The correct answer is: A. d = 0.2 B
The discharge of a drain is the volume of water that flows through it per unit time. It is measured in cubic meters per second (cumecs). The depth of a drain is the vertical distance from the top of the drain to the bottom. The width of a drain is the horizontal distance from one side of the drain to the other.
The discharge of a drain is related to its depth and width by the following equation:
$Q = \frac{1}{2} B d^2$
where:
- $Q$ is the discharge of the drain (in cumecs)
- $B$ is the width of the drain (in meters)
- $d$ is the depth of the drain (in meters)
For a drain with a discharge of 15 cumecs, the depth and width are related by the following equation:
$15 = \frac{1}{2} B d^2$
$30 = B d^2$
$d = \sqrt{\frac{30}{B}}$
If $B = 0.2$ meters, then $d = \sqrt{\frac{30}{0.2}} = 3.5$ meters.
If $B = 0.5$ meters, then $d = \sqrt{\frac{30}{0.5}} = 6$ meters.
Therefore, the correct answer is: A. d = 0.2 B.