Question

Water is flowing at the rate of $5km/hr$ through a pipe of diameter $14cm$ into a rectangular tank which is $50m$ long and $44m$ wide. Determine the time in which the level of the water in the tank will rise by $7cm$.

Answer 1

Suppose the level of the water in the tank will rise by $7cm$ in $x$ hours.

Since the water is flowing at the rate of $5km/hr$.

Length of the water column in $x$ hours $=5x$ km$=5000x$ metresClearly, the water column forms a cylinder whose radius $r=\frac{14}{2}cm=\frac{7}{100}m$

Length $=h=5000x$ metres

Volume of the water flowing through the cylindrical pipe in $x$ hours

$=\pi r^{2}h$

$=\frac{22}{7}\times {\left(\frac{7}{100}\right)}^2\times 5000x{m}^3=77x{m}^3$

Also,
Volume of the water that falls into the tank in $x$ hours $=50\times 44\times \frac{7}{100}{m}^3=154m^3$

But, the volume of the water flowing through the cylindrical pipe in $x$ hours = Volume of the water that falls in the tank in $x$ hours.

$\Rightarrow 77x=154\Rightarrow x=2$

$\Rightarrow x=\frac{154}{77}=2$ $hours$