A dimensional analysis for determining optimal discharge and penstock diameter in impulse and reaction water turbines

This paper presents a dimensional analysis for determining optimal flow discharge and optimal penstock diameter when designing impulse and reaction turbines for hydropower systems. The aim 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%. Two examples of application are presented to illustrate the procedure for determining optimal flow discharge and optimal penstock diameter for impulse and reaction turbines.