Question

Water is following at the rate of 5 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time in which the level of water in the tank will rise by 7 cm. \(\bigg(\text{Take}\,π = \frac{22}{7}\bigg)\)

Answer 1

Rate of flow = 5 km/hr = 5000 m/hour. 

⇒ Length of cylinder for water flowing in one hour = 5000 m. 

Radius = 7 cm = \(\frac{7}{100}\) m.

∴ Volume of water flowing through the pipe per hour = πr²h 

\(=\frac{22}{7}\times\frac{7}{100}\times\frac{7}{100}\times5000\) m³ = 77 m³. 

Volume of water to be filled in the rectangular tank 

= (50 × 44 × 7/100) m³ = 154 m³ 

∴ Reqd. time = \(\frac{154}{77}\) = 2 hours.