In a sudden expansion, if the upstream diameter doubles, how does the fluid velocity change?

• A. It decreases by a factor of 2
• B. It decreases by a factor of 4
• C. It stays the same
• D. It increases by a factor of 2

Answer: (D)

The main idea here is continuity for incompressible, steady flow: the volumetric flow rate Q must be the same across the expansion, so A1 v1 = A2 v2.

If the upstream diameter doubles, the upstream area A1 becomes four times larger (area scales with the square of the diameter). To keep the same Q, the upstream velocity must drop to one quarter of its original value. In other words, the velocity decreases by a factor of four when the diameter doubles in a sudden expansion. The notion that the velocity would double does not align with the continuity requirement, since increasing the cross-sectional area reduces velocity for the same flow rate.