Step 1: Assess each statement concerning spillways.
- Statement A: Sediment accumulation at the exit of a chute spillway would induce a backwater effect, diminishing the effective head and consequently reducing discharge capacity. This statement is correct.
- Statement B: The discharge capacity of a pipe spillway, analogous to flow within a pipe, scales with the head raised to the power of 1/2 (\( Q \propto \sqrt{H} \)), not the cube root. This statement is incorrect.
- Statement C: This statement is imprecisely formulated. "Longitudinal spills" is not a recognized term. It may refer to guide walls or vanes within a spillway designed to channel and align the flow, thereby minimizing turbulence. Under this interpretation, the statement is correct.
- Statement D: Drop inlet spillways are typically employed for minor dams and erosion control structures with limited elevation differences. A drop of approximately 3 meters (around 10 feet) represents a common upper limit for their efficient and economical application. This statement is correct.
Step 2: Re-evaluate judgments based on established principles.
There appears to be ambiguity in the question and potential inaccuracies within the provided statements. Let us re-examine. Statement A is unequivocally correct. Statement B is unequivocally incorrect. Statements C and D are generally considered valid in practical design. If a selection must be made from the options, we need to identify a combination of true statements. Given that B is false, options including A, B, and C are invalid. This leaves D as the sole remaining possibility, suggesting that A is deemed false for an unstated reason, while C and D are considered true. Let us reconsider A. It is possible that downstream sedimentation does not invariably impact capacity if the flow is supercritical. This scenario presents complexity. However, C and D represent robust, generally accepted design principles. We will proceed under the assumption that C and D are the intended correct statements.