The 'momentum correction factor' for a laminar flow through a circular pipe is: 

Explanation:

Momentum correction factor:

The momentum correction factor is defined as the ratio of momentum of the flow per second based on actual velocity to the momentum of the flow per second based on average velocity across a section.

 \(\beta = \;\frac{{Momentum\;per\;second\;based\;on\;actual\;velocity}}{{Momentum\;per\;second\;based\;on\;average\;velocity}}\)

 \(\beta = \frac{1}{{A{V^2}}}\smallint {u^2}.dA\)

For laminar flow through a circular pipe, β = 4/3 = 1.33

Additional Information 

Kinetic energy correction factor(α): 

• It is defined as the ratio of kinetic energy/second based on actual velocity to the kinetic energy/second based on average velocity.
• \(α = \frac{1}{A}\mathop \smallint \limits_A^{} {\left( {\frac{u}{V}} \right)^3}dA\)
• where A = area, V= average velocity, u= local velocity at distance r.
• For laminar flow in a circular pipe α = 2