In energy accounting for fluid flow, which forms of mechanical energy can a fluid particle possess?

Introduction / Context:
Bernoulli-based energy accounting in fluid mechanics tracks mechanical energy per unit weight as the sum of pressure head, velocity head, and elevation head. Recognizing these terms is fundamental to applying the energy equation correctly to pipes, open channels, pumps, and turbines.

Given Data / Assumptions:

• Incompressible, steady flow with negligible shaft work across a short reach.
• Mechanical (not thermal) energy forms are of interest.
• Friction/head losses may be present but are accounted as separate loss terms.

Concept / Approach:
The mechanical energy per unit weight is expressed as p/(gamma) + V^2/(2 g) + z (pressure head + velocity head + elevation head). These correspond to pressure energy, kinetic energy, and potential (elevation) energy respectively. There is no concept of an “initial energy” in the Bernoulli statement; internal energy belongs to thermal accounting and is not a mechanical head term for incompressible flows.

Step-by-Step Solution:
Identify mechanical energy heads: pressure head p/gamma, velocity head V^2/(2 g), and elevation head z.Relate heads to energy per unit weight to build Bernoulli’s equation.Exclude undefined or non-mechanical terms from the head balance.

Verification / Alternative check:
Any standard derivation of Bernoulli’s equation shows only the three heads above; additional “initial” energy terms do not appear in mechanical energy balance.

Why Other Options Are Wrong:
Elevation only / kinetic+elevation only: incomplete; they omit pressure energy.“Initial energy”: not a defined mechanical energy form in fluid mechanics.Internal energy only: relevant to thermodynamics, not Bernoulli’s mechanical energy heads.

Common Pitfalls:

• Calling pressure head “potential energy” without distinguishing elevation head.
• Mixing internal energy and temperature effects into the Bernoulli equation for incompressible flow.

Final Answer:
Pressure, elevation, and kinetic energy