Determining Optimal Discharge and Optimal Penstock Diameter in Water Turbines

Minimizing water consumption for producing hydropower is critical given that overuse of flows for energy production may result in a shortage of flows for other purposes such as irrigation and navigation. This paper presents a dimensional analysis for finding optimal flow discharge and optimal penstock diameter when designing impulse and reaction water turbines for hydropower systems. The objective of this analysis is to provide general insights for minimizing water consumption when producing hydropower. This analysis is based on the geometric and hydraulic characteristics of the penstock, the total hydraulic head and the desired power production. As part of this analysis, various dimensionless relationships between power production, flow discharge and head losses were derived. These relationships were used to withdraw general insights on determining optimal flow discharge and optimal penstock diameter. For instance, it was found that for minimizing water consumption, the ratio of head loss to gross head should not exceed about 15%. An example of application is presented to illustrate the procedure for determining optimal flow discharge and optimal penstock diameter for an impulse turbine. It is worth mentioning that this paper presents part of the material published by the author in Leon and Zhu (2014)