In a Sutro weir, the discharge is proportional to (where H is head) A. $${{\text{H}}^{\frac{1}{2}}}$$ B. $${{\text{H}}^{\frac{3}{2}}}$$ C. $${{\text{H}}^{\frac{5}{2}}}$$ D. $${\text{H}}$$

The correct answer is: A. $${{\text{H}}^{\frac{1}{2}}}$$

A Sutro weir is a type of overflow weir that is used to measure the flow of water. The discharge of a Sutro weir is proportional to the square root of the head, which is the height of the water above the crest of the weir. This is because the higher the head, the greater the pressure on the water and the faster it will flow over the weir.

Option B is incorrect because the discharge of a Sutro weir is not proportional to the cube root of the head. Option C is incorrect because the discharge of a Sutro weir is not proportional to the fifth root of the head. Option D is incorrect because the discharge of a Sutro weir is not proportional to the head itself.