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 m/s. 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. `9.6 xx 10^(-3)m`
C. `3.6 xx 10^(-3)m`
D. `5.0 xx 10^(-3)m`

Answer

C

Explanation

From Bernolli's theorem
`rhogh = (1)/(2)rho(V_(2)^(2) - V_(1)^(2))`
` rArr " "gh = (1)/(2) V_(1)^(2)[((V_(2))/(V_(1)))^(2) -1]`

`rArr" "gh = (1)/(2) V_(1)^(2)[((A_(1))/(A_(2)))^(2) -1]" "(because A_(1)V_(1) = A_(2)V_(2))`
`rArr ((A_(1))/(A_(2)))^(2) = 1 +(2hg)/(V_(1)^(2))`
`rArr ((D_(1))/(D_(2)))^(4) = 1 +(2gh)/(v_(1)^(2))`
`rArr" "D_(2) = (D_(1))/((1+(2gh)/(V_(1)^(2)))^(1//4)) = (8 xx 10^(-3))/([1+(2 xx 10 xx 0.2)/((0.4)^(2))]^(1//4))`
` = 3.6 xx 10^(-3) m`