A farmer connect a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m diameter and 2 m deep. If the water flows through the pipe at the of 4 km/hr, in how much time will the tank be filled completely?
Given: diameter of pipe = 20 cm
∴ radius of pipe = rp = 20/2 = 10 cm = 0.1 m
Diameter of tank = 10 m
∴ radius of cylindrical tank = rc = 10/2 = 5 m
Depth of cylindrical tank = height of cylindrical tank = h = 2 m
Rate of flow of water through pipe = 4 km/hr
1 km = 1000 m
4 km/hr = 4000 m/hr
Volume of water required to completely fill the tank is equal to the volume of cylinder
Time require to fill the tank = volume of cylindrical tank/volume of water flown through pipe per hr
volume of cylindrical tank = π × rc2 × h
= 3.14 × 25 × 2
= 157 m3
volume of water flown through pipe per hr = π × rp2 × 4000
= 3.14 × 0.12 × 4000
= 3.14 × 40
= 125.6 m3/hr
Time require to fill the tank = 157/125.6
= 1.25 hrs
Therefore, it will take 1.25 hours to fill the tank completely.