a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field , which is 10m in diameter and 2 m deep. If water flows through the pipe at the rate of 3km/hr , in how much time the tank be filled ?
Let x hours be the time taken for the pipe to fill the tank.
Since the water is flowing at the rate of 3 Km/h, Therefore,
Length of the water column in x hours is
Therefore, the length of the pipe is
The radius of the pipe is
Therefore, the volume of the water flowing through the pipe in x hours is
Also, Volume of the water that falls into the tank in x hours is
We have the volume of the water flowing through the pipe in x hours = Volume of the water that falls into the tank in x hours
Thus equate equations (1) and (2)
Thus, the water in the tank will fill in 100 minutes.
Given that, Speed of water
Internal radius of the pipe
Area of cross section
Volume of water that flows in 1 minute,
Let the time taken to fill the tank
Volume of water that flows in
Radius of the base of the tank
Depth of the tank
Volume of the cylindrical tank
So, volume of water that flows in t minute = volume of the tank
Hence, the tank will be filled in