Introduction:
When the velocity is zero over half of the cross-sectional area and is uniform over the remaining half, it is important to determine the momentum correction factor. The momentum correction factor is a coefficient that is used to correct the momentum equation in order to account for the non-uniform velocity distribution in the flow.

Explanation:
The momentum correction factor is denoted by the symbol "Cm" and is defined as the ratio of the actual momentum flux to the momentum flux that would be calculated using the average velocity. It takes into account the non-uniform velocity distribution across the cross-section and provides a correction factor to the momentum equation.

Calculation:
To calculate the momentum correction factor, we need to determine the velocity distribution across the cross-sectional area. In this case, the velocity is zero over half of the cross-sectional area and is uniform over the remaining half.

1. Divide the cross-sectional area into two halves: one with zero velocity and the other with uniform velocity.
2. Calculate the average velocity by considering the velocity distribution across the entire cross-sectional area.
3. Calculate the momentum flux using the average velocity.
4. Calculate the actual momentum flux by integrating the velocity distribution across the cross-sectional area.
5. Divide the actual momentum flux by the momentum flux calculated using the average velocity to obtain the momentum correction factor.

Conclusion:
In conclusion, the momentum correction factor is a coefficient that is used to correct the momentum equation when the velocity distribution is non-uniform across the cross-sectional area. In the given scenario where the velocity is zero over half of the cross-sectional area and uniform over the remaining half, the momentum correction factor can be calculated by comparing the actual momentum flux to the momentum flux calculated using the average velocity. This correction factor helps in accurately determining the momentum in the flow and is important in various engineering applications.