A broad pipe having a radius `10 cm` branches into two pipes of radii `5 cm` and `3cm`. If the velocity of flowing water in the pipe of radius `3 cm` is `5 cm//s`, determine the velocities of water in the remaining two pipes. Given that the rate of discharge through the main branch is `600picm^(3)//s`.

Explanation

Consider any three sections `1, 2` and `3` in the three pipes of different radii as shown in figure. If `v_(1)` and `v_(2)` be the velocities of water at section `1` and `2`, respectively, then `a_(1)=pi(10)^(2)cm^(2), a_(2)=pi(5)^(2)cm^(2)`
and `a_(3)=pi(3^(2))cm^(2)`
`v_(1)=?,v_(2)=?, v_(3)=5cm//s`
The rates of discharge through the three pipes are
`a_(1)v_(1)=100piv_(1)cm^(3)//s`
`a_(2)v_(2)=25piv_(2)cm^(2)//s`
`a_(3)v_(3)=9pixx5=45picm^(3)//s`

Now `Q=a_(1)v_(1)=a_(2)v_(2)+a_(3)v_(3)implies600pi=100piv_(1)=25piv_(2)+45pi` solving we get `v_(1)=6cm//s` and `v_(2)=22.2cm//s`