Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?
Solution
Given data is as follows:
Internal diameter of the pipe = 2 cm
Water flow rate through the pipe = 6 m/sec
Radius of the tank = 60 cm
Time = 30 minutes
The volume of water that flows for 1 sec through the pipe at the rate of 6 m/sec is nothing but the volume of the cylinder with h = 6.
Also, given is the diameter which is 2 cm. Therefore,
r = 1 cm
Since the speed with which water flows through the pipe is in meters/second, let us convert the radius of the pipe from centimeters to meters. Therefore,
` r = 1/100 m`
Volume of water that flows for 1 sec = `22/7 xx 1/100 xx 1/100 xx 6 `
Now, we have to find the volume of water that flows for 30 minutes.
Since speed of water is in meters/second, let us convert 30 minutes into seconds. It will be 30 × 60
Volume of water that flows for 30 minutes = `22/7 xx 1/100 xx 1/100 xx 6 xx 30 xx 60`
Now, considering the tank, we have been given the radius of tank in centimeters. Let us first convert it into meters. Let radius of tank be ‘R’.
R= 60 cm
R=`60/100 `
Volume of water collected in the tank after 30 minutes= `22/7 xx 60/100 xx 60/100 xx h`
We know that,
Volume of water collected in the tank after 30 minutes= Volume of water that flows through the pipe for 30 minutes
`22/7 xx 60/100 xx 60/100 xx h = 22/7 xx 1/100 xx 1/100 xx 6 xx 30 xx 60`
h = 3 m
Therefore, the height of the tank is 3 meters.
