Understanding Total Energy in Fluid Flow

When we talk about a perfect incompressible fluid flowing in a continuous stream, a fundamental principle of fluid dynamics comes into play: Bernoulli's principle. This principle is essentially an application of the conservation of energy for ideal fluids in steady flow.

Bernoulli's Principle Explained

Bernoulli's principle states that for a non-viscous, incompressible fluid in steady flow, the sum of pressure energy per unit volume, kinetic energy per unit volume, and potential energy per unit volume is constant at every point along a streamline.

This constant sum represents the total energy per unit volume of the fluid. For each individual particle within this ideal fluid flow, its total energy, which is the sum of:

• Pressure energy
• Kinetic energy (energy due to its motion)
• Potential energy (energy due to its height or position)

remains the same as it moves along its path (a streamline).

Applying Bernoulli's Principle to the Question

The question describes a "perfect incompressible fluid flowing in continuous stream". This perfectly matches the conditions under which Bernoulli's principle is applicable. 'Perfect' implies non-viscous, and 'incompressible' means the density doesn't change. 'Continuous stream' implies steady flow along streamlines.

Therefore, according to Bernoulli's principle, the total energy of each particle in such a fluid, at various places along its flow path, does not change.

Conclusion

For a perfect incompressible fluid flowing in a continuous stream, the total energy of each particle at various places remains constant because the flow adheres to Bernoulli's principle, which is a statement of energy conservation for ideal fluids.