The discharge over a broad crested weir is maximum when the depth of flow is (where H is the available head)

In the field of hydraulics and fluid mechanics, a broad-crested weir is employed to manage water flow in open channels. This structure is pivotal for measurement and control purposes. The discharge over such a weir is contingent on the depth of flow, which is referred to as the head over the weir. Various empirical equations govern the relationship between discharge and head.

Among the given options, the correct choice is Option B: $$\frac{{2H}}{3}$$. This signifies that the discharge over a broad-crested weir reaches its maximum when the depth of flow (head) equals two-thirds of the available head (H). This specific proportion maximizes the flow rate of discharge over the weir.

Therefore, the accurate answer is Option B: $$\frac{{2H}}{3}$$.