Question

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

• A. 4 times that of Q
• B. 2 times that of Q
• C. 1/2 times that of Q
• D. 1/4 times that of Q

Answer 1

Answer: (A)

Using theorem of continuity, we have
$\pi D_{p}^{2}v_{p}=\pi D_{Q}^{2}v_{Q};$
$v_{p}=\left(\frac{D_{Q}}{D_{P}}\right)^{2}v_{Q}=\left(\frac{4 \times \left(10\right)^{- 2}}{2 \times \left(10\right)^{- 2}}\right)^{2}\times v_{Q}=4v_{Q}$