Using D1 = 0.15 m and D2 = 0.30 m, what is the ratio V2/V1 for a sudden expansion?

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Multiple Choice

Using D1 = 0.15 m and D2 = 0.30 m, what is the ratio V2/V1 for a sudden expansion?

Explanation:
For incompressible flow through a sudden expansion, the flow rate must be the same on both sides, so the continuity equation applies: A1 V1 = A2 V2. Since area scales with the square of the diameter, A ∝ D^2, the ratio of velocities is V2/V1 = (A1/A2) = (D1^2 / D2^2) = (D1/D2)^2. Plugging in D1 = 0.15 m and D2 = 0.30 m gives V2/V1 = (0.15/0.30)^2 = (0.5)^2 = 0.25. Interpretation: Doubling the diameter increases the cross-sectional area by a factor of 4, so the velocity drops to one-fourth.

For incompressible flow through a sudden expansion, the flow rate must be the same on both sides, so the continuity equation applies: A1 V1 = A2 V2. Since area scales with the square of the diameter, A ∝ D^2, the ratio of velocities is V2/V1 = (A1/A2) = (D1^2 / D2^2) = (D1/D2)^2.

Plugging in D1 = 0.15 m and D2 = 0.30 m gives V2/V1 = (0.15/0.30)^2 = (0.5)^2 = 0.25.

Interpretation: Doubling the diameter increases the cross-sectional area by a factor of 4, so the velocity drops to one-fourth.

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