Water is flowing through a pipe with a constriction. The diameter of the narrow section is one-half the diameter of the wide section. If the velocity of the incompressible fluid is 3.20 m/s in the wide section, then what is the velocity of the fluid in the narrow section?
A) 16.5 m/s
B) 18.7 m/s
C) 19.8 m/s
D) 10.5 m/s
E) 12.8 m/s

Question

Quizplus · Accepted Answer

The velocity of the fluid in the narrow section can be found using the principle of continuity, which states that the product of the cross-sectional area and the velocity of the fluid must be constant throughout the pipe. Since the diameter of the narrow section is half that of the wide section, its area is one-fourth (since area is proportional to the square of the diameter). To conserve the flow rate, the velocity in the narrow section must be four times the velocity in the wide section, thus 4 * 3.20 m/s = 12.8 m/s.

Water Is Flowing Through a Pipe with a Constriction