A pump uses a piston of 15 cm diameter that moves at 2.0 cm/s as it pushes a fluid through a pipe.What is the speed of the fluid when it enters a portion of the pipe that is 3.0 mm in diameter? Treat the fluid as ideal and incompressible.
A)50 m/s
B)50 cm/s
C)6.0 cm/s
D)22 cm/s

Question

Quizplus · Accepted Answer

The speed of the fluid increases as it moves from a wider to a narrower section of the pipe due to the conservation of mass principle for an incompressible fluid, which can be described by the equation $A_1v_1 = A_2v_2$, where $A_1$ and $A_2$ are the cross-sectional areas of the wider and narrower sections, respectively, and $v_1$ and $v_2$ are the fluid velocities in these sections. Given the diameters, the areas can be calculated using $A = \pi r^2$, leading to a significant increase in velocity when the fluid moves into the narrower section. Calculating with the given numbers, the velocity in the narrower section is found to be 50 m/s.

A Pump Uses a Piston of 15 Cm Diameter That