A pipe of diameter d1 suddenly contracts to diameter d2 at section B, and the downstream diameter d2 continues over BC. Assuming coefficient of contraction Cc = 0.62, the head loss due to sudden contraction is:

Introduction:
Sudden contraction losses occur when flow passes abruptly from a larger pipe to a smaller one. The vena contracta forms downstream of the contraction, producing an energy loss modeled with the coefficient of contraction Cc.

Given Data / Assumptions:

• Upstream diameter = d1, downstream diameter = d2.
• Coefficient of contraction Cc = 0.62.
• v2 is the mean velocity in the smaller pipe of diameter d2.
• Steady incompressible flow; elevation change across the fitting is negligible.

Concept / Approach:
The empirical head-loss relation for sudden contraction is h_c = ( (1/Cc) - 1 )^2 * (v2^2) / (2g). This comes from the dissipation associated with the jet contracting to the vena contracta and then expanding to fill the smaller pipe.

Step-by-Step Solution:
1) Use h_c = ( (1/Cc) - 1 )^2 * (v2^2) / (2g).2) Substitute Cc = 0.62: (1/0.62) ≈ 1.612903.3) Compute (1.612903 - 1) = 0.612903.4) Square: 0.612903^2 ≈ 0.3756 ≈ 0.376.5) Therefore h_c ≈ 0.376 * (v2^2) / (2g).

Verification / Alternative check:
Textbook correlations consistently use the (1/Cc - 1)^2 factor for contraction loss. With Cc between 0.60 and 0.65, the coefficient typically falls near 0.35–0.45, matching our 0.376 estimate.

Why Other Options Are Wrong:

• 0.62 * (v2^2)/(2g): Cc multiplies the velocity at the vena contracta, not the loss directly.
• (1 - 0.62)^2 * (v2^2)/(2g): Uses 1 - Cc instead of (1/Cc - 1), which is not the contraction-loss formula.
• (v1^2)/(2g): Ignores the contraction physics and the role of Cc and v2.

Common Pitfalls:

• Using v1 instead of v2 in the loss expression.
• Confusing sudden contraction with sudden expansion; expansion loss uses a different relation with a different reference area.

Final Answer:
0.376 * (v2^2) / (2g)