Question

Water in a rectangular reservoir having base 80 m by 60 m is 6.5 m deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km/hr.

Answer 1

$\text{Length of reservoir (l)}=80m$

$\text{Breadth (b)}=60m$

$\text{and depth (h)}=6.5m$

$\therefore \text{Volume of water in it}=lbh$

$=80\times 60\times 6.5m^3=31200m^3$

$\text{Area of cross-section of the mouth of pipe}$

$=20\times 20=400c{m}^2$

$=\frac{400}{10000}{m}^2=\frac{4}{100}{m}^2$

$\text{Speed of water}=15km/h$

$\text{Now length of flow of water in the pipe}$

$=\frac{Volume}{\text{Area of cross-section}}$

$=\frac{31200\times 100}{4}m=780000m=780km$

$\therefore \text{Time taken}=\frac{Length}{Speed}=\frac{780}{15}hr$

$=52hours$