Question

Water is flowing with velocity $4 \,m\,s^{-1}$ in a cylinder of diameter $8\,cm$, it is connected to a pipe with it end tip of diameter $2\,cm$, calculate the velocity of water at this free end.

• A. $4 \,m\,s^{-1}$
• B. $8 \,m\,s^{-1}$
• C. $32 \,m\,s^{-1}$
• D. $64 \,m\,s^{-1}$

Answer 1

Answer: (D)

Here, $v_{1}=4\, m \,s^{-1}, A_{1}= \pi r^{2}_{1}=16\pi \times 10^{-4}\,m^{2}$
$A_{2}=\pi r^{2}_{2}=\pi \times 10^{-4} m^{2}$
Using, $A_{1}v_{1} = A_{2}v_{2}$
$\therefore v_{2}=\frac{A_{1}v_{1}}{A_{2}}$
$=\frac{16 \pi \times 10^{-4} \times4}{\pi\times10^{-4}}$
$= 64 \,m\, s^{ -1}$
Velocity of water at free end, $v_{2} = 64 \,m \,s^{-1}$