Water flows at 2 m/s through a pipe of diameter 0.8m into a pipe of diameter 0.2

Question

Water flows at 2 m/s through a pipe of diameter 0.8m into a pipe of diameter 0.2m and then empties into the bottom of a reservoir that is 20m deep as shown below. What is the speed of water flow in the smaller pipe? What is the volume rate of flow of water into the lake? What is the mass rate of flow of water into the lake? A small bubble, of volume 10 cm^3 flows out of the small pipe into the bottom of the lake. Describe specifically what happens to the bubble as it rises to the surface in terms of volume.

Explanation / Answer

1. Since the smaller pipe has an area one sixteenth of the large pipe, it must have sixteen times the velocity, 32 m/s. 2. The volume rate is the area of the pipe times the velocity of the water, pi*r^2*v = 4.02 m^3/s. 3. For water, the mas rate equals 1000*4.02 = 4,020 kg/s. 4. The bubble would first contract upon entering the higher-pressure lake, then expand smoothly as it climbs the negative pressure gradient to the top of the lake.

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