Question

Water flows through a cylindrical pipe of internal diameter $7cm$ at $5m/s$. Calculate:
(i) the volume, in litres, of water discharged by the pipe in $1$ minute
(ii) the time, in minutes, the pipe would take to fill an empty rectangular tank $4m$ by $3m$ by $2.31m$.

Answer 1

In one sec. length of water flow in pipe $=5m$

Radius $=\frac{7}{2}=3.5cm=0.00355m$

Volume of water flow per sec $=\pi r^{2}h=\pi (0.0035{)}^2\times 5$

$=192.5\times {10}^{-6}{m}^3$

Volume of water discharged per minute $=192.5\times {10}^{-6}{m}^3\times 60$

$=11.55\times {10}^{-3}{m}^3$

$=0.01155m^3$

$=11.55litre$

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

$\because 1m^3=1000litre$

Volume of tank $=27720litre$

Time to fill the tank $=\frac{27720}{11.55}=2400minutes$

$=\frac{2400}{60}=40hours$