ANS:D - All of the above.

Sewer pipes are designed with a maximum discharge with 25% to 33% vacant cross-sectional area for all of the above reasons:

1. Unexpected large-scale infiltration of stream water: During heavy rainfall or flooding events, there can be significant infiltration of stormwater into sewer systems. Designing sewer pipes with a vacant cross-sectional area allows for accommodating these sudden surges in flow without causing overflow or backups.
2. Unexpected increase in population: As populations grow or urban areas expand, there may be an increase in wastewater generation. Designing sewer pipes with extra capacity ensures that the system can handle higher flows resulting from population growth without becoming overloaded.
3. Underestimates of maximum and average flows: Designing sewer systems involves estimating the maximum and average flows based on various factors such as population density, land use, and rainfall patterns. However, these estimates may sometimes be underestimated. By providing extra capacity in sewer pipes, the system can accommodate higher-than-anticipated flows without experiencing operational issues.

Incorporating a vacant cross-sectional area in sewer pipe design provides flexibility and resilience to the system, allowing it to effectively manage varying flow conditions and unexpected events while maintaining performance and preventing overflows. Therefore, all of the mentioned reasons contribute to the inclusion of vacant cross-sectional area in sewer pipe design.