`A` laminar stream is flowing vertically down from a tap of cross-section area `1cm^(2)`. At a distance `10` below the tap, the cross-section area of the stream has reduced to `1//2cm^(2)`. Find the volumetric flow rate of water from the tap.

Answer

`4.9"litre"//"min"`

Explanation

From equation of continuity
`V=a_(1)v_(1)= a_(2)v_(2) " "1xxv_(1)=(1)/(2)v_(2)`
`v_(2)=2v_(1)`
From energy conservation
`V_(2)^(2)=v_(1)^(2) + 2gh`
`(2v_(1))^(2)=v^(2)+2gh " "implies " "v_(1)=sqrt((2)/(3)gh)`
`V=a_(1)v_(1)impliesV=1sqrt((2)/(3)xx1000xx10) cm^(3)//secimpliesV=100sqrt((2)/(3))cm^(3)//secimpliesV=(1)/(10)sqrt((2)/(3))"litre"//"sec"`
`V=6sqrt((2)/(3))"m litre"//"min" implies V=4.9"litre"//"min"`