Energy flow rate equation for river networks

Rational allocation of water flow energy in river networks is essential to addressing water-related issues in river network areas. However, current methods of calculating the spatiotemporal distribution of flow energy in river networks lack precision and efficiency. This paper introduces a novel hydrodynamic representation, the energy flow rate, defined as the product of the flow rate and kinetic energy head, to quantify the kinetic energy stored and transported in river networks. A linear equation system for the energy flow rate in a river network has been theoretically derived, enabling rapid calculations under steady flow conditions. A simplified equation is proposed to describe the exponential decay of the energy flow rate, accompanied by potential energy conversion. The coefficients in the linear equation system are determined using control equations at flow confluence and diversion nodes. This study provides foundational insights that can be used to develop new hydrodynamic modeling strategies to regulate water flow energy and achieve coordinated management of water-related issues in river networks.