Question

A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km / h, in how much time will the tank be filled?

Answer 1

Let the time-taken by the pipe to fill the tank be x hrs. 

Since the water is flowing at a rate of 3 kmph, 

therefore 

Length of water column in x hrs is 

3 × x = 3x km = 3000x m 

Therefore the length of the pipe is \(\frac{20}2\) = 10 cm = 0.1 m

Therefore, 

the volume of water flowing through the pipe in x hours, V’ = π r² h 

= π (0.1)² (3000x) m³ 

Also, 

volume of water that falls into the tank in x hours = πr² h 

= π (5)² (2) 

The volume of water flowing through the pipe in x hours = volume of water that falls into the tank in x hours 

∴ π (0.1)² (3000x) = π (5)² (2) 

⇒ 30x = 50 

⇒ x = \(\frac{50}{30}\) = \(\frac{100}{60}\) hrs

= 1 hr 40 min