Which form of mechanical energy is not possessed by an independent (unconfined) mass of fluid?

Introduction / Context:
Mechanical energy of a fluid is commonly partitioned into pressure energy, kinetic energy, and potential (elevation) energy. Correctly identifying when each form exists prevents misuse of Bernoulli’s equation and clarifies where work interactions originate.

Given Data / Assumptions:

• Consider a finite “packet” of fluid moving freely in open space (no container walls, no piston).
• External fields like gravity may be present; velocity may be nonzero.
• We distinguish between intrinsic energy stored due to compression at pressure p and the ability to do flow work on boundaries.

Concept / Approach:

Pressure energy (or flow work per unit weight p/γ) is defined via the work needed to push a fluid element into or out of a control volume against a surrounding pressure field—work that occurs at boundaries. An isolated “independent” mass of fluid, with no surrounding confining pressure and no boundary on which to do flow work, does not possess pressure energy in the Bernoulli sense. However, the fluid can still have kinetic energy (1/2 * v^2 per unit mass) if it is moving, and potential energy (g * z per unit mass) in a gravitational field.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Bernoulli along a streamline arises from Euler’s equation and includes p/ρ as “flow work.” Remove boundaries and p/ρ loses mechanical meaning, leaving only v^2/2 and g z terms.

Why Other Options Are Wrong:

Kinetic and potential energies are properties of the state and position/motion; they do not require confinement. “None” and “all” contradict the definitions above.

Common Pitfalls (misconceptions, mistakes):

Assuming “pressure energy” exists even without a boundary; confusing thermodynamic internal energy with mechanical pressure energy used in flow work.

Final Answer:

pressure energy