Figure shows a liquid flowing through a tube at the rate of `0.1 m^(3)//s`. The tube is branched into two semicircular tubes of cross-sectional area `A//3` and `2A//3`. The velocity of liquid at `Q` is (the cross section of the main tube is `A =10^(-2) m^(2)` and `v_(p) = 20 m//s`)

Options

A. `5m//s`
B. `30 m//s`
C. `35 m//s`
D. none of these

Answer

A

Explanation

From a equationof continuity
Rate `=r=A/3V_(p)+(A-A/3)V_(Q)`
`:. V_(P)+2V_(Q)=(3r)/A=(3xx0.1)/10^(-2)=30m//s`
As `V_(P)+2V_(Q)=5m//s`