Water is flowing through a cylindrical pipe, with an internal diameter of , into a cylindrical tank with a base radius of , at the rate of.
Determine the rise in the level of water In the tank in half hours.
Step 1. Find the speed of water.
The radius of a cylindrical pipe,
The radius of the cylindrical tank,
It is known that,
Length of water through a pipe, .
Diameter of cylindrical pipe having circular end
Radius of circular end of pipe is,
Area of cross-section is,
Speed of water is,
Step 2. Find the radius of base of cylindrical tank.
The volume of water that flows in one minute from the pipe will be equal to the area of a cross-section of the cylindrical pipe multiplied by the speed of flow of water through it.
So, the Volume of water that flows in one minute from the pipe is,
So using the unitary method,
The volume of water that flows in minutes from the pipe
Radius of base of cylindrical tank,
Step 3. Find the rise in the level of water.
Let the cylindrical tank be filled up to him in minutes.
We know that,
The volume of water filled in a cylindrical tank in minutes is equal to the volume of water flowing out in 30 minutes from the pipe.
Hence, the rise in the level of water in the tank in half an hour (or in minutes) is .