Question

While walking past a construction site, a person notices a pipe sticking out of a second floor window with water pouring out. As the water flows to the ground, it speeds up due to the effect of gravity. How does the diameter of the flowing stream of water change as it descends? Assuming that the flow remains laminar, its diameter decreases. stays the same. increases.

Answer 1

The flow diameter decreases.

Step-by-step explanation:

From continuity equation,

Q = AV = constant

Where A is the area of the pipe which is proportional to its diameter.

V is the velocity of flow of fluid.

Q is the flow rate.

Let us consider the flow rate through the pipe. Assuming a steady state flow, if the velocity should increase, then the diameter will decrease.

For the flow leaving the pipe and descending to the floor, the flow is accelerated under gravity as it leaves the pipe. This acceleration causes its velocity to increase and consequently causing a reduction in the flow area. The result is the narrowing of the water that flows towards the floor (provided the flow remains laminar).