Momentum correction factor β for fully developed laminar flow in a circular pipe In internal laminar (parabolic) flow of a Newtonian fluid through a round pipe, what is the appropriate value of the momentum correction factor β?

Introduction / Context:The momentum correction factor β accounts for the non-uniform velocity profile when converting between average-velocity-based momentum flux and the actual momentum flux. It is essential in accurate force and thrust computations for ducts and nozzles.

Given Data / Assumptions:

• Newtonian fluid, steady, incompressible, fully developed laminar flow in a circular pipe.
• Parabolic velocity distribution, no slip at the wall.

Concept / Approach:

Definition: β = (∫_A ρ u^2 dA) / (ρ A u_avg^2). For a parabolic profile u(r) = u_max * (1 − (r/R)^2), the integrals can be evaluated analytically to obtain a constant β for laminar flow in a circular pipe.

Step-by-Step Solution:

Verification / Alternative check:

Known standard results: energy correction factor α = 2 (laminar pipe), momentum correction factor β = 4/3. For turbulent flow, both factors are closer to 1 due to flatter profiles.

Why Other Options Are Wrong:

1/2, 2/3, 3/4, 3/2 do not match the parabolic-profile integration result for laminar pipe flow.

Common Pitfalls:

Confusing α (energy correction) with β (momentum correction), or using turbulent values (near 1) for laminar cases.

Final Answer:

4/3