Kinetic energy correction factor (α) for different regimes Which of the following statements regarding the kinetic energy correction factor α in internal flow are true?

Introduction / Context:
The kinetic energy correction factor α accounts for non-uniform velocity profiles when converting average velocity into kinetic energy per unit weight in the energy equation. It multiplies V^2/(2g) to correct for profile shape.

Given Data / Assumptions:

• Fully developed flow in circular pipes for the canonical values.
• Definition: α = (1/A ∫ v^3 dA) / (V^3), where V is area-mean velocity.

Concept / Approach:
In laminar pipe flow, the parabolic profile makes α exactly 2. In turbulent flow, the flatter profile makes α close to 1; typical measured values lie near 1.03–1.06, and engineers often take α = 1 for simplicity unless very high accuracy is required.

Step-by-Step Solution:

Verification / Alternative check:
Energy equation with correction: z + p/(rho g) + α V^2/(2g) + h_pump − h_loss = const; choice of α is standard in textbooks.

Why Other Options Are Wrong:

• Each individual statement (a), (b), (c) is correct; hence “all the above” is the best choice.

Common Pitfalls:
Confusing momentum correction factor β with α; using α = 2 in turbulent cases or α = 1 in laminar cases.

Final Answer:
all the above