A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field which is 10 cm in diameter and 2m deep. If water flows through 3 kmph, in how much time will the tank be filled completely?
Answers
The time required to fill the tank completely is 100 minutes.
Step-by-step explanation:
From question, internal diameter of pipe = 20 cm
Now, the internal radius of pipe = 10 cm = 10/100 m = 1/10 m
From question, the rate of flow of water = 3 km/h = 3000 m/h
Let the time required to fill the tank be x
Volume of water flowing from pipe = Area of cross section × Speed × Time
Volume of water that flows from pipe = πr² × Speed × Time
On substituting the known values, we get,
Volume of water that flows from pipe = π(1/10)² × 3000 × x
Volume of water that flows from pipe = 30 πt m³
Diameter of the cylinder = 10 m
Radius of the cylinder = 5 m
Depth of the cylinder = 2 m
Volume of tank = πr²h
On substituting the known values, we get,
Volume of tank = π × (5)² × 2
Volume of tank = 50π m³
Volume of water that flows from pipe = Volume of tank
30 πt = 50π
t = 50/30 hours
t = 50/30 × 60 minutes
Therefore, t = 100 minutes