Question

Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in the level of water in the tank in half hours.

Answer 1

Hint: In order to solve this problem we need to find the volume of water flowing through the pipe in one second and then multiply 30 x 60 to get the volume of pipe in 30 minutes of half an hour. Then we need to find the volume of the cylinder taking height as variable and then we need to equate the volume we found earlier through the pipe to that of the filled cylinder’s volume to get the value of height. Doing this will solve your problem and will give you the right answer.

Complete step-by-step answer:
The figure of the system can be drawn as:

Internal diameter of cylindrical pipe is equal to 2cm
Radius(r) = 1cm
Now it is given that base radius of cylindrical tank is 40 cm and the rate of flow of water is flowing at rate of 0.4 m/s through cylindrical pipe
The water is flowing at rate of 0.4 m in 1 sec through cylindrical pipe
So the volume of water flowing in the pipe = $\pi {r^2}H$
$ \Rightarrow \pi {(1)^2} \times 0.4 \times 100c{m^3}$
So the volume of water which is flowing through the pipe in 30 minutes that is 30x60 sec is
$ \Rightarrow \pi {(1)^2} \times 0.4 \times 100 \times 30 \times 60$…………………………. (1)
Let H be the height of cylindrical tank so its volume is given as $\pi {R^2}H$where R=40 cm
So the volume of water in the cylindrical tank after 30 minutes = $\pi {(40)^2}H$…………………. (2)
Since the water from pipe is flowing into the tank hence equation1 should be equal to equation 2
$ \Rightarrow \pi {(1)^2} \times 0.4 \times 100 \times 30 \times 60$=$\pi {(40)^2}H$
On solving we get H=45cm

Note: Whenever we are solving such type of problem statements, always remember that the volume of water flowing through the cylindrical pipe for the given time interval will eventually contribute to raising the water height into the cylindrical tank. Doing this will solve your problem and will give you the right answer.