Question

A rectangular reservoir is $120m$ long and $75m$ wide. At what speed per hour must water flow into it through a square pipe of $20cm$ wide so that water rises by $2.4m$ in $18$ hours

Answer 1

Length of the reservoir $=120m$
Breadth of the reservoir $=75m$
The height of the water level in $18$ hours $=2.4m$
Volume of the water collected in the reservoir $120\times 75\times 2.4$
$=21600m^3$
Let the speed of the flowing water $=xm/hr$
the water flowing in the pipe eventually forms a cuboid of width $20cm$ or $0.2m$ and height of $20cm$ or $0.2m.$ [$\because$ Width $=$ height $=$ side of square pipe]
The length of the cuboid so formed in the pipe in $18$ hours $=18xm$ [$\because$ Distance $=$ Speed$\times$ Time]
Therefore, the volume of the water flows out of the pipe in $18$ hours $=0.2\times 0.2\times 18x$
$=0.72x{m}^3$
Therefore,
Volume of the water collected in the reservoir $=$ volume of the water flows out of the pipe in $18$ hours.

$21600=0.72x$

$\Rightarrow x=\frac{21600}{0.72}$

$\Rightarrow x=30000m/hr$

Or, speed of the water $=30km/hr$ [$\because 1km=1000m$]