Fluid Mechanics – Applicability of Bernoulli’s equation along a streamline Bernoulli’s energy equation written along a streamline is strictly valid for which flow condition?

Introduction / Context:
Bernoulli’s equation expresses conservation of mechanical energy per unit weight between two points on the same streamline. It is a cornerstone of ideal fluid flow analysis and provides intuition about how pressure, velocity, and elevation trade off in ducts, jets, and around bodies.

Given Data / Assumptions:

• Equation form: p/(gamma) + V^2/(2g) + z = constant along a streamline.
• Gravity field uniform; body forces limited to weight.
• No pump/turbine shaft work between sections unless explicitly added.

Concept / Approach:

The strict derivation assumes steady flow, negligible viscosity (inviscid or frictionless), incompressible fluid, and flow along a streamline. Under these conditions, mechanical energy is conserved and the sum of pressure head, velocity head, and elevation head remains constant. In real flows with friction, energy grade lines drop due to head losses; in compressible flows with significant density changes, compressible-flow forms must be used; in unsteady flows, local acceleration terms violate the steady assumption.

Step-by-Step Solution:

Verification / Alternative check:

Experimental pressure and velocity measurements in low-Re flows with short, smooth passages often approximate Bernoulli predictions closely, validating applicability under idealized conditions.

Why Other Options Are Wrong:

(a) Compressibility invalidates the simple form; (b) includes friction losses that must be accounted for; (d) unsteady behavior violates steady assumption; (e) strong viscous dissipation contradicts the frictionless premise.

Common Pitfalls:

Applying Bernoulli across streamlines where swirl exists, ignoring pump/turbine work or head losses, and using it in high Mach number flows without compressibility corrections.

Final Answer:

Steady, frictionless, incompressible fluid