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?
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AFor turbulent flow, α typically lies between 1.03 and 1.06.
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BFor laminar flow in a circular pipe, α = 2.
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CIn practice for many turbulent flows, α is often taken as 1.0.
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Dall the above
Answer
Correct Answer: all the above
Explanation
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:
Laminar: compute α from parabolic profile → α = 2.Turbulent: flatter profile → α slightly above 1 (≈ 1.03–1.06).Engineering practice often sets α = 1 for turbulent calculations.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