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 an incompressible fluid, the product of the cross-sectional area and velocity must remain constant. If the diameter decreases to 86%, the area decreases to $0.86^2$ of its original value. Therefore, the velocity increases by a factor of $1/0.86^2$, resulting in a new speed of approximately 43 m/s.

Water Flowing Through a Cylindrical Pipe Suddenly Comes to a Section