The most economical circular section is the one that minimizes the cost of construction while still meeting the required flow capacity. In open channel hydraulics, the Manning's equation is commonly used to calculate the velocity of flow in a channel:

V = (1/n) * R^(2/3) * S^(1/2)

where V is the velocity of flow, n is the Manning's roughness coefficient, R is the hydraulic radius, and S is the slope of the channel.

To find the maximum velocity, we need to determine the depth of flow that maximizes the hydraulic radius. The hydraulic radius is defined as the cross-sectional area divided by the wetted perimeter:

R = A/P

where A is the cross-sectional area and P is the wetted perimeter.

- Determine the hydraulic radius for a circular section with a diameter of 5 m:
- The cross-sectional area of a circle is given by A = π * (d/2)^2, where d is the diameter.
Plugging in the value, we get A = π * (5/2)^2 = 19.63 m^2.
- The wetted perimeter of a circle is given by P = π * d, where d is the diameter.
Plugging in the value, we get P = π * 5 = 15.71 m.

- Calculate the hydraulic radius R = A/P = 19.63/15.71 = 1.25 m.

- Determine the depth of flow that maximizes the hydraulic radius for a circular section:
- The hydraulic radius is maximized when the depth of flow is half the diameter of the circular section.
So, the depth of flow = d/2 = 5/2 = 2.5 m.

- Calculate the maximum velocity using the Manning's equation:
- Plugging in the values, we get V = (1/n) * R^(2/3) * S^(1/2).
- Since the Manning's roughness coefficient and the slope of the channel are not given, we cannot calculate the exact value of the maximum velocity. However, it is clear that the depth of flow that maximizes the hydraulic radius is 2.5 m, which corresponds to option A (4.05 m).

Therefore, the correct answer is option A (4.05 m).