Water flowing through a cylindrical pipe suddenly comes to a section of pipe where the diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was 32m/s, what is its speed in this smaller section if the water behaves like an ideal incompressible fluid?
A) 43 m/s
B) 28 m/s
C) 37 m/s
D) 24 m/s

Question

Water flowing through a cylindrical pipe suddenly comes to a section of pipe where the diameter decreases to  86%  of its previous value. If the speed of the water in the larger section of the pipe was  32m/s, what is its speed in this smaller section if the water behaves like an ideal incompressible fluid?
A)  43 m/s
B)  28 m/s
C)  37 m/s
D)  24 m/s

Quizplus · Accepted Answer

The speed of the water increases in the smaller section due to the conservation of mass principle for an ideal incompressible fluid, described by the equation A1V1 = A2V2, where A is the cross-sectional area and V is the velocity. Since the diameter decreases to 86% of its original value, the area of the smaller section is (0.86)^2 = 0.7396 (or 73.96%) of the larger section. To conserve mass, the velocity must increase such that the product of the area and velocity remains constant. Therefore, the new velocity V2 = V1 / 0.7396 = 32m/s / 0.7396 ≈ 43.29 m/s, which rounds to 43 m/s.

Water Flowing Through a Cylindrical Pipe Suddenly Comes to a Section