Question

In a horizontal pipe of non-uniform cross-section, water flows with a velocity of $1$ $m{s}^{-1}$ at a point where the diameter of the pipe is $20$cm. The velocity of water in $\left(m{s}^{-1}\right)$ at a point where the diameter of the pipe is $5$cm is:

• A. $64$
• B. $24$
• C. $8$
• D. $32$
• E. $16$

Answer 1

The correct option is E $16$

Diameter of pipe at first point $\left(d_1\right)=20cm=0.2m$.
Radius of pipe at first point
$\left(r_1\right)=\frac{0.2}{2}=0.1$m
Velocity of water at first point
$\left(v_1\right)=1m{s}^{-1}$
Diameter of pipe at second point
$\left(d_2\right)=5cm=0.05$m
Radius of pipe at second point,
$\left(r_2\right)=\frac{0.05}{2}=0.025$m
According to equation of continuity,
$A_1{v}_1=A_2{v}_2$
$\pi r_1^2{v}_1=\pi r_2^2{v}_2$
$v_2=\left(\frac{r_1}{r_2}\right)\times v_1$
$v_2={\left(\frac{0.1}{0.025}\right)}^2\times 1$
$v_2=16m{s}^{-1}$.