Orifice coefficients – variation of Cv with head for a sharp-edged orifice How does the coefficient of velocity (Cv) of a sharp-edged orifice typically vary as the head of water (H) increases within normal operating ranges?

Introduction:
Performance coefficients for orifices—coefficient of contraction Cc, coefficient of velocity Cv, and coefficient of discharge Cd—depend modestly on head. Understanding the trend helps in selecting appropriate Cd for design and in interpreting laboratory results.

Given Data / Assumptions:

• Sharp-edged orifice discharging freely.
• Head H varied within a practical range where flow remains stable and non-cavitating.
• Fluid is water; temperature effects small.

Concept / Approach:

Cv represents the ratio of actual jet speed to ideal speed sqrt(2 * g * H). As H increases, entrance effects and relative influence of viscous losses diminish slightly; the jet accelerates more nearly ideally, so Cv tends to increase and approach a value near unity (often 0.97–0.99). The change is not dramatic but is monotonic over ordinary laboratory ranges, whereas Cc remains about 0.62 for sharp edges and Cd ≈ Cc * Cv rises slightly due to Cv's increase.

Step-by-Step Solution:

Verification / Alternative check:

Textbook datasets typically report Cv ≈ 0.95 at low heads rising toward ≈ 0.98–0.99 at higher heads for sharp-edged plates, confirming the trend.

Why Other Options Are Wrong:

Decreases / constant at 1.0 / random: Do not match experimental behavior.Non-monotonic strong decrease: Not supported under normal conditions.

Common Pitfalls:

Assuming Cd changes dramatically with head; Cv’s increase is modest, and Cc remains roughly constant for sharp edges.

Final Answer:

increases