Final answer:
In the context of steady flow along a streamline following Bernoulli's equation, the total energy remains constant. This total energy is the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume, and changes in one component must be offset by changes in the others to maintain the total energy constant.
Step-by-step explanation:
When considering steady flow along a streamline, if the flow satisfies the conditions necessary for the Bernoulli equation, then total energy has a constant value along the streamline. This total energy includes the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume. Bernoulli's equation, which applies to incompressible and frictionless fluids, is given by P + ½pv² + pgh = constant, reflecting the conservation of energy principle.
According to Bernoulli's equation, if the pressure in a given fluid is constant and the kinetic energy per unit volume increases, it implies that the potential energy per unit volume of the fluid decreases. Conversely, if the pressure and kinetic energy both increase, the potential energy must decrease to maintain the energy balance. Similarly, if the pressure increases but the kinetic energy remains constant, the potential energy must decrease because the total energy is conserved.