Core assumptions behind Bernoulli’s equation (inviscid, steady, along a streamline) Which set of statements best reflects the assumptions under which Bernoulli’s equation applies?

Introduction / Context:Bernoulli’s equation is derived from the mechanical energy balance for steady, incompressible, inviscid flow along a streamline with no pumps/turbines and only gravity as a body force. Recognizing its assumptions prevents misuse in diffusers, across valves, or in highly viscous flows.

Given Data / Assumptions:

• Steady flow (no local acceleration).
• Incompressible fluid of constant density.
• Negligible viscosity (inviscid), hence no dissipation between sections.
• Body force is gravity only; no shaft work added or removed.
• Uniform section-wise velocity is an engineering approximation used when applying average velocity with a kinetic energy correction factor near 1.

Concept / Approach:

Bernoulli states p/γ + v^2/(2 g) + z = constant along a streamline for the above conditions. In practice, a kinetic energy correction factor may be used if velocity is non-uniform; the “uniform velocity” statement reflects that simplified use without correction factors.

Step-by-Step Solution:

Verification / Alternative check:

Compare with the full energy equation including head loss and pump/turbine head; Bernoulli is the special case with h_L = 0 and h_pump = h_turbine = 0.

Why Other Options Are Wrong:

Options (a), (b), and (c) individually are partial statements; the correct comprehensive assumption set is captured by “All of the above”.

Common Pitfalls:

Applying Bernoulli across components with significant losses or work exchange; ignoring the need for correction factors when velocity is highly non-uniform.

Final Answer:

All of the above