Which expression correctly gives V2 for a sudden expansion in terms of V1 and the pipe diameters?

• A. V2 = V1 (A1/A2)
• B. V2 = V1 (D2^2 / D1^2)
• C. V2 = V1 (A2/A1)
• D. V2 = V1 (D1/D2)

Answer: (C)

The key idea is the continuity of flow for an incompressible fluid through a sudden expansion. The same volume per unit time must pass through both sections, so the volumetric flow rate before the expansion equals the flow rate after: Q = A1 V1 = A2 V2.

From this, solve for the downstream velocity: V2 = V1 (A1/A2). Since cross-sectional area scales with the square of the diameter (A ∝ D^2), this becomes V2 = V1 (D1^2 / D2^2).

This shows why the velocity decreases in the larger pipe: the same flow rate spread over a bigger area means a smaller velocity. The expression using the inverse ratio (A2/A1) would imply a velocity increase in the larger section, which contradicts the continuity condition for an incompressible flow.