The value of the momentum correction factor for laminar flow through a pipe is 1.33. This factor is used to correct the momentum equation for laminar flow in order to account for the viscous effects in the flow.

1. Definition of the Momentum Correction Factor:
The momentum correction factor is defined as the ratio of the actual momentum flux to the ideal momentum flux. It is denoted by the symbol Φ and is given by the equation:
Φ = (Pactual / Pideal)

2. Explanation of Laminar Flow:
Laminar flow is a type of flow in which the fluid particles move in parallel layers, with little or no mixing between the layers. In laminar flow, the flow velocity profile is parabolic, with the maximum velocity at the center of the pipe and zero velocity at the walls.

3. Importance of Momentum Correction Factor for Laminar Flow:
In laminar flow, the momentum equation is derived based on the assumption of ideal flow, where the flow is considered to be inviscid (no friction) and the velocity profile is fully developed. However, in reality, there are viscous effects present in the flow, which cause a deviation from the ideal flow conditions. The momentum correction factor is used to account for these viscous effects and correct the momentum equation accordingly.

4. Determination of Momentum Correction Factor for Laminar Flow:
The momentum correction factor for laminar flow through a pipe can be determined using experimental or analytical methods. The analytical method involves solving the Navier-Stokes equations for laminar flow and obtaining an expression for the momentum correction factor.

For laminar flow through a smooth pipe, the momentum correction factor is given by the equation:
Φ = 1 + (2/Re)

where Re is the Reynolds number, defined as the ratio of inertial forces to viscous forces in the flow. For laminar flow, the Reynolds number is less than 2000.

5. Calculation of the Momentum Correction Factor:
To calculate the momentum correction factor, we need to know the Reynolds number of the flow. Once the Reynolds number is determined, we can substitute it into the equation Φ = 1 + (2/Re) to obtain the value of the momentum correction factor.

In this case, the correct answer is option B, which states that the momentum correction factor is 1.33. This means that for laminar flow through a pipe, the actual momentum flux is 1.33 times the ideal momentum flux, taking into account the viscous effects in the flow.