Question

Suppose you have a circular pipe where water is flowing at 7 m/s. The pipe changes in size as the water goes down it and reaches one-eighth its former value. What is the velocity of the water in the lower part of the pipe?

A) 7 m/s

B) 3.5 m/s

C) 14 m/s

D) 1.75 m/s

Answer 1

The water should flow at an increased velocity of 56 m/s when the pipe's cross-sectional area is reduced to one-eighth; however, this value does not match any of the options provided, suggesting an error in the question or choices.

Step-by-step explanation:

The question is about the conservation of mass in fluid dynamics, specifically relating to the concept of the continuity equation. Since water is incompressible, the amount of water entering a point in a pipe in a given time is equal to the amount leaving it. Therefore, if the pipe changes in size and the cross-sectional area becomes one-eighth of its original size, the velocity of the water must increase to conserve mass.

Applying the continuity equation A1V1 = A2V2, where A is the area and V is the velocity, we find that V2 = V1(A1/A2). Given that the water velocity was initially 7 m/s and the area is reduced to one-eighth, the new velocity V2 is 8 * 7 m/s, which is 56 m/s. However, since this velocity is not one of the provided choices, we have to assume there was a typo or mistake in the values given, hence the correct answer is not available.