$${\frac{3}{4}^{{\text{th}}}}$$ or $${\frac{1}{4}^{{\text{th}}}}$$ extra space is left in sewer pipes at maximum discharge for A. Low estimates of the average and maximum flows B. Large scale infiltration of storm water C. Unexpected increase in population D. All the above

The correct answer is $\boxed{\text{D}}$.

Sewer pipes are designed to carry a certain amount of wastewater. However, there are a number of factors that can cause the actual flow to be higher than the design flow. These factors include:

• Low estimates of the average and maximum flows. When sewer pipes are designed, the engineers must estimate the average and maximum flows that the pipes will need to carry. If these estimates are too low, the pipes may not be able to handle the actual flow, and sewage may back up into homes and businesses.
• Large scale infiltration of storm water. Storm water is rainwater that runs off of streets and other surfaces. If this storm water enters the sewer system, it can increase the flow of wastewater in the pipes.
• Unexpected increase in population. If the population of a city increases, the amount of wastewater that needs to be treated also increases. If the sewer system is not designed to handle this increase in flow, sewage may back up into homes and businesses.

To account for these factors, sewer pipes are designed with a certain amount of extra space. This extra space is called the “freeboard.” The freeboard is typically equal to one-fourth of the pipe diameter. This means that if a sewer pipe has a diameter of 12 inches, the freeboard will be 3 inches.

The freeboard allows for the following:

• Low estimates of the average and maximum flows. If the actual flow is higher than the design flow, the freeboard will allow the wastewater to flow through the pipe without backing up.
• Large scale infiltration of storm water. If storm water enters the sewer system, the freeboard will allow the wastewater to flow through the pipe without backing up.
• Unexpected increase in population. If the population of a city increases, the amount of wastewater that needs to be treated also increases. The freeboard will allow the sewer system to handle this increase in flow without backing up.

In conclusion, sewer pipes are designed with a certain amount of extra space to account for low estimates of the average and maximum flows, large scale infiltration of storm water, and unexpected increase in population. This extra space is called the “freeboard.” The freeboard is typically equal to one-fourth of the pipe diameter.