5. Conclusions
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. The key
findings are as follows:
1. The analysis is based on the geometric and hydraulic characteristics
of the penstock, the total hydraulic head, and the
desired power production.
2. This analysis resulted in various dimensionless relationships
between power production, flow discharge and head losses.
3. The derived 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
(hL/Hg) should not exceed about 15%.
4. To facilitate the calculations, a Matlab hydropower calculator
was developed which is available at http://web.engr.
oregonstate.edu/~leon/Codes/Hydropower/.
5. Overall, the present analysis is general and can be used for
determining optimal design flow and penstock diameter when
designing impulse and reaction turbines.