The flow velocity in a 6-in diameter pipe is twice that in a 12-in diameter pipe if both are carrying 50 gal/min of wastewater.

The flow velocity in a 6-in diameter pipe is twice that in a 12-in diameter pipe if both are carrying 50 gal/min of wastewater.

• A. TRUE
• B. CANNOT BE DETERMINED
• C. NOT APPLICABLE
• D. FALSE

Answer: (D)

Flow rate through a pipe is the product of cross-sectional area and velocity (Q = vA). With the same flow rate in both pipes, the velocity is inversely proportional to the area. A circle’s area is A = πD^2/4, so the 6-in pipe has A6 = 9π in^2 and the 12-in pipe has A12 = 36π in^2. The velocity in each is v = Q/A, so the ratio v6/v12 = A12/A6 = (36π)/(9π) = 4. This means the 6-in pipe’s velocity is four times that of the 12-in pipe, not twice.

Flow rate through a pipe is the product of cross-sectional area and velocity (Q = vA). With the same flow rate in both pipes, the velocity is inversely proportional to the area. A circle’s area is A = πD^2/4, so the 6-in pipe has A6 = 9π in^2 and the 12-in pipe has A12 = 36π in^2. The velocity in each is v = Q/A, so the ratio v6/v12 = A12/A6 = (36π)/(9π) = 4. This means the 6-in pipe’s velocity is four times that of the 12-in pipe, not twice.