# 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?

Jun 22, 2014

Assuming the water leaves the facet with a speed $V \frac{m}{\sec}$, 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 $1.6 c m$ (radius $0.8 c m = 0.008 m$). So, in cubic meters it's equal to: $\pi \cdot V \cdot {0.008}^{2}$.

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 $V \left(\frac{m}{\sec}\right)$:
$\pi \cdot V \cdot {0.008}^{2} \cdot 20 = 0.03$
Solution of this linear equation (speed the water leaves the facet in m/sec) is
$V = 7.46 \frac{m}{\sec}$

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