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
Jun 22, 2014

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.