Difficulty: Easy
Correct Answer: Head H is less than five times the orifice diameter d (H < 5d).
Explanation:
Introduction / Context:
Orifices are categorized as “small” or “large” depending on the head of liquid relative to the orifice size. This classification determines whether the velocity can be assumed uniform across the opening and which analytical approach to use in discharge calculations.
Given Data / Assumptions:
Concept / Approach:
For a small orifice, the head is large compared with the orifice size, so the variation of velocity of approach across the opening is negligible and the jet is assumed to have nearly uniform velocity. The conventional rule of thumb is that an orifice is “small” when H ≥ 5d. Conversely, it is considered “large” when the head is not sufficiently greater than the orifice size—often expressed as H < 5d—so velocity and pressure vary appreciably over the opening and more detailed analysis (e.g., subdividing the opening) is required.
Step-by-Step Solution:
Verification / Alternative check:
Handbooks and standard hydraulics texts adopt the 5d criterion, sometimes with minor variations depending on orifice shape; the engineering implication remains the same.
Why Other Options Are Wrong:
(b) H > 10d defines a very “small” orifice regime. (c) An equality threshold is not the classification rule by itself. (d) Head dependence is central to the definition. (e) H < d is too restrictive; many large orifices operate with H between d and 5d.
Common Pitfalls:
Assuming a single discharge coefficient works for all heads; ignoring that non-uniform velocity distribution increases with larger relative orifice size.
Final Answer:
Head H is less than five times the orifice diameter d (H < 5d).
Discussion & Comments