Question

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

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

Answer 1

Answer: (D)

Here, $v_1=4m{s}^{-1},A_1=\pi r_1^2=16\pi \times 10^{-4}{m}^2$
$A_2=\pi r_2^2=\pi \times 10^{-4}{m}^2$
Using, $A_1{v}_1=A_2{v}_2$
$\therefore v_2=\frac{A_1{v}_1}{A_2}$
$=\frac{16\pi \times 10^{-4}\times 4}{\pi \times 10^{-4}}$
$=64m{s}^{-1}$
Velocity of water at free end, $v_2=64m{s}^{-1}$