Bernoulli concept – Components of total head/energy per unit weight For a moving liquid particle, the total mechanical energy per unit weight equals which combination of energy terms?

Introduction:
Bernoulli’s equation is fundamentally an energy statement along a streamline for steady, inviscid, incompressible flow with no shaft work or heat transfer. Recognizing the composition of the total head (energy per unit weight) is essential before applying corrections for pumps, turbines, or losses.

Given Data / Assumptions:

• Incompressible, steady flow along a streamline.
• No shaft work, no significant viscous dissipation along the considered segment (idealization).
• Gravity acts as a conservative body force.

Concept / Approach:

The Bernoulli head H_total is the sum of three terms: pressure head p/(ρ * g) (pressure energy per unit weight), velocity head v^2/(2 * g) (kinetic energy per unit weight), and elevation head z (potential energy per unit weight). Thus total energy per unit weight is the sum of pressure, kinetic, and potential contributions.

Step-by-Step Solution:

Verification / Alternative check:

Including pump head adds to H; including loss head subtracts from H, but the basic composition remains the sum of the three ideal heads, confirming the option.

Why Other Options Are Wrong:

Subtractive combinations: Contradict the Bernoulli statement of additive energies.Thermal/chemical/nuclear: Not included in the mechanical energy balance of standard fluid dynamics problems.

Common Pitfalls:

Confusing “per unit mass” with “per unit weight”; the former uses p/ρ and v^2/2 + g * z, while the latter divides by g. The combination of terms is the same.

Final Answer:

pressure energy + kinetic energy + potential energy