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?

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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?

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Answer 1 · 2014-06-22T03:18:09

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

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

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

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

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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?

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