Saint-Venant's equations

Saint-Venant's equations describe how water flows in open channels like rivers and streams. They consist of two main parts: one ensures water mass conservation (continuity), stating that the amount of water entering a section equals the amount exiting plus any change in storage; the other accounts for energy and momentum (momentum), including the effects of gravity, friction, and pressure. These equations help predict how waves, floods, or changes in flow move downstream, providing a foundation for hydraulic engineering and flood management. They assume the flow is gradually varying and primarily horizontal, simplifying complex flow behaviors into manageable calculations.