Applicability of the basic small-orifice discharge formula For a sharp-edged rectangular orifice with constant head H across the opening, the commonly used discharge formula Q = C_d * A * sqrt(2 g H) is applicable to:

Introduction / Context:The basic orifice formula Q = C_d * A * sqrt(2 g H) is ubiquitous in hydraulics. However, its straightforward use assumes a uniform head H over the entire opening—an assumption violated in large orifices where head varies significantly with depth.

Given Data / Assumptions:

• Sharp-edged orifice discharging freely to the atmosphere.
• Coefficient of discharge C_d accounts for contraction and losses.
• “Small orifice” implies that H is essentially constant from top to bottom of the opening.

Concept / Approach:Derivation assumes uniform energy head at the orifice plane, allowing V = sqrt(2 g H) to multiply a constant area A. For a large orifice, hydrostatic pressure (hence local velocity) varies with depth, so the discharge must be integrated: dQ = C_d * b * √(2 g y) dy across the vertical extent, not merely A * √(2 g H).

Step-by-Step Explanation:

Verification / Alternative check:Compare computed Q using the simple formula vs. integrated expression for large vertical extents; discrepancies confirm the need for integration.

Why Other Options Are Wrong:“Large orifices only” and “small and large orifices only” ignore head variation. “All types” is overgeneralization. Venturimeters are different devices using differential pressure over a throat—not orifices per se.

Common Pitfalls:Using the small-orifice formula on sluice openings or gates with large vertical extent; neglecting submergence corrections.

Final Answer:small orifices only