ANS:C -
The ratio of depths at partial flow with a central angle α and at full flow of a sewer can be determined using hydraulic principles, specifically the concept of flow depth in open channels.
For a sewer pipe, the depth of flow depends on factors such as the diameter of the pipe, the flow rate, and the slope of the pipe. At partial flow with a central angle α, the flow depth will be less than the flow depth at full flow.
Let's denote:
- dpartial: Depth of flow at partial flow with central angle α
- Dfull: Depth of flow at full flow
The ratio of depths at partial flow with central angle α and at full flow can be expressed as:
dfull/dpartial
This ratio depends on the specific conditions of the sewer system, such as the shape and dimensions of the sewer pipe, the flow rate, and the hydraulic gradient. It can be determined using hydraulic calculations or empirical relationships based on experimental data.
Without additional information or specific conditions provided, it's challenging to provide a precise expression for this ratio. The ratio may vary depending on the characteristics of the sewer system and the flow regime (e.g., subcritical, supercritical). Typically, engineers use hydraulic equations or software tools to calculate flow depths for given flow rates and conditions.
If you have specific information about the sewer system, such as the diameter of the pipe, the flow rate, and the angle α, I can help you calculate the ratio of depths. Otherwise, a general expression cannot be provided without more details.
