Assessing and auditing water transport systems by applying the energy equations

In improving the energy efficiency of water transport systems, two critical stages are involved: assessment (to understand the system's operation and identify potential energy savings) and auditing (to locate and break down the energy losses). Both stages are based on energy balances, which can be conducted using either the extended Bernoulli equation or the energy integral equation. Both equations can be applied, but depending on the system, data availability, and the kind of study to be performed, one is preferable over the other. This paper analyses, applies and compares both equations, with a particular focus on the less commonly used energy integral equation in the hydraulic field. This more general equation includes thermal and transient effects and it is more suitable for analyzing complex systems. In contrast, the extended Bernoulli equation, while simpler to apply, can lead to the loss of relevant information, such as the evaluation of the topographic energy. The main objective of this work is to bridge the gap between these two fundamental energy equations and recommend the most appropriate one for hydraulic problems. Real examples are presented to show their differences and validate our recommendations.