Question

A water connection is made in a colony from main water supply plant. Water is flowing through a pipe line of area of cross - section $70c{m}^2$ after entering into colony it is divided into five pipe line network of area $A_1,A_2,A_3,A_4$ in which water flows with velocities $5m/s,5m/s,2m/s$ and $1m/s$ respectively. What is the velocity of water in main pipe line? (in $m/s$ )

• A. 2.57
• B. 3.4
• C. 5.1
• D. 6.2

Answer 1

Answer: (A)

According to the equation of continuity
$AV=A_1{V}_1+A_2{V}_2+A_3{V}_3+A_4{V}_4$
$\Rightarrow 70\times 10^{-4}\times V$
$=10\times 10^{-4}\times 5+10\times 10^{-4}\times 5+20\times$
$10^{-4}\times 2+40\times 10^{-4}\times 1$
$\Rightarrow 70\times 10^{-4}V=10^{-4}(50+50+40+40)$
$\Rightarrow 70V=180$
$\Rightarrow V=\frac{180}{70}=2.57m/s$