Select the most familiar Bernoulli energy equation form used along a streamline for steady, incompressible, inviscid flow.

Introduction / Context:
Bernoulli’s equation is the energy conservation statement for steady, inviscid, incompressible flow along a streamline. It relates pressure head, velocity head, and elevation head, and is ubiquitous in hydraulics and aerodynamics.

• Steady flow.
• Incompressible, homogeneous fluid.
• Negligible viscous dissipation (inviscid).
• Evaluation along a streamline.

Concept / Approach:

The “familiar” head form sums three terms: pressure head p/γ (where γ = ρ * g), velocity head v^2/(2g), and elevation head z. Their sum equals a constant along a streamline in the absence of pumps, turbines, or losses. Extensions add pump/turbine heads and losses as needed.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Dimensional analysis confirms each term has dimensions of length (head). Laboratory ventures (Venturi, Pitot) rely on this relation.

Why Other Options Are Wrong:

Option (b) is the differential Euler form; (c) mixes per-unit-mass constants with raw terms; (d) and (e) omit key terms, valid only under very restrictive conditions.

Common Pitfalls (misconceptions, mistakes):

Applying Bernoulli across devices with energy addition/removal without correction; using it across widely separated streamlines in rotational flows.

Final Answer:

p/γ + v^2/(2g) + z = constant