Discharge coefficients – relation among Cv, Cc, and Cd For a sharp-edged orifice/mouthpiece, the coefficient of discharge (Cd) is __________ the coefficient of velocity (Cv):

Introduction:
Practical orifice flow accounts for contraction and losses via three coefficients: coefficient of velocity (Cv), coefficient of contraction (Cc), and coefficient of discharge (Cd). This question asks about their ordering.

Given Data / Assumptions:

• Sharp-edged orifice with a vena contracta.
• Steady incompressible flow.
• Losses and contraction are not negligible.

Concept / Approach:
Definitions: Cv = V_actual / V_ideal, Cc = A_jet / A_orifice, and Cd = Q_actual / Q_ideal. Since Q = A_jet * V_actual and Q_ideal = A_orifice * V_ideal, it follows that Cd = Cc * Cv. Because 0 < Cc < 1 for a contracting jet, Cd is necessarily less than Cv.

Step-by-Step Solution:
1) Write Cd = Q_actual / Q_ideal.2) Substitute Q expressions to get Cd = (A_jet/A_orifice) * (V_actual/V_ideal) = Cc * Cv.3) Since Cc < 1, Cd < Cv.

Verification / Alternative check:
Typical values for sharp edges: Cc ~ 0.62, Cv ~ 0.97, hence Cd ~ 0.62 * 0.97 ≈ 0.60, confirming Cd < Cv.

Why Other Options Are Wrong:

• Same as / more than: contradicts Cd = Cc * Cv with Cc < 1.
• Indeterminate: the inequality follows directly from definitions.

Common Pitfalls:
Confusing Cd with Cv or ignoring the contraction effect that reduces effective area.

Final Answer:
less than