The water supply of a 36-story building is fed through a main 8-centimeter diameter pipe. a 1.6-centimeter diameter faucet tap located 22 meters above the main pipe is observed to fill a 30-liter container in 20 seconds. what is the speed at which the water leaves the faucet?

1 Answer
Zor Shekhtman
Jun 22, 2014

Assuming the water leaves the facet with a speed Vmsec, the amount of water that goes through this facet in 1sec equals to the volume of a cylinder of a height Vm and a diameter of a base 1.6cm (radius 0.8cm=0.008m). So, in cubic meters it's equal to: π⋅V⋅0.0082.

In 20sec the amount of water going through this facet is 20 times larger and equals to 30l (this equals to 0.03m3) since there are 1000 liters in one cubic meter).

So, we have an equation with one unknown V(msec):
π⋅V⋅0.0082⋅20=0.03
Solution of this linear equation (speed the water leaves the facet in m/sec) is
V=7.46msec

Personally, I think that this is a very high speed and the numbers in this problem might not be practical.

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