Water is flowing through a pipe with a constriction. The area of the narrow section is one-half the area of the wide section. If the velocity of the incompressible fluid is 3.2 m/s in the narrow section, then what is the velocity of the fluid in the wide section?
A) 0.9 m/s
B) 1.0 m/s
C) 1.6 m/s
D) 1.8 m/s
E) 1.9 m/s

Question

Quizplus · Accepted Answer

The continuity equation states that the volume flow rate of an incompressible fluid is constant throughout a pipe. Therefore, we can equate the product of the area and velocity at the narrow section to the product of the area and velocity at the wide section:
$A_{narrow}V_{narrow} = A_{wide}V_{wide}$
Since $A_{narrow} = \frac{1}{2}A_{wide}$ and $V_{narrow} = 3.2 m/s$, we can solve for $V_{wide}$:
$\frac{1}{2}A_{wide}(3.2 m/s) = A_{wide}V_{wide}$
$V_{wide} = \frac{1}{2}(3.2 m/s)$
$V_{wide} = 1.6 m/s$
Therefore, the answer is (C) 1.6 m/s.

Water Is Flowing Through a Pipe with a Constriction