Water enters a pipe of diameter 3.0 cm with a velocity of 3.0 m/s.The water encounters a constriction where its velocity is 15 m/s.What is the diameter of the constricted portion of the pipe?
A)0.44 cm
B)0.75 cm
C)1.3 cm
D)1.6 cm
E)6.7 cm

Question

Quizplus · Accepted Answer

We know that mass flow rate is conserved, so the product of the area and the velocity of the water is constant before and after the constriction. Thus,
Area1 x Velocity1 = Area2 x Velocity2
π(0.03m)^2 x 3m/s = π(r^2)x 15m/s
Solving for r, we get 0.013 m or 1.3 cm. Therefore, the diameter of the constricted portion of the pipe is 1.3 cm.

Water Enters a Pipe of Diameter 3