A 12-inch pipe carrying 1200 GPM feeds into a 6-inch pipe. If the velocity in the 12-inch pipe is 3.4 ft/s, what is the velocity in the 6-inch pipe?

• A. 13.6
• B. 6.8
• C. 27.2
• D. 3.4

Answer: (A)

Flow rate must stay the same as water moves from one pipe to another, so Q = A V is constant. The cross-sectional area scales with the square of the diameter, so the area ratio from the 12-in pipe to the 6-in pipe is (12/6)^2 = 4. With the 12-in pipe velocity at 3.4 ft/s, the velocity in the 6-in pipe increases by the same factor: 3.4 × 4 = 13.6 ft/s. A quick check using Q = A V confirms this: A1 ≈ 0.785 ft^2, Q ≈ 0.785 × 3.4 ≈ 2.67 ft^3/s; A2 ≈ 0.196 ft^2, V2 ≈ 2.67 / 0.196 ≈ 13.6 ft/s.