Water is flowing continuously from a tap having an internal diameter `8 xx 10^(-3) m`. The water velocity as it leaves the tap is 0.4 `ms^(-1)`. The diameter of the water stream at a distance `2 xx 10^(-1)` m below the tap is close to:

Options

A. `7.5 xx 10^(-3) m`
B. `9.6xx10^(-3)m`
C. `3.6xx10^(-3)m`
D. `5.0xx10^(-3)m`

Answer

C

Explanation

From Bernoulli.s theorem
`P_(0)+1/2pv_(1)^(2)+pgh=P_(0)+1/2pv_(2)^(2)+0`
`v_(2)=sqrt(v_(1)^(2)+2gh)=sqrt(0.16+2xx10xx0.2)=2.03m//s`
From continuity equation `A_(2)v_(2)=A_(1)v_(1)`
`pi(D_(2)^(2))/4v_(2)=pi(D_(1)^(2))/4v_(1)`
`D_(2)D_(1)sqrt((v_(1))/(v_(2)))3.5510^(-3)m`
Correct choice : ( c)