Total head of a moving liquid particle (Bernoulli form):\nThe total head equals the sum of which components?

Introduction / Context:
Bernoulli’s equation expresses energy conservation along a streamline for steady, incompressible, inviscid flow with negligible shaft work and heat exchange. In “head” form (energy per unit weight), the total head is the sum of elevation, pressure, and velocity heads. Recognizing these components is fundamental for pump sizing, flow measurement, and piping calculations.

Given Data / Assumptions:

• Steady, incompressible flow.
• No shaft work or heat transfer across the streamline section considered.
• Negligible viscous losses between the two points (or accounted separately as head loss).

Concept / Approach:
Total head H_t is H_t = z + p/(ρ g) + v^2/(2 g). Here, z is potential (elevation) head, p/(ρ g) is pressure head, and v^2/(2 g) is kinetic (velocity) head. In real systems, an additional loss term h_f is subtracted when moving from one section to another to account for friction and fittings.

Step-by-Step Solution:

Verification / Alternative check:
Piezometric head is z + p/(ρg); adding kinetic head gives total head. Pitot measurements recover total (stagnation) pressure related to total head via p_t/(ρg) = z_ref difference + v^2/(2g) when referenced appropriately.

Why Other Options Are Wrong:

• Subtractive forms contradict energy conservation statement in the absence of loss/work terms.

Common Pitfalls:
Confusing piezometric vs total head; forgetting to include elevation in sloped piping; misapplying head loss signs.

Final Answer:
pressure head + kinetic head + potential head