Question

Water is flowing through a horizontal tube of non-uniform cross section. At a place, the radius of the tube is $2\text{cm}$ and velocity is $6\text{m/s}$. What will be the velocity of water where the radius of pipe is $4\text{cm}$?

• A. $6\text{m/s}$
• B. $1.5\text{m/s}$
• C. $3\text{m/s}$
• D. $2\text{m/s}$

Answer 1

The correct option is B $1.5\text{m/s}$


Let $A_1,V_1$ and $A_2,V_2$ be the area of cross section, velocity of water at inlet and outlet respectively.
Using equation of continuity.
$A_1{V}_1=A_2{V}_2$ ----(1)
Given,
Radius of tube at inlet $\left(r_1\right)=2\text{cm}$
Radius of tube at outlet $\left(r_2\right)=4\text{cm}$
Velocity of water at inlet $\left(V_1\right)=6\text{m/s}$
Area at inlet, $A_1=\pi r_1^2$
Area of cross-section at outlet, $A_2=\pi r_2^2$
From equation (1), we get
$\left(\pi r_1^2\right)\left(V_1\right)=\left(\pi r_2^2\right)\left(V_2\right)$
$\Rightarrow V_2=\frac{r_1^2}{r_2^2}\times V_1={\left(\frac{2}{4}\right)}^2\times 6=\frac{6}{4}\text{m/s}=1.5\text{m/s}$