For steady laminar flow through a circular pipe, the kinetic energy correction factor (α) equals:

Introduction / Context:
The kinetic energy correction factor α accounts for non-uniform velocity profiles when converting average velocity to actual kinetic energy of the flow. It is important in energy equation applications where velocity profiles deviate from uniform, such as laminar pipe flow.

Given Data / Assumptions:

• Circular pipe, fully developed laminar flow.
• Parabolic velocity distribution (Hagen–Poiseuille profile).
• Steady, incompressible flow.

Concept / Approach:
α is defined by KE per unit weight = α * (V̄^2 / (2 g)), where V̄ is mean velocity. For a parabolic profile, kinetic energy is greater than if the same discharge moved uniformly at V̄, hence α > 1. Integration over the circular cross-section yields α = 2 for laminar flow.

Step-by-Step Solution:
Let local velocity u(r) = umax * (1 − (r/R)^2).Compute mean velocity V̄ = (1/A) ∫ u dA = umax/2.Compute ∫ u^3 dA and relate to V̄ to obtain α = (∫ u^3 dA)/(A V̄^3) = 2.

Verification / Alternative check:
For turbulent pipe flow with flatter profiles, α approaches 1.0–1.1. The contrast reinforces that laminar profiles have a larger α due to stronger non-uniformity.

Why Other Options Are Wrong:
0.5, 1.0, 1.5, 2.5: do not match the integrated result for laminar parabolic distribution.

Common Pitfalls:

• Confusing kinetic energy correction factor α with momentum correction factor β (which equals 1.33 for laminar pipe flow).
• Assuming α ≈ 1 for all cases; that is only near-true for turbulent flows.

Final Answer:
2.0