Water flows through a cylinder pipe of radius 0.74 cm. It fills a 12 litre bucket in 4 minutes. Calculate the speed of water through the pipe in...

Thursday, October 11, 2012

We are given the volumetric flow rate to be:

$\displaystyle\frac{{{12}{L}}}{{{4}\min{u}{t}{e}{s}}}={3}\frac{{L}}{\min}$

Also since our final answer has to be in centimeters, we have to convert the volumetric flowrate obtained above into square centimeters:

$\displaystyle{3}{L}={3000}{c}{{m}}^{{3}}$

Therefore the volumetric flowrate is:

$\displaystyle{3000}\frac{{{c}{{m}}^{{3}}}}{\min}$

In order to determine the speed of the water, we have to first know that the volume of the cylinder is:

$\displaystyle{V}=\pi\cdot{{r}}^{{2}}\cdot{h}$

$\displaystyle\pi={3.14}$

$\displaystyle{r}={0.74}{c}{m}$ ( r = raduis)

$\displaystyle{V}={3000}\frac{{{c}{{m}}^{{3}}}}{\min}$ Note in this equation V is volumetric flowrate, not volume.

Now we need to determine, h - the height:

$\displaystyle{h}={\left(\frac{{3000}}{{\pi\cdot{{\left({0.74}\right)}}^{{2}}}}\right)}$

$\displaystyle{h}={1744.69}\frac{{{c}{m}}}{\min}$

We can round off the above answer to as the following:

$\displaystyle{h}={1745}\frac{{{c}{m}}}{\min}$

The speed of the water going through the pipe is 1745 cm/min

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