss on conventional relations, concluding with a graphical summary. The methodology encompasses the calculation of shaft cost based on the segmented weight of the penstock, incorporating a necessary safety factor and installation expenses, as is conventional practice.  The monthly analysis of the cost of energy loss to optimize the size provides dynamic insight into the cost of energy losses using Microsoft Excel. The economic diameter was found to be 3.9 m within the study range of 2.8 m to 4.6 m for a design flow rate of 52.85 m³/s and a gross head of 144 m. Further, it can be more precise by incorporating additional losses and sensitivity analysis, with the expectation of being used as a practical tool in designing new plants of different capacities.