Question

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?

Answer 1

Assuming the water leaves the facet with a speed `V m/sec`, the amount of water that goes through this facet in `1 sec` equals to the volume of a cylinder of a height `V m` and a diameter of a base `1.6 cm` (radius `0.8 cm = 0.008 m`). So, in cubic meters it's equal to: `pi*V*0.008^2`.

In `20 sec` the amount of water going through this facet is 20 times larger and equals to `30 l` (this equals to `0.03 m^3`) since there are 1000 liters in one cubic meter).

So, we have an equation with one unknown `V(m/sec)`:
`pi*V*0.008^2*20 = 0.03`
Solution of this linear equation (speed the water leaves the facet in m/sec) is
`V = 7.46 m/sec`

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