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 $32 \mathrm {~m} / \mathrm { s }$ what is its speed in this smaller section if the water behaves like an ideal incompressible fluid?
A)43 m/s
B)37 m/s
C)28 m/s
D)24 m/s

Question

Quizplus · Accepted Answer

According to the principle of continuity for incompressible fluids, the product of cross-sectional area and velocity remains constant. If the diameter decreases to 86%, the area decreases to $0.86^2$. Therefore, the velocity increases by a factor of $1/0.86^2$, resulting in a speed of approximately 43 m/s in the smaller section.

Water Flowing Through a Cylindrical Pipe Suddenly Comes to a Section