Question

Water is flowing through two horizontal pipes of different diameters which are connected together. The diameter of the two pipes are $3\text{cm}$ and $6\text{cm}$ respectively. If the speed of water in the narrower tube is $4\text{m/s}$, then the speed of water in the wider tube is

• A. $16\text{m/s}$
• B. $1\text{m/s}$
• C. $4\text{m/s}$
• D. $2\text{m/s}$

Answer 1

The correct option is B $1\text{m/s}$

From continuity equation,
$A_1{v}_1=A_2{v}_2$
$\Rightarrow \frac{v_1}{v_2}=\frac{A_2}{A_1}$
$A_2\&v_2$ represents the cross-sectional area and velocity in the wider tube.
If $d=$ diameter of pipe, then $A\propto d^2$
$\Rightarrow \frac{v_1}{v_2}=\frac{d_2^2}{d_1^2}$
$\because v_1=4\text{m/s}$
$\Rightarrow \frac{4}{v_2}=\frac{6^2}{3^2}$
$\therefore v_2=4\times \frac{3^2}{6^2}=1\text{m/s}$