Question

Two water pipes of diameters $2cm$ and $4cm$ are connected with the main supply line. The velocity of flow of water in the pipe of $2cm$ diameter is

• A. $4$ times that in the other pipe
• B. $\frac{1}{4}$ times that in the other pipe
• C. $2$ times that in the other pipe
• D. $\frac{1}{2}$ times that in the other pipe

Answer 1

Answer: (A)

Given, $d_A=2cm$ and $d_B=4cm$
$\therefore r_A=1cm$ and $r_B=2cm$
From the equation of continuity $aV=$ constant, where $a$ is area of cross-section of pipe and $V$ is speed of water in pipe.
$\therefore \frac{V_A}{V_B}=\frac{a_B}{a_A}=\frac{\pi (r_B{)}^2}{\pi (r_A{)}^2}={\left(\frac{2}{1}\right)}^2$
$\Rightarrow V_A=4V_B$
Hence, speed of water in pipe of $2cm$ diameter is $4$ times that of pipe of $4cm$ diameter.