Question

Water is flowing at the rate of $7$ meters per second through a circular pipe whose internal diameter is $2cm$ into a cylindrical tank the radius of whose base is $40cm$. Determine the increase in the water level in $\frac{1}{2}$ hour.

Answer 1

We have

Rate of flow of water $=7m/sec=700cm/sec$

Length of the water column in $\frac{1}{2}hours=(700\times 30\times 60)cm$

Clearly water column forms a cylinder of radius $1cm$ and length $(700\times 30\times 60)cm$

volume of the water that flows in the tank in $\frac{1}{2}hour$

$=(\frac{22}{7}\times 1\times 1\times 700\times 30\times 60)c{m}^3$ ........(i)

Let $h$ cm be the rise in the level of water in the tank.

Then, volume of the water in the tank $=\frac{22}{7}\times 40\times 40\times hc{m}^3$ .......(ii)

From (i) and (ii) we have

$\frac{22}{7}\times 40\times 40\times h=\frac{22}{7}\times 1\times 1\times 700\times 30\times 60$

$\Rightarrow h=787.5\approx 788cm$