Classification of orifices by head–size ratio:\nAn orifice is termed “large” when which condition on head and orifice height (or diameter) is satisfied?

Introduction / Context:
Small and large orifices are distinguished not merely by physical size but by the ratio of available head to the characteristic dimension of the opening. This classification determines whether the velocity distribution changes appreciably between the top and bottom of the orifice and whether simple small-orifice formulas remain valid.

Given Data / Assumptions:

• Head H measured from the upstream free surface to the orifice center (or top).
• Characteristic orifice height or diameter a.
• Steady flow under gravity.

Concept / Approach:
A “small” orifice assumes nearly uniform head across the opening, typically valid when H ≥ 5a (some texts use 5 times the orifice depth). When H is not sufficiently large (H < 5a), head varies across the orifice and the discharge must be obtained by integrating element-wise; such an opening is classified as a “large” orifice. The rule-of-thumb threshold of 5 separates these regimes for standard practice and MCQ conventions.

Step-by-Step Solution:

Verification / Alternative check:
Deriving discharge by integrating over the orifice depth shows velocity v(y) = sqrt(2g(H − y)) varies from top to bottom; this variation is negligible only when H ≫ a, underpinning the 5-times guideline.

Why Other Options Are Wrong:

• Physical “size is large” or “velocity is large”: Vague and not the accepted criterion.
• Head more than 5 times: That defines a small orifice, not a large one.

Common Pitfalls:
Using small-orifice coefficients for large-orifice conditions; defining a using radius instead of height/diameter inconsistently; forgetting elevation head variation across the opening.

Final Answer:
the available head of liquid is less than 5 times the height of orifice