Question

A farmer connects 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 rate of 3 km/h, in how much time will the tank be filled?

Answer 1

Given:

Pipe internal diameter = 20 cm ⇒ radius = 10 cm = 0.1 m.

Tank diameter = 10 m ⇒ radius = 5 m; depth = 2 m.

Water speed in pipe = 3 km/h = 3000 m/h.

Step-wise calculation:

1. Cross-sectional area of pipe = πr² 

= π(0.1 m)²

= 0.01π m²

2. Volumetric flow = Area × Speed

= 0.01π × 3000

= 30π  m³/h

3. Volume of cylindrical tank = π(5 m)² × 2 m 

= 50π m³

4. Time to fill = `"Tank volume"/"Flow"` 

= `(50π)/(30π)` 

= `50/30`

= `5/3` hours

= 1.666... hours

5. Convert to hours and minutes: `5/3` h

= 1 hour + `2/3` hour 

= 1 hour 40 minutes (= 100 minutes).

The tank will be filled in `5/3` hours = 1 hour 40 minutes (100 minutes).