Question

Question 8
Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

Answer 1

Given, length of the pond = 50 m.
Width of the pond = 44 m.

Depth required of water
$=21cm=\frac{21}{100}m$ (1m=100cm)

$\therefore$ Volume of water in the pond $=l\times b\times h=(50\times 44\times \frac{21}{100})=462m^3$

Also, given radius of the pipe $=7cm=\frac{7}{100}m$

Speed of water flowing through the pipe
$=(15\times 1000)=15000m{h}^{-1}$ (1km= 1000m)

$Volumeofwaterflowin1h=\pi R^{2}H\times speedofwaterflowingthroughpipe$
$=(\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 15000)=231m^3\times h^{-1}$

Since, $231m^3$ of water falls in the pond in 1h

Also, $462m^3$of water falls in the pond in $(\frac{1}{231}\times 462)h=2h$

Hence, the required time is 2h.