Question

Two water pipes P and Q having diameters $2\times {10}^{-2}m$, and $4\times {10}^{-2}m$ respectively, are joined in series with the main supply line of water. The velocity of water flowing in the pipe P is

• A. $4$ times that of Q
• B. $2$ times that of Q
• C. $\frac{1}{2}$ times that of Q
• D. $\frac{1}{4}$ times that of Q

Answer 1

Answer: (A)

$4$ times that of Q

Given
$d_p=2\times {10}^{-2}m$
$\Rightarrow r_p={10}^{-2}m$
$d_q=4\times {10}^{-2}m$
$\Rightarrow r_p=2\times {10}^{-2}m$
The velocity of water flowing through the pipe is
inversely proportional to the cross-sectional area of tube, hence we can write
$\frac{v_p}{v_q}=\frac{a_q}{a_p}$
where,
$v_p,v_q$ are velocities of water through both pipes
and $a_p,a_q$ are the cross-sectional area of tubes.
Also,
$a_p=\pi (r_p{)}^2$ and $a_q=\pi (r_q{)}^2$
$\frac{v_p}{v_q}=\frac{\pi (r_q{)}^2}{\pi (r_p{)}^2}$
$\frac{v_p}{v_q}=\frac{(2\times {10}^{-2}{)}^2}{({10}^{-2}{)}^2}$
$\frac{v_p}{v_q}=4$
Hence,
$v_p=4\times v_q$