Statement on coefficient of discharge (Cd) and actual discharge through an orifice: If the value of Cd increases, the discharge through the orifice decreases. State whether this statement is true or false.

Introduction / Context:Discharge through a sharp-edged orifice (or nozzle) under a constant head is often estimated using the empirical relation Q = Cd * A * sqrt(2 * g * H). This question checks conceptual understanding of how the coefficient of discharge Cd influences the actual discharge Q when all other quantities remain the same.

Given Data / Assumptions:

• Steady flow through an orifice under head H.
• Orifice area A is constant.
• Acceleration due to gravity g is constant.
• Coefficient of discharge Cd lumps together contraction and velocity effects (Cd = Cc * Cv).

Concept / Approach:The discharge formula for an orifice is Q = Cd * A * sqrt(2 * g * H). For fixed A, g, and H, Q is directly proportional to Cd. Therefore, if Cd increases, Q must increase proportionally. The given statement says the opposite and is therefore incorrect.

Step-by-Step Solution:

Verification / Alternative check:Consider two orifices of the same size under the same head, one with Cd1 = 0.60 and another with Cd2 = 0.65. The second orifice yields Q2/Q1 = Cd2/Cd1 = 0.65/0.60 ≈ 1.083, that is, roughly 8.3% more discharge, confirming the direct proportionality.

Why Other Options Are Wrong:

• True: Contradicts Q ∝ Cd.
• Depends on head only: Discharge depends on both head and Cd (and area).
• Cannot be determined: It can be determined from the standard formula.

Common Pitfalls:Confusing Cd with velocity coefficient only; ignoring the role of contraction; assuming Q depends only on H; forgetting that Cd accounts for real flow losses and thus scales the ideal discharge to the actual value.

Final Answer:False