Applicability of the energy (Bernoulli) equation in fluid mechanics The standard energy equation between two sections is primarily applicable under which flow condition?

Introduction / Context:
Bernoulli’s (energy) equation is a cornerstone of fluid mechanics used to relate pressure, velocity, and elevation between two sections in a streamline flow, with appropriate loss terms. Understanding when and how it applies is essential for correct engineering use.

Given Data / Assumptions:

• Incompressible fluid.
• Single-phase flow without significant shaft work between sections.
• Flow along a streamline or averaged over a section with correction factors.
• Steady conditions for the simplest form of the equation.

Concept / Approach:

The classical form assumes steady flow so that energy per unit weight at a section is time-invariant. With unsteadiness, additional unsteady terms appear. The equation does not depend on laminar vs. turbulent per se; turbulence is handled by head-loss terms and kinetic energy correction factors, provided the flow is statistically steady.

Step-by-Step Solution:

Verification / Alternative check:

In unsteady flow, the energy equation includes local acceleration terms; for steady flow, these vanish, matching the standard textbook form.

Why Other Options Are Wrong:

(a) Non-uniformity in space is allowed; the equation is routinely applied in gradually varied flow with loss terms. (b) and (c) do not decide applicability; both regimes can be handled if the flow is steady and losses are modeled.

Common Pitfalls:

Ignoring head losses; assuming α = 1 when profiles are highly non-uniform; applying the equation across rotating machinery without including shaft work terms.

Final Answer:

steady flow.