Introduction:
In this question, we are given the diameter of a circular sewer and we need to determine the desired depth of flow. The correct answer is option C, which states that the desired depth of flow is half of the circular section of the sewer.

Explanation:
To understand why the desired depth of flow is half of the circular section of the sewer, let's consider the properties of a circular section and the concept of hydraulic radius.

1. Circular Section:
A circular section has a diameter, which is the distance across the circle passing through its center. In this question, the diameter of the circular sewer is given as 0.2m.

2. Hydraulic Radius:
The hydraulic radius of a flow section is defined as the ratio of the cross-sectional area of flow to the wetted perimeter of the flow section. It is a measure of the efficiency of flow through a channel or pipe.

For a circular section, the hydraulic radius (Rh) is defined as the ratio of the area (A) to the circumference (C) of the circular section:
Rh = A/C

3. Depth of Flow:
The depth of flow (h) is the vertical distance from the water surface to the bottom of the channel or pipe. In this question, we need to determine the desired depth of flow.

4. Relationship between Depth of Flow and Hydraulic Radius:
In open channel flow, the depth of flow is related to the hydraulic radius by a specific equation called the Manning's equation:

Q = (1/n) * A * Rh^(2/3) * S^(1/2),

where Q is the flow rate, n is the Manning's roughness coefficient, A is the cross-sectional area of flow, Rh is the hydraulic radius, and S is the slope of the energy grade line.

From this equation, we can see that the flow rate is directly proportional to the hydraulic radius raised to the power of 2/3. Therefore, to achieve a desired flow rate, we can manipulate the hydraulic radius by adjusting the depth of flow.

5. Conclusion:
Based on the information given in the question, the desired depth of flow is half of the circular section of the sewer. This means that the depth of flow (h) is equal to half of the diameter of the circular sewer.

Therefore, the correct answer is option C - the desired depth of flow is 1/2 of the circular section of the sewer.