A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep? if the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?
Given: Internal diameter of the pipe$=20\ cm$, diameter of cylinderical tank$=10\ m$, depth of the tank =2 m and rate of water-flow in the pipe$=4\ km/h$
To do: To find the time taken to be filled the tank completely.
Solution: For the given tank.
Diameter $=10\ m$
Radius, $R = \frac{Diameter}{2}=5\ m$
Depth, $H= 2\ m$
For the pipe ,
Internal diameter$=20\ cm$
Internal radius of the pipe , r =$\frac{20}{2} =10\ cm =\frac{10}{100}\ m=\frac{1}{10} m$
Rate of flow of water $= v=4\ km/h=4\times 1000=4000\ m/h$
Let us assume t be the time taken to fill the tank,
So, the water flown through the pipe in t hours will equal to the volume of the of the cylinderical tank
$\therefore \pi r^{2} \times v\times t=\pi \times R^{2} \times H$
$\Rightarrow t=\frac{R^{2} H}{r^{2} \times v}$
$\Rightarrow t=\frac{5^{2} \times 2}{\left(\frac{1}{10}\right)^{2} \times 4000}$
$\Rightarrow t=\frac{50}{40}$
$\Rightarrow t=1\frac{1}{4}$
$\Rightarrow t=\ 1\ hour\ 15\ minues$
Therefore, it will take 1 hour 15 minutes to fill the tank completely.
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