Question

Water flows through a cylindrical pipe of internal diameter $7cm$ at $5m$ per sec. Calculate
(i) the volume in litres of water discharged by the pipe in one minute.
(ii) the time in minutes, the pipe would take to fill an empty rectangular tank of size $4m\times 3m\times 2.31m$ .

Answer 1

Given,

Speed of water flows through cylindrical pipe $=5m/sec$

Internal diameter of the pipe $=7cm$

So, radius $\left(r\right)=7.2cm$

Now, length of water flow in $1$ minutes $\left(h\right)=5\times 60=300m$

Volume of water $=\pi r^{2}h=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 300\times 100{cm}^3=1155000{cm}^3=1155litres$

(i) the volume of water $=1155000{cm}^3$

Volume of rectangular tank of size $=4m\times 3m\times 2.31m=27.72m^3$

Also, given speed of water $4m/sec$

Radius of pipe $=\frac{7}{2}cm$

Volume of water in $1sec=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 5\times 100{cm}^3=19250{cm}^3$

Hence

(ii) Time taken to empty the tank $=\frac{27.72m^3}{19250}=\frac{(2772\times 100\times 100\times 100)}{(100\times 19250)}=1440sec=\frac{1440}{60}=24minutes$