A 3.00-m long tube with circular crosssection tapers from a diameter of 10.0 cm at one end down to 4.00 cm at the other end. If an incompressible fluid flows irrotationally through the tube at a speed of 2.00 m/s at the 10.0 cm end, what is the speed of the flow at the 4.00 cm diameter end?
A)2.00 m/s
B)0.800 m/s
C)12.5 m/s
D)1.60 m/s
E)6.25 m/s

Question

Quizplus · Accepted Answer

The flow rate is constant, so the speed must increase as the diameter decreases. The cross-sectional area of the tube is proportional to the square of the diameter, so the speed is inversely proportional to the square of the diameter. Therefore, the speed at the 4.00 cm end is 12.5 m/s.

A 300-M Long Tube with Circular Crosssection Tapers from a Diameter