Question

Water is flowing through a horizontal tube of non - uniform cross - section. At a place the radius of the tube is $1.0\text{cm}$ and the velocity of water is $2\text{m/s}$. Then, what will be the velocity of water at a point where the radius of the pipe is $2.0\text{cm}$?

• A. $1\text{m/s}$
• B. $0.25\text{m/s}$
• C. $20\text{m/s}$
• D. $0.5\text{m/s}$

Answer 1

The correct option is D $0.5\text{m/s}$

Using equation of continuity,
$A_1{v}_1=A_2{v}_2$
$v_2=\left(\frac{A_1}{A_2}\right)v_1$
or $v_2=\left(\frac{\pi r_1^2}{\pi r_2^2}\right)v_1={\left(\frac{r_1}{r_2}\right)}^2{v}_1$
Substituting the values, we get
$v_2={\left(\frac{1.0\times {10}^{-2}}{2.0\times {10}^{-2}}\right)}^2\left(2\right)$
or $v_2=0.5\text{m/s}$