Orifice and Vena Contracta — Coefficient of Contraction A jet of water issues from a 40 mm diameter orifice. At the vena contracta, the jet diameter is measured as 32 mm. Compute the coefficient of contraction (Cc) using area ratio.

Introduction:
When fluid discharges through a sharp-edged orifice, the jet contracts to a minimum cross-section called the vena contracta. The coefficient of contraction (Cc) quantifies the ratio between the jet area at vena contracta and the orifice area, reflecting streamline curvature and energy losses.

Given Data / Assumptions:

• Orifice diameter D = 40 mm.
• Vena contracta diameter d = 32 mm.
• Sharp-edged orifice, steady discharge, water at standard conditions.

Concept / Approach:
The contraction coefficient is Cc = A_vc / A_o. Since areas scale with diameter squared, Cc = (d/D)^2 for circular sections.

Step-by-Step Solution:
Compute diameter ratio: d/D = 32/40 = 0.8.Compute area ratio: Cc = (0.8)^2 = 0.64.Hence, the coefficient of contraction is 0.64.

Verification / Alternative check:
Typical Cc for sharp-edged orifices lies around 0.61–0.65. The computed 0.64 is within the expected practical range, supporting the calculation.

Why Other Options Are Wrong:
0.46 and 0.78 or 0.87 do not match the squared ratio (0.8)^2 and are outside typical sharp-edge values.

Common Pitfalls:
Using diameter ratio directly instead of squaring; mixing Cc with coefficient of discharge Cd or velocity coefficient Cv. Remember Cd = Cc * Cv.

Final Answer:
0.64