What principle states that the total energy in a steady-flowing stream remains constant at every point along its path?

The principle that states the total energy in a steady-flowing stream remains constant at every point along its path is derived from Bernoulli's equation. This fundamental concept in fluid dynamics considers the conservation of energy within a fluid system, integrating kinetic energy, potential energy, and pressure energy into a single equation.

Bernoulli's equation recognizes that as a fluid moves through a system, any decrease in pressure energy must correspond to an increase in kinetic energy or potential energy, thereby maintaining constant total energy. This principle is crucial for understanding fluid behavior in various engineering applications, such as hydraulics and aerodynamics, as it allows for predictions about fluid velocities, pressures, and elevations in systems where there is no energy loss due to friction or other dissipative forces.

While the continuity equation relates to the conservation of mass in a flowing fluid, and the hydraulic radius pertains to geometric and flow characteristics in open channel flow, these do not encapsulate the concept of total energy conservation that Bernoulli's principle expresses. Energy balance, a broader concept, can apply to various systems but does not specifically address the steady-flowing stream's energy conservation as precisely as Bernoulli's equation does.