Question

A farmer connects a pipe of internal diameter 20cm from a canal into a cylindrical tank in his field, which is 10cm in diameter and 2m deep. If water flows through the pipe at the rate of 3km/h, in how much time will the tank be filled?

Answer 1

Hint: Start by computing the volume of water discharged from the pipe , similarly the volume of water collected in the cylindrical tank , and we know volume discharged will be equal to volume collected and solve for the value of length of pipe . Use the given data of the rate of water flowing to find out the time taken to fill the tank.

Complete step-by-step answer:
As we know,
The volume of water coming out from the pipe is equal to the volume of water falling into the cylindrical tank.
Now,
Volume of water discharged from pipe = volume of pipe
And we know , Volume of pipe = $\pi {r^2}h$, Where r is radius of pipe and h is length of pipe
$r = \dfrac{d}{2} = 10cm = 0.1m$
So, The Volume of pipe $ = \pi {\left( {0.1} \right)^2}h = \dfrac{{\pi h}}{{100}}$
Now , The volume of water fall into cylinder tank = volume of cylinder tank
Volume of cylindrical tank $ = \pi {\left( 5 \right)^2}\left( 2 \right) = 50\pi $
As we know,
Volume of pipe = volume of cylindrical tank
$ \Rightarrow \dfrac{{\pi h}}{{100}} = 50\pi \Rightarrow h = 5000m$
$ \Rightarrow h = 5km$
Now, Speed of water = 3km/h
Therefore , Time taken to fill the tank = $\dfrac{h}{3} = \dfrac{5}{3}hr = 100\min = 1hr40\min $

Note: Similar questions can be asked involving more inlet or outlet pipes with varied rates of flow or dimensions, In that case take the sum of all the inlets or outlets available. Always remember that volume discharged is equal to volume collected. Students must also know the distance - time relation.