Question

Water is flowing at the rate of $15km/hr$ through a cylindrical pipe of diameter $14cm$ into rectangular tank which is $50m$ long and $44m$ wide. In how many hours will the water level in the tank raise by $21cm$? (Take $\pi =\frac{22}{7}$)

Answer 1

Speed of water $=15km/hr$
$=15000m/hr$
Diameter of the pipe, $2r=14cm$
Thus, radius $r=\frac{7}{100}m$
Let $h$ be the water level to be raised
Thus, height $h=21cm=\frac{21}{100}m$
Now the volume of water discharged$=$ Cross section area of the pipe $\times$ Time $\times$ Speed
Volume of water discharged in one hour
$=\pi r^2\times 1\times 15000$
$=\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 15000cu.m$

Assume that $T$ hours are needed to get the required quantity of water

Volume of water discharged in $T$ hours$=\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 15000\times Tcu.m$
Volume of required quantity of water in the tank $=lbh=50\times 44\times \frac{21}{100}cu.m$
$\therefore$ Volume of water discharged in $T$ hours $=$ Required quantity of water in the tank
$\Rightarrow \frac{22}{7}\times {\left(\frac{7}{100}\right)}^2\times 15000\times T=50\times 44\times \frac{21}{100}$

$\Rightarrow T=\frac{50\times 44\times \frac{21}{100}}{\frac{22}{7}\times {\left(\frac{7}{100}\right)}^2\times 15000}$
Solving the equation, we get $T=2$ hours
Hence, it will take $2$ hours to raise the required water level.