If H and d are the water depth and drop in the bed level at a Sarda fall, the width B of the trapezoidal crest, is given by A. $${\text{B}} = 0.22\sqrt {{\text{H}} + {\text{d}}} $$ B. $${\text{B}} = 0.33\sqrt {{\text{H}} + {\text{d}}} $$ C. $${\text{B}} = 0.44\sqrt {{\text{H}} + {\text{d}}} $$ D. $${\text{B}} = 0.55\sqrt {{\text{H}} + {\text{d}}} $$

The correct answer is $\boxed{\text{B} = 0.33\sqrt{H + d}}$.

The width of the trapezoidal crest of a Sarda fall is given by the following equation:

$$\text{B} = 0.33\sqrt{H + d}$$

where $H$ is the water depth and $d$ is the drop in the bed level.

The equation is derived from the following considerations:

• The width of the crest must be sufficient to allow the water to flow over the fall without overflowing.
• The width of the crest must be sufficient to provide a stable foundation for the fall.
• The width of the crest must be aesthetically pleasing.

The equation takes into account all of these considerations and provides a width that is both functional and aesthetically pleasing.

The other options are incorrect because they do not take into account all of the considerations that are necessary to determine the width of the crest.