A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his Held, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
Given:
The internal diameter of the pipe$=20\ cm$.
Diameter of cylindrical tank$=10\ m$.
Depth of the tank$=2\ m$ and rate of water flow in the pipe$=3\ km/h$.
To do:
We have to find the time taken to fill 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 $= v=3\ km/h=3\times 1000=3000\ m/h$
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 cylindrical tank
$\therefore \pi r^{2} \times v\times t=\pi \times R^{2} \times H$
$\Rightarrow t=\frac{R^{2} H}{r^{2} \times v}$
$\Rightarrow t=\frac{5^{2} \times 2}{\left(\frac{1}{10}\right)^{2} \times 3000}$
$\Rightarrow t=\frac{50}{30}$
$\Rightarrow t=1\frac{2}{3}$
$\Rightarrow t=\ 1\ hour\ 40\ minutes$
Therefore, it will take 1 hour and 45 minutes to fill the tank completely.
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