Bernoulli head components According to Bernoulli’s principle for steady incompressible flow along a streamline, the total head of a fluid particle equals the sum of which components?

Introduction / Context:Bernoulli’s equation is foundational in fluid mechanics for relating pressure, velocity, and elevation along a streamline in steady, inviscid, incompressible flow. It states that the total mechanical energy per unit weight (total head) remains constant, barring losses or addition of energy.

Given Data / Assumptions:

• Steady flow along a streamline.
• Incompressible fluid with negligible viscosity (idealization).
• No shaft work, pumps, or turbines between the two points considered.

Concept / Approach:The total head H is written as H = z + p/(ρ g) + V^2/(2 g), where z is potential (elevation) head, p/(ρ g) is pressure head, and V^2/(2 g) is velocity (kinetic) head. These components sum to a constant in an ideal flow without losses.

Step-by-Step Solution:

Verification / Alternative check:Units check: each term has units of length (metres of fluid), confirming all are “heads.” Including losses would add h_f on the right-hand side to balance real systems.

Why Other Options Are Wrong:

• Pairs of two heads omit one essential component of Bernoulli.
• “Turbulence head” is not a standard Bernoulli term; turbulence contributes to losses, not an ideal head component.

Common Pitfalls:Confusing pressure head with pressure; forgetting to divide by ρ g; mixing energy per unit mass with energy per unit weight; ignoring head losses in real pipelines.

Final Answer:Potential head, kinetic head, and pressure head