Question

Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank rises by 21 cm.

Answer 1

Length of the tank = 50 m; width of the tank = 44 m
Required height to which water level has to rise$=\frac{21}{100}\text{m}$
Volume of water in the tank$=\left(50\times 44\times \frac{21}{100}\right){\mathrm{m}}^3=462{\mathrm{m}}^3$

Radius of the pipe$=\frac{7}{100}\text{m}$

Speed of water flowing through the pipe$=\left(15\times 1000\right)\text{m/hour}$
= 15000 m/hour

Volume of water flowing per hour$=\mathrm{\pi }{r}^{2}h$
$=\left(\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 15000\right){\text{m}}^3$
= 231 m^​3

Time required to fill the tank$=\left(\frac{1}{231}\times 462\right)$
= 2 hours