Question

Water is flowing at the rate of $6km/hr$ through a pipe of diameter $14cm$ into a rectangular tank which is 60 m long and $22m$ wide. Determine the time in which the level of water in the tank will rise by $7cm.$

Answer 1

We have, Speed of the water flowing through the pipe, $H=6km/h$

$=\frac{600000cm}{3600s}=\frac{500}{3}cm/s$

The radius of the pipe, $R=\frac{14}{2}=7cm,$

Length of the rectangular tank, $l=60m=6000cm,$

The breadth of the rectangular tank, $b=22m=2200cm$

and Rise in the level of water in the tank, $h=7cm$

Now, the Volume of the water in the rectangular tank $=lbh$

$=6000\times 2200\times 7=92400000c{m}^3$

Also, the Volume of the water flowing through the pipe in 1 s

$=\pi R^{2}H=\frac{22}{7}\times 7\times 7\times \frac{500}{3}=\frac{77000}{3}c{m}^3$

So, The time taken to rise water by $7cm$

$=\frac{\text{Volume of the water in the rectangular tank}}{\text{Volume of the water flowing through the pipe in 1 s}}$

$=\frac{92400000}{\frac{77000}{3}}$

$=92400\times \frac{3}{77}$

$=3600$ second $=1$ hour

So, the time in which the level of water in the tank will rise by $7cm$ is $1$ hour.