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 $70 cm ^{2}$ 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 $5 m / s , 5 m / s , 2 m / s$ and $1 m / s$ 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$
$10^{-4} \times 2+40 \times 10^{-4} \times 1$
$\Rightarrow 70 \times 10^{-4} V =10^{-4}(50+50+40+40)$
$\Rightarrow 70 V =180$
$ \Rightarrow V =\frac{180}{70}=2.57 m / s$