During steady fluid motion, a fluid particle can possess multiple forms of mechanical energy simultaneously. Which combination best represents the energy forms available to a liquid particle in an internal flow?

Introduction / Context:
Bernoulli’s equation is an energy balance along a streamline for incompressible, inviscid flow, enumerating the forms of mechanical energy carried by a fluid particle. Understanding these components clarifies how head is exchanged between elevation, pressure, and velocity in pipelines and open channels.

Given Data / Assumptions:

• Steady, incompressible flow assumption for conceptual explanation.
• Neglecting viscous dissipation and pump/turbine work for the basic statement.

Concept / Approach:
Bernoulli’s equation in head form is z + p/(γ) + V^2/(2g) = constant along a streamline (without losses and shaft work). Terms correspond to elevation (potential) head, pressure head, and velocity (kinetic) head respectively.

Step-by-Step Reasoning:
Potential energy: related to elevation z in a gravitational field.Pressure energy: ability to do work via expansion/compression represented by p/γ for liquids.Kinetic energy: proportional to velocity squared V^2 with coefficient 1/(2g) in head form.All coexist; the relative magnitudes change with geometry and operating conditions.

Verification / Alternative Check:
Practical examples: a nozzle converts pressure energy into kinetic energy; a rising pipe converts kinetic/pressure energy into potential energy. Measurements corroborate the trade-offs predicted by Bernoulli’s principle.

Why Other Options Are Wrong:
Single-energy answers ignore the coupled nature of flow energy.Thermal energy is not a mechanical energy term in Bernoulli’s mechanical energy balance.

Common Pitfalls:

• Confusing pressure energy with static head measurement points.
• Neglecting head losses (friction) in real systems, which reduce the total mechanical energy.

Final Answer:
all of the above (potential, kinetic, and pressure energy)